Asymptotic and structural properties of special cases of the Wright function arising in probability theory

This analysis paper presents previously unknown properties of some special cases of the Wright function whose consideration is necessitated by our work on probability theory and the theory of stochastic processes. Specifically, we establish new asymptotic properties of the particular Wright function 1Ψ1(ρ, k; ρ, 0; x) = X∞ n=0 Γ(k + ρn) Γ(ρn) x n n! (|x| < ∞) when the parameter ρ ∈ (−1, 0)∪(0, ∞) and the argument x is real. In the probability theory applications, which are focused on studies of the Poisson-Tweedie mixtures, the parameter k is a non-negative integer. Several representations involving well-known special functions are given for certain particular values of ρ. The asymptotics of 1Ψ1(ρ, k; ρ, 0; x) are obtained under numerous assumptions on the behavior of the arguments k and x when the parameter ρ is both positive and negative. We also provide some integral representations and structural properties involving the ‘reduced’ Wright function 0Ψ1(−−; ρ, 0; x) with ρ ∈ (−1, 0) ∪ (0, ∞), which might be useful for the derivation of new properties of members of the power-variance family of distributions. Some of these imply a reflection principle that connects the functions 0Ψ1(−−;±ρ, 0; ·) and certain Bessel functions. Several asymptotic relationships for both particular cases of this function are also given. A few of these follow under additional constraints from probability theory results which, although previously available, were unknown to analysts.

A novel mechanism of action of HER2 targeted immunotherapy is explained by inhibition of NRF2 function in ovarian cancer cells

Nuclear erythroid related factor-2 (NRF2) is known to promote cancer therapeutic detoxification and crosstalk with growth promoting pathways. HER2 receptor tyrosine kinase is frequently overexpressed in cancers leading to uncontrolled receptor activation and signaling. A combination of HER2 targeting monoclonal antibodies shows greater anticancer efficacy than the single targeting antibodies, however, its mechanism of action is largely unclear. Here we report novel actions of anti-HER2 drugs, Trastuzumab and Pertuzumab, involving NRF2. HER2 targeting by antibodies inhibited growth in association with persistent generation of reactive oxygen species (ROS), glutathione (GSH) depletion, reduction in NRF2 levels and inhibition of NRF2 function in ovarian cancer cell lines. The combination of antibodies produced more potent effects than single alone; downregulated NRF2 substrates by repressing the Antioxidant Response (AR) pathway with concomitant transcriptional inhibition of NRF2. We showed the antibody combination produced increased methylation at the NRF2 promoter consistent with repression of NRF2 antioxidant function, as HDAC and methylation inhibitors reversed such produced transcriptional effects. These findings demonstrate a novel mechanism and role for NRF2 in mediating the response of cancer cells to the combination of Trastuzumab and Pertuzumab and reinforce the importance of NRF2 in drug resistance and as a key anticancer target.

Role of membrane lipids in the regulation of erythrocytic oxygen-transport function in cardiovascular diseases

The composition and condition of membrane lipids, the morphology of erythrocytes, and hemoglobin distribution were explored with the help of laser interference microscopy (LIM) and Raman spectroscopy. It is shown that patients with cardiovascular diseases (CVD) have significant changes in the composition of their phospholipids and the fatty acids of membrane lipids. Furthermore, the microviscosity of the membranes and morphology of the erythrocytes are altered causing disordered oxygen transport by hemoglobin. Basic therapy carried out with the use of antiaggregants, statins, antianginals, beta-blockers, and calcium antagonists does not help to recover themorphofunctional properties of erythrocytes. Based on the results the authors assume that, for the relief of the ischemic crisis and further therapeutic treatment, it is necessary to include, in addition to cardiovascular disease medicines, medication that increases the ability of erythrocytes’ hemoglobin to transport oxygen to the tissues. We assume that the use of LIM and Raman spectroscopy is advisable for early diagnosis of changes in the structure and functional state of erythrocytes when cardiovascular diseases develop.