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Given a multi-valued function Φ : X ⊸ X on a topological space X we study the properties of its fixed fractal, which is defined as the closure of the orbit Φω(*Φ) = ⋃n∈ωΦn(*Φ) of the set *Φ = {x ∈ X : x ∈ Φ(x)} of fixed points of Φ. A special attention is paid to the duality between micro-fractals and macro-fractals, which are fixed fractals and for a contracting compact-valued function Φ : X ⊸ X on a complete metric space X. With help of algorithms (described in this paper) we generate various images of macro-fractals which are dual to some well-known micro-fractals like the fractal cross, the Sierpiński triangle, Sierpiński carpet, the Koch curve, or the fractal snowflakes. The obtained images show that macro-fractals have a large-scale fractal structure, which becomes clearly visible after a suitable zooming. [ABSTRACT FROM AUTHOR]

Aberrant DNA hypermethylation of promoter of tumor suppressor genes is commonly observed in cancer, and its inhibition by small molecules is promising for their reactivation. Here we designed bisubstrate analogues-based inhibitors, by mimicking each substrate, the S-adenosyl-l-methionine and the deoxycytidine, and linking them together. This approach resulted in quinazoline-quinoline derivatives as potent inhibitors of DNMT3A and DNMT1, some showing certain isoform selectivity. We highlighted the importance of (i) the nature and rigidity of the linker between the two moieties for inhibition, as (ii) the presence of the nitrogen on the quinoline group, and (iii) of a hydrophobic group on the quinazoline. The most potent inhibitors induced demethylation of CDKN2A promoter in colon carcinoma HCT116 cells and its reactivation after 7 days of treatment. Furthermore, in a leukemia cell model system, we found a correlation between demethylation of the promoter induced by the treatment, chromatin opening at the promoter, and the reactivation of a reporter gene.

DNA methylation is the most studied epigenetic event. Since the methylation profile of the genome is widely modified in cancer cells, DNA methyltransferases are the target of new anticancer therapies. Nucleosidic inhibitors suffer from toxicity and chemical stability, while non-nucleosidic inhibitors lack potency. Here, we found a novel DNMT inhibitor scaffold by enzymatic screening and structure-activity relationship studies. The optimization studies led to an inhibitor containing three fragments: a gallate frame, a hydrazone linker and a benzothiazole moiety. Interestingly, the compound inhibits DNMT3A with micromolar potency (EC50 = 1.6 μM) and does not inhibit DNMT1; this DNMT3A selectivity is supported by a docking study. Finally, the compound reactivates a reporter gene in leukemia KG-1 cells.

DNA methylation, an epigenetic modification regulating gene expression, is a promising target in cancer. In an effort to identify new non nucleosidic inhibitors of DNA methyltransferases, the enzymes responsible for DNA methylation, we carried out a high-throughput screening of 66,000 chemical compounds based on an enzymatic assay against catalytic DNMT3A. A family of propiophenone derivatives was identified. After chemical optimization and structure activity relationship studies, a new inhibitor (33) was obtained with an EC50 of 2.1 μM against DNMT3A. The mechanism of inhibition of the compound was investigated as it forms a reactive Michael acceptor group in situ. Thereby, the Michael acceptor 20 was identified. This compound was further characterized for its biological activity in cancer cells., (Copyright © 2015 Elsevier Ltd. All rights reserved.)

5-azacytidine and 5-aza-2'-deoxycytidine are clinically used to treat patients with blood neoplasia. Their antileukemic property is mediated by the trapping and the subsequent degradation of a family of proteins, the DNA methyltransferases (DNMT1, DNMT3A, and DNMT3B) leading to DNA demethylation, tumor suppressor gene re-expression and DNA damage. Here we studied the respective role of each DNMT in the human leukemia KG1 cell line using a RNA interference approach. In addition we addressed the role of DNA damage formation in DNA demethylation by 5-aza-2'-deoxycytidine. Our data show that DNMT1 is the main DNMT involved in DNA methylation maintenance in KG1 cells and in mediating DNA damage formation upon exposure to 5-aza-2'-deoxycytidine. Moreover, KG1 cells express the DNMT1 protein at a level above the one required to ensure DNA methylation maintenance, and we identified a threshold for DNMT1 depletion that needs to be exceeded to achieve DNA demethylation. Most interestingly, by combining DNMT1 siRNA and treatment with low dose of 5-aza-2'-deoxycytidine, it is possible to uncouple DNA damage formation from DNA demethylation. This work strongly suggests that a direct pharmacological inhibition of DNMT1, unlike the use of 5-aza-2'-deoxycytidine, should lead to tumor suppressor gene hypomethylation and re-expression without inducing major DNA damage in leukemia.

Quinoline derivative SGI-1027 (N-(4-(2-amino-6-methylpyrimidin-4-ylamino)phenyl)-4-(quinolin-4-ylamino)benzamide) was first described in 2009 as a potent inhibitor of DNA methyltransferase (DNMT) 1, 3A and 3B. Based on molecular modeling studies, performed using the crystal structure of Haemophilus haemolyticus cytosine-5 DNA methyltransferase (MHhaI C5 DNMT), which suggested that the quinoline and the aminopyridimine moieties of SGI-1027 are important for interaction with the substrates and protein, we designed and synthesized 25 derivatives. Among them, four compounds—namely the derivatives 12, 16, 31 and 32—exhibited activities comparable to that of the parent compound. Further evaluation revealed that these compounds were more potent against human DNMT3A than against human DNMT1 and induced the re-expression of a reporter gene, controlled by a methylated cytomegalovirus (CMV) promoter, in leukemia KG-1 cells. These compounds possessed cytotoxicity against leukemia KG-1 cells in the micromolar range, comparable with the cytotoxicity of the reference compound, SGI-1027. Structure–activity relationships were elucidated from the results. First, the presence of a methylene or carbonyl group to conjugate the quinoline moiety decreased the activity. Second, the size and nature of the aromatic or heterocycle subsitutents effects inhibition activity: tricyclic moieties, such as acridine, were found to decrease activity, while bicyclic substituents, such as quinoline, were well tolerated. The best combination was found to be a bicyclic substituent on one side of the compound, and a one-ring moiety on the other side. Finally, the orientation of the central amide bond was found to have little effect on the biological activity. This study provides new insights in to the structure-activity relationships of SGI-1027 and its derivative.