New poly(d-glucaramidoamine)s induce DNA nanoparticle formation and efficient gene delivery into mammalian cells

In this report, four new poly(d-glucaramidoamine)s (1-4) have been designed to lower the toxicity of conventional polymeric nucleic acid delivery vehicles by incorporating a carbohydrate comonomer within a polyethylenimine (PEI)-like backbone. Polymers 1-4 were synthesized via polycondensation of esterified d-glucaric acid and four different amine-containing comonomers [diethylenetriamine (1), triethylenetetramine (2), tetraethylenepentamine (3), and pentaethylenehexamine (4)] in methanol. Viscometry and NMR studies suggest that the polymers are mostly linear (for 1-4, the alpha value in the Mark-Houwink-Sakurada equation = 0.6-0.7), thus indicating that polymerization occurs predominantly through the primary amines with a low degree of branching off the secondary amines. Results of gel electrophoresis shift assays show that polymers 1-4 bind pDNA at N/P ratios of 5, 3, 2, and 2, respectively. Also, dynamic light scattering and TEM experiments indicate that 1-4 compact DNA into nanoparticles (polyplexes) between 140 and 440 nm at an N/P ratio of 30. Furthermore, polyplexes formed with 1-4 deliver pDNA (plasmid DNA) containing the firefly luciferase reporter gene to BHK-21 cells in a nontoxic and highly efficient manner (as determined by luciferase gene expression). In particular, polymer 4 reveals very high delivery efficiency (equivalent to linear PEI). This result may be due in part to the "proton sponge" hypothesis proposed by Behr et al. Polymers containing amines that are protonated in the endosomal pH range (between about 7.4-5.0) reveal enhanced gene delivery profiles.     

Thermally Activated Delayed Fluorescence in a Y3N@C80 Endohedral Fullerene: Time‐Resolved Luminescence and EPR Studies

The endohedral fullerene Y₃N@C₈₀ exhibits luminescence with reasonable quantum yield and extraordinary long lifetime. By variable‐temperature steady‐state and time‐resolved luminescence spectroscopy, it is demonstrated that above 60 K the Y₃N@C₈₀ exhibits thermally activated delayed fluorescence with maximum emission at 120 K and a negligible prompt fluorescence. Below 60 K, a phosphorescence with a lifetime of 192±1 ms is observed. Spin distribution and dynamics in the triplet excited state is investigated with X‐ and W‐band EPR and ENDOR spectroscopies and DFT computations. Finally, electroluminescence of the Y₃N@C₈₀/PFO film is demonstrated opening the possibility for red‐emitting fullerene‐based organic light‐emitting diodes (OLEDs).     

The Monoid of Families of Quiver Representations

A monoid structure on families of representations of a quiveris introduced by taking extensions of representations in families,that is, subvarieties of the varieties of representations. Thestudy of this monoid leads to interesting interactions betweenrepresentation theory, algebraic geometry and quantum grouptheory. For example, it produces a wealth of interesting examplesof families of quiver representations, which can be analysedby representation-theoretic and geometric methods. Conversely,results from representation theory, in particular A. Schofield'swork on general properties of quiver representations, allowus to relate the monoid to certain degenerate forms of quantizedenveloping algebras. 2000 Mathematical Subject Classification: 16G20, 14L30, 17B37.     

A Polycation Scaffold Presenting Tunable “Click” Sites: Conjugation to Carbohydrate Ligands and Examination of Hepatocyte‐Targeted pDNA Delivery

A versatile polycation scaffold that can easily be modified with targeting ligands has been designed, synthesized, and characterized. A series of galactose‐containing polymers has been produced to demonstrate the ease of modification of this polynucleotide delivery vehicle motif via the click reaction and to study how various structural modifications affect recognition by ASGPr on hepatocytes. A small library of structures was created where DCS and alkyl spacer length between the targeting group and the polymer backbone was varied. The novel polymer scaffold described proves to be a valuable tool for understanding structure/activity relationships of complexes made with receptor‐targeted polymers.

     

The Harder-Narasimhan system in quantum groups and cohomology of quiver moduli

Inventiones mathematicae - Methods of Harder and Narasimhan from the theory of moduli of vector bundles are applied to moduli of quiver representations. Using the Hall algebra approach to quantum...     

Refined GW/Kronecker correspondence

Gromov–Witten invariants of weighted projective planes and Euler characteristics of moduli spaces of representations of bipartite quivers are related via the tropical vertex, a group of formal automorphisms of a torus. On the Gromov–Witten side, this uses the work of Gross, Pandharipande and Siebert. The quiver moduli side features quiver wall-crossing formulas, functional equations for Euler characteristics, and localization techniques. We derive several explicit formulas for Gromov–Witten invariants.     

Desingularization of quiver Grassmannians for Dynkin quivers

A desingularization of arbitrary quiver Grassmannians for representations of Dynkin quivers is constructed in terms of quiver Grassmannians for an algebra derived equivalent to the Auslander algebra of the quiver.