On an integral equation of the first kind arising in the theory of Cosserat

In this paper we study an integral equation of the first kind concerning an indirect boundary integral method for the Dirichlet problem in the theory of Cosserat continuum. Our method hinges on the theory of reducible operators and on the theory of differential forms

5-(carbamoylmethylene)-oxazolidin-2-ones as a promising class of heterocycles inducing apoptosis triggered by increased ROS levels and mitochondrial dysfunction in breast and cervical cancer

Oxazolidinones are antibiotics that inhibit protein synthesis by binding the 50S ribosomal subunit. Recently, numerous worldwide researches focused on their properties and possible involvement in cancer therapy have been conducted. Here, we evaluated in vitro the antiproliferative activity of some 5-(carbamoylmethylene)-oxazolidin-2-ones on MCF-7 and HeLa cells. The tested compounds displayed a wide range of cytotoxicity on these cancer cell lines, measured by MTT assay, exhibiting no cytotoxicity on non-tumorigenic MCF-10A cells. Among the nine tested derivatives, four displayed a good anticancer potential. Remarkably, OI compound showed IC50 values of 17.66 and 31.10 µM for MCF-7 and HeLa cancer cells, respectively. Furthermore, we assessed OI effect on the cell cycle by FACS analysis, highlighting a G1 phase arrest after 72 h, supported by a low expression level of Cyclin D1 protein. Moreover, mitochondrial membrane potential was reduced after OI treatment driven by high levels of ROS. These findings demonstrate that OI treatment can inhibit MCF-7 and HeLa cell proliferation and induce apoptosis by caspase-9 activation and cytochrome c release in the cytosol. Hence, 5-(carbamoylmethylene)-oxazolidin-2-ones have a promising anticancer activity, in particular, OI derivative could represent a good candidate for in vivo further studies and potential clinical use

Glutamine-Derived Aspartate Biosynthesis in Cancer Cells: Role of Mitochondrial Transporters and New Therapeutic Perspectives

Aspartate has a central role in cancer cell metabolism. Aspartate cytosolic availability is crucial for protein and nucleotide biosynthesis as well as for redox homeostasis. Since tumor cells display poor aspartate uptake from the external environment, most of the cellular pool of aspar-tate derives from mitochondrial catabolism of glutamine. At least four transporters are involved in this metabolic pathway: the glutamine (SLC1A5_var), the aspartate/glutamate (AGC), the as-partate/phosphate (uncoupling protein 2, UCP2), and the glutamate (GC) carriers, the last three belonging to the mitochondrial carrier family (MCF). The loss of one of these transporters causes a paucity of cytosolic aspartate and an arrest of cell proliferation in many different cancer types. The aim of this review is to clarify why different cancers have varying dependencies on metabolite transporters to support cytosolic glutamine-derived aspartate availability. Dissecting the precise metabolic routes that glutamine undergoes in specific tumor types is of upmost importance as it promises to unveil the best metabolic target for therapeutic intervention

The finite index basis property

We describe in this paper a connection between bifix codes, symbolic dynamical systems and free groups. This is in the spirit of the connection established previously for the symbolic systems corresponding to Sturmian words. We introduce a class of sets of factors of an infinite word with linear factor complexity containing Sturmian sets and regular interval exchange sets, namely the class of tree sets. We prove as a main result that for a uniformly recurrent tree set S, a finite bifix code X on the alphabet A is S-maximal of S-degree d if and only if it is the basis of a subgroup of index d of the free group on