Lp theory for the multidimensional aggregation equation

We consider well‐posedness of the aggregation equation ∂_tu + div(uv) = 0, v = −▿K * u with initial data in \input amssym ${\cal P}_2 {\rm (\Bbb R}^d {\rm )} \cap L^p ({\Bbb R}^d )$ in dimensions 2 and higher. We consider radially symmetric kernels where the singularity at the origin is of order |x|^α, α > 2 − d, and prove local well‐posedness in \input amssym ${\cal P}_2 { (\Bbb R}^d {\rm )} \cap L^p ({\Bbb R}^d )$ for sufficiently large p < p_s. In the special case of K(x) = |x|, the exponent p_s = d/(d = 1) is sharp for local well‐posedness in that solutions can instantaneously concentrate mass for initial data in \input amssym ${\cal P}_2 { (\Bbb R}^d {\rm )} \cap L^p ({\Bbb R}^d )$ with p < p_s. We also give an Osgood condition on the potential K(x) that guarantees global existence and uniqueness in \input amssym ${\cal P}_2 { (\Bbb R}^d {\rm )} \cap L^p ({\Bbb R}^d )$ . © 2010 Wiley Periodicals, Inc.     

Stereoselective synthesis of myo-inositol via ring-closing metathesis: a building block for glycosylphosphatidylinositol (GPI) anchor synthesis

Here we report a concise stereoselective synthesis of myo-inositol via ring-closing metathesis. A readily available bis-Weinreb amide of D-tartrate served as a key intermediate. [reaction: see text]     

Formation of 1,1-alpha,alpha-glycosidic bonds by intramolecular aglycone delivery. A convergent synthesis of trehalose

[reaction: see text] We report a new synthesis of trehalose analogs that involves the use of intramolecular aglycone delivery for stereoselective formation of the 1,1-alpha,alpha-glycosidic bond. The glycosylation reaction afforded the desired isomer exclusively and in good yield.     

Measurement of the exclusive 3He(e,e'p) reaction below the quasielastic peak

New, high-precision measurements of the 3He(e,e(')p) reaction using the A1 Collaboration spectrometers at the Mainz microtron MAMI are presented. These were performed in antiparallel kinematics at energy transfers below the quasielastic peak, and at a central momentum transfer of 685 MeV/c. Cross sections and distorted momentum distributions were extracted and compared to theoretical predictions and existing data. The longitudinal and transverse behavior of the cross section was also studied. Sizable differences in the cross-section behavior from theoretical predictions based on the plane wave impulse approximation were observed in both the two- and three-body breakup channels. Full Faddeev-type calculations account for some of the observed excess cross-section, but significant differences remain.     

A Bioorthogonal Reaction of N‐Oxide and Boron Reagents

The development of bioorthogonal reactions has classically focused on bond‐forming ligation reactions. In this report, we seek to expand the functional repertoire of such transformations by introducing a new bond‐cleaving reaction between N‐oxide and boron reagents. The reaction features a large dynamic range of reactivity, showcasing second‐order rate constants as high as 2.3×10³ M ^?1 s^?1 using diboron reaction partners. Diboron reagents display minimal cell toxicity at millimolar concentrations, penetrate cell membranes, and effectively reduce N‐oxides inside mammalian cells. This new bioorthogonal process based on miniscule components is thus well‐suited for activating molecules within cells under chemical control. Furthermore, we demonstrate that the metabolic diversity of nature enables the use of naturally occurring functional groups that display inherent biocompatibility alongside abiotic components for organism‐specific applications.     

Hierarchical assembly of model cell surfaces: synthesis of mucin mimetic polymers and their display on supported bilayers

Molecular level analysis of cell-surface phenomena could benefit from model systems comprising structurally defined components. Here we present the first step toward bottom-up assembly of model cell surfaces-the synthesis of mucin mimetics and their incorporation into artificial membranes. Natural mucins are densely glycosylated O-linked glycoproteins that serve numerous functions on cell surfaces. Their large size and extensive glycosylation makes the synthesis of these biopolymers impractical. We designed synthetically tractable glycosylated polymers that possess rodlike extended conformations similar to natural mucins. The glycosylated polymers were end-functionalized with lipid groups and embedded into supported lipid bilayers where they interact with protein receptors in a structure-dependent manner. Furthermore, their dynamic behavior in synthetic membranes mirrored that of natural biomolecules. This system provides a unique framework with which to study the behavior of mucin-like macromolecules in a controlled, cell surface-mimetic environment.     

The lubrication approximation for thin viscous films: Regularity and long-time behavior of weak solutions

We consider the fourth-order degenerate diffusion equation, in one space dimension. This equation, derived from a lubrication approximation, models the surface-tension-dominated motion of thin viscous films and spreading droplets [15]. The equation with f(h) = |h| also models a thin neck of fluid in the Hele-Shaw cell [10], [11], [23]. In such problems h(x,t) is the local thickness of the the film or neck. This paper considers the properties of weak solutions that are more relevant to the droplet problem than to Hele-Shaw. For simplicity we consider periodic boundary conditions with the interpretation of modeling a periodic array of droplets. We consider two problems: The first has initial data h₀ ≥ 0 and f(h) = |h|ⁿ, 0 < n < 3. We show that there exists a weak nonnegative solution for all time. Also, we show that this solution becomes a strong positive solution after some finite time T*, and asymptotically approaches its means as t → ∞. The weak solution is in the classical sense of distributions for 3/8 < n < 3 and in a weaker sense introduced in [1] for the remaining 0 < n ≤ 3/8. Furthermore, the solutions have high enough regularity to just include the unique source-type solutions [2] with zero slope at the edge of the support. They do not include any of the less regular solutions with positive slope at the edge of the support. Second, we consider strictly positive initial data h₀ ≥ m > 0 and f(h) = |h|ⁿ, 0 < n < ∞. For this problem we show that even if a finite-time singularity of the form h → 0 does occur, there exists a weak nonnegative solution for all time t. This weak solution becomes strong and positive again after some critical time T*. As in the first problem, we show that the solution approaches its mean as t → ∞. The main technical idea is to introduce new classes of dissipative entropies to prove existence and higher regularity. We show that these entropies are related to norms of the difference between the solution and its mean to prove the relaxation result. © 1996 John Wiley & Sons, Inc.     

Resolvin D5 (RvD5) Reduces Renal Damage Caused by LPS Endotoxemia in Female Mice

In self-revolving gram-negative Escherichia coli infection, Resolvin D5 (RvD5) was found to enhance bacteria phagocytosis and reduce the production of inflammatory mediators, contributing to the resolution of infection. LPS (lipopolysaccharide) is a gram-negative bacterial structure product which activates the immune system and, at high doses, leads to endotoxemia. To our knowledge, the effect of RvD5 against LPS endotoxemia has not been investigated to date. Female Swiss mice received an i.p. treatment with RvD5 (0.1, 1 or 10 ng/animal). After 1 h, they were stimulated with LPS (10 mg/kg, i.v.), and samples were collected after additional 6 h. The resulting data demonstrated that RvD5 protected the kidneys (urea and creatinine serum levels) from tissue injury. These effects were related to an improvement in histopathological parameters and a reduction of enzymatic markers of leukocyte infiltration, pro-inflammatory cytokine (IL-1β, TNF-α, and IL-6) production, and oxidative stress. Antioxidant markers were also increased by RvD5, but IL-10 (an anti-inflammatory cytokine) levels were unaltered. We also observed that RvD5 reduced the infiltration of CD45⁺ hematopoietic cells into the kidneys, reduced the activation of NFκB and promoted the Nrf2 pathway by reducing Keap-1 levels. Our data indicate that RvD5 may be a therapeutic possibility to reduce kidney lesions in LPS endotoxemia.