Decay Estimates for Solutions of Porous Medium Equations with Advection

In this paper, we show that bounded weak solutions of the Cauchy problem for general degenerate parabolic equations of the form

$$ u_{t} + \operatorname{div}f(x,t,u) = \operatorname{div}\bigl( |u|^{\alpha } \nabla u\bigr), \quad x \in \mathbb{R}^{n} , \ t > 0, $$

where \(\alpha > 0 \) is constant, decrease to zero, under fairly broad conditions on the advection flux \(f\). Besides that, we derive a time decay rate for these solutions.

     

Application of affinity selection-mass spectrometry assays to purification and affinity-based screening of the chemokine receptor CXCR4

Affinity selection-mass spectrometry (AS-MS) is a sensitive technology for identifying small molecules that bind to target proteins, and assays enabled by AS-MS can be used to delineate relative binding affinities of ligands for proteins. 'Indirect' AS-MS assays employ size-exclusion techniques to separate target-ligand complexes from unbound ligands, and target-associated ligands are then specifically detected by liquid chromatography mass spectrometry. We report how indirect AS-MS binding assays with known reference control compounds were used as guideposts for development of an optimized purification method for CXCR4, a G-protein coupled chemokine receptor, for which we sought novel antagonists. The CXCR4 purification method that was developed was amenable to scale-up and enabled the screening of purified recombinant human CXCR4 against a large combinatorial library of small molecules by high throughput indirect AS-MS. The screen resulted in the discovery of new ligands that competed off binding of reference compounds to CXCR4 in AS-MS binding assays and that antagonized SDF1α-triggered responses and CXCR4-mediated HIV1 viral uptake in cell-based assays. This report provides a methodological paradigm whereby indirect AS-MS-based ligand binding assays may be used to guide optimal integral membrane protein purification methods that enable downstream affinity selection-based applications such as high throughput AS-MS screens.     

The Dielectric Tensor for Magnetized Dusty Plasmas with Superthermal Plasma Populations and Dust Particles of Different Sizes

We present general expressions for the components of the dielectric tensor of magnetized dusty plasmas, valid for arbitrary direction of propagation and for situations in which populations of dust particles of different sizes are present in the plasma. These expressions are derived using a kinetic approach which takes into account the variation of the charge of the dust particles due to inelastic collisions with electrons and ions, and features the components of the dielectric tensor in terms of a finite and an infinite series, containing all effects of harmonics and Larmor radius, and is valid for the whole range of frequencies above the plasma frequency of the dust particles, which are assumed to be motionless. The integrals in velocity space which appear in the dielectric tensor are solved assuming that the electron and ion populations are described by anisotropic non-thermal distributions characterized by parameters κ _∥ and κ _⊥, featuring the Maxwellian as a limiting case. These integrals can be written in terms of generalized dispersion functions, which can be expressed in terms of hypergeometric functions. The formulation therefore becomes specially suitable for numerical analysis.     

Peptides that mimic glycosaminoglycans: high-affinity ligands for a hyaluronan binding domain.

BACKGROUND: Hyaluronan (HA) is a non-sulfated glycosaminoglycan (GAG) that promotes motility, adhesion, and proliferation in mammalian cells, as mediated by cell-surface HA receptors. We sought to identify non-carbohydrate ligands that would bind to and activate cell-surface HA receptors. Such analogs could have important therapeutic uses in the treatment of cancer, wound healing, and arthritis, since such ligands would be resistant to degradation by hyaluronidase (HAse). RESULTS: Peptide ligands that bind specifically to the recombinant HA binding domain (BD) of the receptor for hyaluronan-mediated motility (RHAMM) were obtained by screening two peptide libraries: (i) random 8-mers and (ii) biased 8-mers with alternating acidic side chains, i.e. XZXZXZXZ (X=all-L-amino acids except Cys, Lys, or Arg; Z=D-Asp, L-Asp, D-Glu, or L-Glu). Selectivity of the peptide ligands for the HABD was established by (i) detection of binding of biotin- or fluorescein-labeled peptides to immobilized proteins and (ii) fluorescence polarization of FITC-labeled peptides with the HABD in solution. HA competitively displaced binding of peptides to the HABD, while other GAGs were less effective competitors. The stereochemistry of four biased octapeptides was established by synthesis of the 16 stereoisomers of each peptide. Binding assays demonstrated a strong preference for alternating D and L configurations for the acidic residues, consistent with the calculated orientation of glucuronic acid moieties of HA. CONCLUSIONS: Two classes of HAse-resistant peptide mimetics of HA were identified with high affinity, HA-compatible binding to the RHAMM HABD. This demonstrated that non-HA ligands specific to a given HA binding protein could be engineered, permitting receptor-specific targeting.     

10 Gbit/s Silicon modulator and germanium detector chip-to-chip optical link

Experimental results of a high-speed silicon optical modulator based on carrier depletion in a pipin diode and Germanium photodetectors are presented. 10 Gbit/s data transmission is obtained for both optoelectronic devices, with for the optical modulator an extinction ratio (ER) higher than 8 dB and insertion loss (IL) lower than 6 dB and for Ge photodetector, a zero-bias operating at 10 Gbit/s. Finally, a 10 Gbit/s optical link combining Si modulator and Ge photodetector is demonstrated.