We study the problem of irreducibility of the moduli space I n of rank-2 mathematical instanton vector bundles with second Chern class n ≥ 1 on the projective space P 3 . The irreducibility of I n was known for small values of n: for n = 1 it was proved by , for n = 2 by Hartshorne (1978), for n = 3 by Ellingsrud and Strømme (1981), for n = 4 by Barth (1981), for n = 5 by Coanda, Tikhomirov and Trautmann (2003). In this paper we prove the irreducibility of I n for an arbitrary odd n ≥ 1.Bibliography: 22 items.

The human KRAS transcript contains a G-rich 5'-UTR sequence (77% GC) harboring several G4 motifs capable to form stable RNA G-quadruplex (RG4) structures that can serve as targets for small molecules. A biotin-streptavidin pull-down assay showed that 4,11-bis(2-aminoethylamino)anthra[2,3-b]furan-5,10-dione (2a) binds to RG4s in the KRAS transcript under low-abundance cellular conditions. Dual-luciferase assays demonstrated that 2a and its analogue 4,11-bis(2-aminoethylamino)anthra[2,3-b]thiophene-5,10-dione (2b) repress translation in a dose-dependent manner. The effect of the G4-ligands on Panc-1 cancer cells has also been examined. Both 2a and 2b efficiently penetrate the cells, suppressing protein p21KRAS to <10% of the control. The KRAS down-regulation induces apoptosis together with a dramatic reduction of cell growth and colony formation. In summary, we report a strategy to suppress the KRAS oncogene in pancreatic cancer cells by means of small molecules binding to RG4s in the 5'-UTR of mRNA.

A number of newly discovered natural products, the perspective directions for chemical modifications to optimize the anticancer properties, and novel intracellular targets demonstrate that anthracene- 9,10-diones deserve further in-depth investigation as an important source of drug candidates.

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