Infinite Dimensional Banach spaces of functions with nonlinear properties

The aim of this paper is to show that there exist infinite dimensional Banach spaces of functions that, except for 0, satisfy properties that apparently should be destroyed by the linear combination of two of them. Three of these spaces are: a Banach space of differentiable functions on Rn failing the Denjoy-Clarkson property; a Banach space of non Riemann integrable bounded functions, but with antiderivative at each point of an interval; a Banach space of infinitely differentiable functions that vanish at infinity and are not the Fourier transform of any Lebesgue integrable function.

Rational Design of Acridine-Based Ligands with Selectivity for Human Telomeric Quadruplexes

Structure-based modeling methods have been used to design a series of disubstituted triazole-linked acridine compounds with selectivity for human telomeric quadruplex DNAs. A focused library of these compounds was prepared using click chemistry and the selectivity concept was validated against two promoter quadruplexes from the c-kit gene with known molecular structures, as well as with duplex DNA using a FRET-based melting method. Lead compounds were found to have reduced effects on the thermal stability of the c-kit quadruplexes and duplex DNA structures. These effects were further explored with a series of competition experiments, which confirmed that binding to duplex DNA is very low even at high duplex:telomeric quadruplex ratios. Selectivity to the c-kit quadruplexes is more complex, with some evidence of their stabilization at increasing excess over human telomeric quadruplex DNA. Selectivity is a result of the dimensions of the triazole-acridine compounds; and in particular the separation of the two alkyl-amino terminal groups. Both lead compounds also have selective inhibitory effects on the proliferation of cancer cell lines compared to a normal cell line, and one has been shown to inhibit the activity of the telomerase enzyme, which is selectively expressed in tumor cells, where it plays a role in maintaining telomere integrity and cellular immortalization.