Inner multipliers of de Branges's spaces

For a given functionb in the unit ball ofH and an arbitraryH functionm, the question of whenm is a multiplier of the de Branges space (that is, when is invariant under multiplication bym) is examined. Some necessary and sufficient conditions thatm be a multiplier of are found and it is shown that there are no nonconstant inner multipliers of whenb is a nonconstant extreme point of the unit ball ofH . A new proof is given of the known fact that is invariant under multiplication byz whenb is not an extreme point of the unit ball ofH . Finally, we give a new proof of the known fact that an inner functionm is a multiplier of forb(z)=(1+z)/2 if and only ifm belongs to the range of .Some of the work in this paper originally appeared in the author's doctoral disseratation written at the University of California at Berkeley under the supervision of Donald Sarason.     

Introduction to Session 5

Applied Biochemistry and Biotechnology -     

Expedient synthesis of substituted imidazoles from nitriles

Expedient and practical new methodology for the synthesis of substituted imidazoles was developed to provide a rapid access to a variety of 2-substituted, 1,2-disubstituted and 1,2,4-trisubstituted imidazoles by the direct CuCl-mediated reaction of nitriles with α-amino acetals in an intermolecular as well as intramolecular fashion.     

Phase separation of p53 precedes aggregation and is affected by oncogenic mutations and ligands

Mutant p53 tends to form aggregates with amyloid properties, especially amyloid oligomers inside the nucleus, which are believed to cause oncogenic gain-of-function (GoF). The mechanism of the formation of the aggregates in the nucleus remains uncertain. The present study demonstrated that the DNA-binding domain of p53 (p53C) underwent phase separation (PS) on the pathway to aggregation under various conditions. p53C phase separated in the presence of the crowding agent polyethylene glycol (PEG). Similarly, mutant p53C (M237I and R249S) underwent PS; however, the process evolved to a solid-like phase transition faster than that in the case of wild-type p53C. The data obtained by microscopy of live cells indicated that transfection of mutant full-length p53 into the cells tended to result in PS and phase transition (PT) in the nuclear compartments, which are likely the cause of the GoF effects. Fluorescence recovery after photobleaching (FRAP) experiments revealed liquid characteristics of the condensates in the nucleus. Mutant p53 tended to undergo gel- and solid-like phase transitions in the nucleus and in nuclear bodies demonstrated by slow and incomplete recovery of fluorescence after photobleaching. Polyanions, such as heparin and RNA, were able to modulate PS and PT in vitro. Heparin apparently stabilized the condensates in a gel-like state, and RNA apparently induced a solid-like state of the protein even in the absence of PEG. Conditions that destabilize p53C into a molten globule conformation also produced liquid droplets in the absence of crowding. The disordered transactivation domain (TAD) modulated both phase separation and amyloid aggregation. In summary, our data provide mechanistic insight into the formation of p53 condensates and conditions that may result in the formation of aggregated structures, such as mutant amyloid oligomers, in cancer. The pathway of mutant p53 from liquid droplets to gel-like and solid-like (amyloid) species may be a suitable target for anticancer therapy.

Mutant p53 tends to form aggregates with amyloid properties, especially amyloid oligomers inside the nucleus, which are believed to cause oncogenic gain-of-function (GoF).     

pH dependent self-assembly of dimetallic lanthanide complexes

pH dependent self-association has been observed in a series of DO3A-derived lanthanide complexes bearing a carboxylate group that can act as a bridging ligand at high pH, switching on the luminescence from the lanthanide.     

FLUORESCENCE SPECTRAL CHANGES OF HEMATOPORPHYRIN DERIVATIVE UPON BINDING TO LIPID VESICLES, Staphylococcus aureus AND Escherichia coli CELLS

Abstract— The binding of hematoporphyrin derivated (Hpd) to lipid vesicles and bacterial membranes was determined by fluorescence spectroscopy. The fluorescence measurements of Hpd in aqueous solutions showed two bands at 613 and 677 nm. In lipid environments of lecithin vesicles the fluorescence spectrum was shifted to 631 and 692 nm, respectively. Hpd was rapidly bound to the cell membrane of Staphylococcus aureus while much less binding occurred in the presence of Escherichia coli. At the same time, spheroplasts of both bacteria were shown to bind Hpd to a similar extent. These results are well correlated with the photoinactivation of the gram positive bacteria with Hpd while the gram negative cells were shown to be resistant. The pH dependence of both Hpd binding to S. aureus as well as the photodynamic inhibitory effect of the same bacteria are similar. It is concluded that the segregation of Hpd to the cell membrane is a prerequisite for its photodynamic effect.