Dendronized Hyperbranched Macromolecules: Soft Matter with a Novel Type of Segmental Distribution

Dendronization of a hyperbranched polyester with different generation dendrons leads to pseudo‐dendritic structures. The hyperbranched core is modified by the divergent coupling of protected monomer units to the functional groups. Compared to dendrimers, the synthetic effort is significantly less, but the properties are very close to those of high‐generation dendrimers. The number of functional groups, molar mass, and rheology behavior even in the early generation (G1–G4) pseudo‐dendrimers strongly resembles the behavior of dendrimers in higher generations (G5–G8). Comparison of the segmental and internal structure with perfect dendrimers is performed using SANS, dynamic light scattering and viscosity analysis, microscopy and molecular dynamics simulation. The interpretation of the results reveals unique structural characteristics arising from lower segmental density of the core, which turns into a soft nano‐sphere with a smooth surface even in the first generation.     

Self‐Organization of Gold Nanoparticle Assemblies with 3D Spatial Order and Their External Stimuli Responsiveness

Gold nanoparticles (AuNP) with pyridyl end‐capped polystyrenes (PS‐4VP) as “quasi‐monodentate” ligands self‐assemble into ordered PS‐4VP/AuNP nanostructures with 3D hexagonal spatial order in the dried solid state. The key for the formation of these ordered structures is the modulation of the ratio AuNP versus ligands, which proves the importance of ligand design and quantity for the preparation of novel ordered polymer/metal nanoparticle conjugates. Although the assemblies of PS‐4VP/AuNP in dispersion lack in high dimensional order, strong plasmonic interactions are observed due to close contact of AuNP. Applying temperature as an external stimulus allows the reversible distortion of plasmonic interactions within the AuNP nanocomposite structures, which can be observed directly by naked eye. The modulation of the macroscopic optical properties accompanied by this structural distortion of plasmonic interaction opens up very interesting sensoric applications.

     

Versatile bio-ink for covalent immobilization of chimeric avidin on sol-gel substrates

A bio-ink for covalent deposition of thermostable, high affinity biotin-binding chimeric avidin onto sol-gel substrates was developed. The bio-ink was prepared from heterobifunctional crosslinker 6-maleimidohexanoic acid N-hydroxysuccinimide which was first reacted either with 3-aminopropyltriethoxysilane or 3-aminopropyldimethylethoxysilane to form silane linkers 6-maleimide-N-(3-(triethoxysilyl)propyl)hexanamide or -(ethoxydimethylsilyl)propyl)-hexanamide. C-terminal cysteine genetically engineered to chimeric avidin was reacted with the maleimide group of silane linker in methanol/PBS solution to form a suspension, which was printed on sol-gel modified PMMA film. Different concentrations of chimeric avidin and ratios between silane linkers were tested to find the best properties for the bio-ink to enable gravure or inkjet printing. Bio-ink prepared from 3-aminopropyltriethoxysilane was found to provide the highest amount of active immobilized chimeric avidin. The developed bio-ink was shown to be valuable for automated fabrication of avidin-functionalized polymer films.     

A semisynthetic Eph receptor tyrosine kinase provides insight into ligand-induced kinase activation

We have developed a methodology for generating milligram amounts of functional Eph tyrosine kinase receptor using the protein engineering approach of expressed protein ligation. Stimulation with ligand induces efficient autophosphorylation of the semisynthetic Eph construct. The in vitro phosphorylation of key Eph tyrosine residues upon ligand-induced activation was monitored via time-resolved, quantitative phosphoproteomics, suggesting a precise and unique order of phosphorylation of the Eph tyrosines in the kinase activation process. To our knowledge, this work represents the first reported semisynthesis of a receptor tyrosine kinase and provides a potentially general method for producing single-pass membrane proteins for structural and biochemical characterization.     

The equivalence between pointwise Hardy inequalities and uniform fatness

We prove an equivalence result between the validity of a pointwise Hardy inequality in a domain and uniform capacity density of the complement. This result is new even in Euclidean spaces, but our methods apply in general metric spaces as well. We also present a new transparent proof for the fact that uniform capacity density implies the classical integral version of the Hardy inequality in the setting of metric spaces. In addition, we consider the relations between the above concepts and certain Hausdorff content conditions.     

Flat forms, bi-Lipschitz parametrizations, and smoothability of manifolds

We give a sufficient condition for a metric (homology) manifold to be locally bi-Lipschitz equivalent to an open subset in R ⁿ . The condition is a Sobolev condition for a measurable coframe of flat 1-forms. In combination with an earlier work of D. Sullivan, our methods also yield an analytic characterization for smoothability of a Lipschitz manifold in terms of a Sobolev regularity for frames in a cotangent structure. In the proofs, we exploit the duality between flat chains and flat forms, and recently established differential analysis on metric measure spaces. When specialized to R ⁿ , our result gives a kind of asymptotic and Lipschitz version of the measurable Riemann mapping theorem as suggested by Sullivan.     

On stochastic approximation of the eigenvectors and eigenvalues of the expectation of a random matrix

In applications of signal processing and pattern recognition, eigenvectors and eigenvalues of the statistical mean of a random matrix sequence are needed. Iterative methods are suggested and analyzed, in which no sample moments are used. Convergence is shown by stochastic approximation theory.