Integral geometry of translation invariant functionals,II: The case of general convex bodies

In continuation of Part I, we study translative integral formulas for certain translation invariant functionals, which are defined on general convex bodies. Again, we consider local extensions and use these to show that the translative formulas extend to arbitrary continuous and translation invariant valuations. Then, we discuss applications to Poisson particle processes and Boolean models which contain, as a special case, some new results for flag measures.     

Gabor systems and almost periodic functions

Inspired by results of Kim and Ron, given a Gabor frame in $L^2(\mathbb{R})$, we determine a non-countable generalized frame for the non-separable space ${\mathit{AP}}_2(\mathbb{R})$ of the Besicovic almost periodic functions. Gabor type frames for suitable separable subspaces of ${\mathit{AP}}_2(\mathbb{R})$ are constructed. We show furthermore that Bessel-type estimates hold for the AP norm with respect to a countable Gabor system using suitable almost periodic norms of sequences.     

Approximations in Sobolev spaces by prolate spheroidal wave functions

Recently, there is a growing interest in the spectral approximation by the Prolate Spheroidal Wave Functions (PSWFs) ${\psi }_{n,c},c>0$. This is due to the promising new contributions of these functions in various classical as well as emerging applications from Signal Processing, Geophysics, Numerical Analysis, etc. The PSWFs form a basis with remarkable properties not only for the space of band-limited functions with bandwidth c, but also for the Sobolev space $H^s([?1,1])$. The quality of the spectral approximation and the choice of the parameter c when approximating a function in $H^s([?1,1])$ by its truncated PSWFs series expansion, are the main issues. By considering a function $f\in H^s([?1,1])$ as the restriction to $[?1,1]$ of an almost time-limited and band-limited function, we try to give satisfactory answers to these two issues. Also, we illustrate the different results of this work by some numerical examples.     

Conifers Phytochemicals: A Valuable Forest with Therapeutic Potential

Conifers have long been recognized for their therapeutic potential in different disorders. Alkaloids, terpenes and polyphenols are the most abundant naturally occurring phytochemicals in these plants. Here, we provide an overview of the phytochemistry and related commercial products obtained from conifers. The pharmacological actions of different phytochemicals present in conifers against bacterial and fungal infections, cancer, diabetes and cardiovascular diseases are also reviewed. Data obtained from experimental and clinical studies performed to date clearly underline that such compounds exert promising antioxidant effects, being able to inhibit cell damage, cancer growth, inflammation and the onset of neurodegenerative diseases. Therefore, an attempt has been made with the intent to highlight the importance of conifer-derived extracts for pharmacological purposes, with the support of relevant in vitro and in vivo experimental data. In short, this review comprehends the information published to date related to conifers’ phytochemicals and illustrates their potential role as drugs.     

Species Diversity and Secondary Metabolites of Sarcophyton-Associated Marine Fungi

Soft corals are widely distributed across the globe, especially in the Indo-Pacific region, with Sarcophyton being one of the most abundant genera. To date, there have been 50 species of identified Sarcophyton. These soft corals host a diverse range of marine fungi, which produce chemically diverse, bioactive secondary metabolites as part of their symbiotic nature with the soft coral hosts. The most prolific groups of compounds are terpenoids and indole alkaloids. Annually, there are more bio-active compounds being isolated and characterised. Thus, the importance of the metabolite compilation is very much important for future reference. This paper compiles the diversity of Sarcophyton species and metabolites produced by their associated marine fungi, as well as the bioactivity of these identified compounds. A total of 88 metabolites of structural diversity are highlighted, indicating the huge potential these symbiotic relationships hold for future research.     

Camu-Camu Fruit Extract Inhibits Oxidative Stress and Inflammatory Responses by Regulating NFAT and Nrf2 Signaling Pathways in High Glucose-Induced Human Keratinocytes

Myrciaria dubia (HBK) McVaugh (camu-camu) belongs to the family Myrtaceae. Although camu-camu has received a great deal of attention for its potential pharmacological activities, there is little information on the anti-oxidative stress and anti-inflammatory effects of camu-camu fruit in skin diseases. In the present study, we investigated the preventative effect of 70% ethanol camu-camu fruit extract against high glucose-induced human keratinocytes. High glucose-induced overproduction of reactive oxygen species (ROS) was inhibited by camu-camu fruit treatment. In response to ROS reduction, camu-camu fruit modulated the mitogen-activated protein kinases (MAPK)/activator protein-1 (AP-1), nuclear factor kappa-light-chain-enhancer of activated B cells (NF-κB), and nuclear factor of activated T cells (NFAT) signaling pathways related to inflammation by downregulating the expression of proinflammatory cytokines and chemokines. Furthermore, camu-camu fruit treatment activated the expression of nuclear factor E2-related factor 2 (Nrf2) and subsequently increased the NAD(P)H:quinone oxidoreductase1 (NQO1) expression to protect keratinocytes against high-glucose-induced oxidative stress. These results indicate that camu-camu fruit is a promising material for preventing oxidative stress and skin inflammation induced by high glucose level.     

Protective Effect of Ferulic Acid against Hydrogen Peroxide Induced Apoptosis in PC12 Cells

Ferulic Acid (FA) is a highly abundant phenolic phytochemical which is present in plant tissues. FA has biological effects on physiological and pathological processes due to its anti-apoptotic and anti-oxidative properties, however, the detailed mechanism(s) of function is poorly understood. We have identified FA as a molecule that inhibits apoptosis induced by hydrogen peroxide (H₂O₂) or actinomycin D (ActD) in rat pheochromocytoma, PC12 cell. We also found that FA reduces H₂O₂-induced reactive oxygen species (ROS) production in PC12 cell, thereby acting as an anti-oxidant. Then, we analyzed FA-mediated signaling responses in rat pheochromocytoma, PC12 cells using antibody arrays for phosphokinase and apoptosis related proteins. This FA signaling pathway in PC12 cells includes inactivation of pro-apoptotic proteins, SMAC/Diablo and Bad. In addition, FA attenuates the cell injury by H₂O₂ through the inhibition of phosphorylation of the extracellular signal-regulated kinase (ERK). Importantly, we find that FA restores expression levels of brain-derived neurotrophic factor (BDNF), a key neuroprotective effector, in H₂O₂-treated PC12 cells. As a possible mechanism, FA increases BDNF by regulating microRNA-10b expression following H₂O₂ stimulation. Taken together, FA has broad biological effects as a neuroprotective modulator to regulate the expression of phosphokinases, apoptosis-related proteins and microRNAs against oxidative stress in PC12 cells.     

On the Protein Fibrillation Pathway: Oligomer Intermediates Detection Using ATR-FTIR Spectroscopy

Oligomeric intermediates on the pathway of amyloid fibrillation are suspected as the main cytotoxins responsible for amyloid-related pathogenicity. As they appear to be a part of the lag phase of amyloid fibrillation when analyzed using standard methods such as Thioflavin T (ThT) fluorescence, a more sensitive method is needed for their detection. Here we apply Fourier transform infrared spectroscopy (FTIR) in attenuated total reflectance (ATR) mode for fast and cheap analysis of destabilized hen-egg-white lysozyme solution and detection of oligomer intermediates of amyloid fibrillation. Standard methods of protein aggregation analysis— Thioflavin T (ThT) fluorescence, atomic force microscopy (AFM), and 8-anilinonaphthalene-1-sulphonic acid (ANS) fluorescence were applied and compared to FTIR spectroscopy data. Results show the great potential of FTIR for both, qualitative and quantitative monitoring of oligomer formation based on the secondary structure changes. While oligomer intermediates do not induce significant changes in ThT fluorescence, their secondary structure changes were very prominent. Normalization of specific Amide I region peak intensities by using Amide II peak intensity as an internal standard provides an opportunity to use FTIR spectroscopy for both qualitative and quantitative analysis of biological samples and detection of potentially toxic oligomers, as well as for screening of efficiency of fibrillation procedures.     

Ocular Delivery of Polyphenols: Meeting the Unmet Needs

Nature has become one of the main sources of exploration for researchers that search for new potential molecules to be used in therapy. Polyphenols are emerging as a class of compounds that have attracted the attention of pharmaceutical and biomedical scientists. Thanks to their structural peculiarities, polyphenolic compounds are characterized as good scavengers of free radical species. This, among other medicinal effects, permits them to interfere with different molecular pathways that are involved in the inflammatory process. Unfortunately, many compounds of this class possess low solubility in aqueous solvents and low stability. Ocular pathologies are spread worldwide. It is estimated that every individual at least once in their lifetime experiences some kind of eye disorder. Oxidative stress or inflammatory processes are the basic etiological mechanisms of many ocular pathologies. A variety of polyphenolic compounds have been proved to be efficient in suppressing some of the indicators of these pathologies in in vitro and in vivo models. Further application of polyphenolic compounds in ocular therapy lacks an adequate formulation approach. Therefore, more emphasis should be put in advanced delivery strategies that will overcome the limits of the delivery site as well as the ones related to the polyphenols in use. This review analyzes different drug delivery strategies that are employed for the formulation of polyphenolic compounds when used to treat ocular pathologies related to oxidative stress and inflammation.