Stability of Transonic Shock Solutions for One-Dimensional Euler-Poisson Equations

In this paper, both structural and dynamical stabilities of steady transonic shock solutions for one-dimensional Euler-Poission system are investigated. First, a steady transonic shock solution with supersonic backgroumd charge is shown to be structurally stable with respect to small perturbations of the background charge, provided that the electric field is positive at the shock location. Second, any steady transonic shock solution with the supersonic background charge is proved to be dynamically and exponentially stable with respect to small perturbation of the initial data, provided the electric field is not too negative at the shock location. The proof of the first stability result relies on a monotonicity argument for the shock position and the downstream density, and a stability analysis for subsonic and supersonic solutions. The dynamical stability of the steady transonic shock for the Euler-Poisson equations can be transformed to the global well-posedness of a free boundary problem for a quasilinear second order equation with nonlinear boundary conditions. The analysis for the associated linearized problem plays an essential role

Assembly of Protein Building Blocks Using a Short Synthetic Peptide

Combining proteins or their defined domains offers new enhanced functions. Conventionally, two proteins are either fused into a single polypeptide chain by recombinant means or chemically cross-linked. However, these strategies can have drawbacks such as poor expression (recombinant fusions) or aggregation and inactivation (chemical cross-linking), especially in the case of large multifunctional proteins. We developed a new linking method which allows site-oriented, noncovalent, yet irreversible stapling of modified proteins at neutral pH and ambient temperature. This method is based on two distinct polypeptide linkers which self-assemble in the presence of a specific peptide staple allowing on-demand and irreversible combination of protein domains. Here we show that linkers can either be expressed or be chemically conjugated to proteins of interest, depending on the source of the proteins. We also show that the peptide staple can be shortened to 24 amino acids still permitting an irreversible combination of functional proteins. The versatility of this modular technique is demonstrated by stapling a variety of proteins either in solution or to surfaces

Prodrug Strategy for PSMA-targeted Delivery of TGX-221 to Prostate Cancer Cells

TGX-221 is a potent, selective, and cell membrane permeable inhibitor of the PI3K p110β catalytic subunit. Recent studies showed that TGX-221 has anti-proliferative activity against PTEN-deficient tumor cell lines including prostate cancers. The objective of this study was to develop an encapsulation system for parenterally delivering TGX-221 to the target tissue through a prostate-specific membrane aptamer (PSMAa10) with little or no side effects. In this study, PEG-PCL micelles were formulated to encapsulate the drug, and a prodrug strategy was pursued to improve the stability of the carrier system. Fluorescence imaging studies demonstrated that the cellular uptake of both drug and nanoparticles were significantly improved by targeted micelles in a PSMA positive cell line. The area under the plasma concentration time curve of the micelle formulation in nude mice was 2.27-fold greater than the naked drug, and the drug clearance rate was 17.5-fold slower. These findings suggest a novel formulation approach for improving site-specific drug delivery of a molecular-targeted prostate cancer treatment