On Infinite Camina Groups

A group G is called a Camina group if G′ ≠ G and each element x ∈ G?G′ satisfies the equation x ^G  = xG′, where x ^G denotes the conjugacy class of x in G. Finite Camina groups were introduced by Alan Camina in 1978, and they had been studied since then by many authors. In this article, we start the study of infinite Camina groups. In particular, we characterize infinite Camina groups with a finite G′ (see Theorem 3.1) and we show that infinite non-abelian finitely generated Camina groups must be nonsolvable (see Theorem 4.3). We also describe locally finite Camina groups, residually finite Camina groups (see Section 3) and some periodic solvable Camina groups (see Section 5).     

Approximation of semigroups and cosine functions in spaces of periodic functions

In this article we furnish a representation of the solutions of some classes of first-order and second-order evolution problems as limit of iterates of classical sequences of approximating operators. The method is based on Trotter's theorem on the approximation of semigroups which is applied here also for the approximation of groups and cosine functions. We apply this method in spaces of continuous periodic functions and using some classical sequences of trigonometric polynomials.     

Towards an Improvement of Anticancer Activity of Benzyl Adenosine Analogs

N6-Isopentenyladenosine (i6A) is a naturally occurring modified nucleoside displaying in vitro and in vivo antiproliferative and pro-apoptotic properties. In our previous studies, including an in silico inverse virtual screening, NMR experiments and in vitro enzymatic assays, we demonstrated that i6A targeted farnesyl pyrophosphate synthase (FPPS), a key enzyme involved in the mevalonate (MVA) pathway and prenylation of downstream proteins, which are aberrant in several cancers. Following our interest in the anticancer effects of FPPS inhibition, we developed a panel of i6A derivatives bearing bulky aromatic moieties in the N6 position of adenosine. With the aim of clarifying molecular action of N6-benzyladenosine analogs on the FPPS enzyme inhibition and cellular toxicity and proliferation, herein we report the evaluation of the N6-benzyladenosine derivatives’ (compounds 2a–m) effects on cell viability and proliferation on HCT116, DLD-1 (human) and MC38 (murine) colorectal cancer cells (CRC). We found that compounds 2, 2a and 2c showed a persistent antiproliferative effect on human CRC lines and compound 2f exerted a significant effect in impairing the prenylation of RAS and Rap-1A proteins, confirming that the antitumor activity of 2f was related to the ability to inhibit FPPS activity.     

A New Oxadiazole-Based Topsentin Derivative Modulates Cyclin-Dependent Kinase 1 Expression and Exerts Cytotoxic Effects on Pancreatic Cancer Cells

Pancreatic ductal adenocarcinoma (PDAC) is a highly lethal form of cancer characterized by drug resistance, urging new therapeutic strategies. In recent years, protein kinases have emerged as promising pharmacological targets for the treatment of several solid and hematological tumors. Interestingly, cyclin-dependent kinase 1 (CDK1) is overexpressed in PDAC tissues and has been correlated to the aggressive nature of these tumors because of its key role in cell cycle progression and resistance to the induction of apoptosis. For these reasons, CDK1 is one of the main causes of chemoresistance, representing a promising pharmacological target. In this study, we report the synthesis of new 1,2,4-oxadiazole compounds and evaluate their ability to inhibit the cell growth of PATU-T, Hs766T, and HPAF-II cell lines and a primary PDAC cell culture (PDAC3). Compound 6b was the most active compound, with IC₅₀ values ranging from 5.7 to 10.7 µM. Molecular docking of 6b into the active site of CDK1 showed the ability of the compound to interact effectively with the adenosine triphosphate binding pocket. Therefore, we assessed its ability to induce apoptosis (which increased 1.5- and 2-fold in PATU-T and PDAC3 cells, respectively) and to inhibit CDK1 expression, which was reduced to 45% in Hs766T. Lastly, compound 6b passed the ADME prediction, showing good pharmacokinetic parameters. These data demonstrate that 6b displays cytotoxic activity, induces apoptosis, and targets CDK1, supporting further studies for the development of similar compounds against PDAC.     

13C-enriched end groups of poly(3,7-dimethyl-1-octene) prepared in the presence of isotactic specific catalysts

Polymerizations of (R,S)-3,7-dimethyl-1-octene in the presence of heterogeneous or homogeneous isotactic specific catalysts give very similar products with a homopolymeric isotactic structure. The insertion of (R,S)-3,7-dimethyl-1-octene into the metal-CH₃ bond (both heterogeneous and homogeneous catalysts) is highly stereospecific and stereoselective.