Dynamical Collapse of Boson Stars

We study the time evolution in system of $N$ bosons with a relativistic dispersion law interacting through an attractive Coulomb potential with coupling constant $G$. We consider the mean field scaling where $N$ tends to infinity, $G$ tends to zero and $\lambda = G N$ remains fixed. We investigate the relation between the many body quantum dynamics governed by the Schr\"odinger equation and the effective evolution described by a (semi-relativistic) Hartree equation. In particular, we are interested in the super-critical regime of large $\lambda$ (the sub-critical case has been studied in \cite{ES,KP}), where the nonlinear Hartree equation is known to have solutions which blow up in finite time. To inspect this regime, we need to regularize the Coulomb interaction in the many body Hamiltonian with an $N$ dependent cutoff that vanishes in the limit $N\to \infty$. We show, first, that if the solution of the nonlinear equation does not blow up in the time interval $[-T,T]$, then the many body Schr\"odinger dynamics (on the level of the reduced density matrices) can be approximated by the nonlinear Hartree dynamics, just as in the sub-critical regime. Moreover, we prove that if the solution of the nonlinear Hartree equation blows up at time $T$ (in the sense that the $H^{1/2}$ norm of the solution diverges as time approaches $T$), then also the solution of the linear Schr\"odinger equation collapses (in the sense that the kinetic energy per particle diverges) if $t \to T$ and, simultaneously, $N \to \infty$ sufficiently fast. This gives the first dynamical description of the phenomenon of gravitational collapse as observed directly on the many body level.Comment: 40 page

Age-associated physiological and pathological changes at the blood–brain barrier: A review

The age-associated decline of the neurological and cognitive functions becomes more and more serious challenge for the developed countries with the increasing number of aged populations. The morphological and biochemical changes in the aging brain are the subjects of many extended research projects worldwide for a long time. However, the crucial role of the blood–brain barrier (BBB) impairment and disruption in the pathological processes in age-associated neurodegenerative disorders received special attention just for a few years. This article gives an overview on the major elements of the blood–brain barrier and its supporting mechanisms and also on their alterations during development, physiological aging process and age-associated neurodegenerative disorders (Alzheimer's disease, multiple sclerosis, Parkinson's disease, pharmacoresistant epilepsy). Besides the morphological alterations of the cellular elements (endothelial cells, astrocytes, pericytes, microglia, neuronal elements) of the BBB and neurovascular unit, the changes of the barrier at molecular level (tight junction proteins, adheres junction proteins, membrane transporters, basal lamina, extracellular matrix) are also summarized. The recognition of new players and initiators of the process of neurodegeneration at the level of the BBB may offer new avenues for novel therapeutic approaches for the treatment of numerous chronic neurodegenerative disorders currently without effective medication

The Use of Microdialysis Techniques in Mice to Study P-gp Function at the Blood-Brain Barrier.

An integrated assay system involving dual/triple-probe microdialysis techniques in rats was developed earlier for testing interactions with P-glycoprotein (P-gp) at the blood-brain barrier using quinidine/PSC-833 as a P-gp substrate/inhibitor combination. The aim of the present study was to expand our assay system to mice using microdialysis with simultaneous sampling of blood and brain and to compare the result with a primary mouse brain endothelial cell monolayer (pMBMEC) assay. Brain penetration of quinidine was dose dependent in both anesthetized and awake mice after intraperitoneal drug administration. PSC-833 pretreatment caused a 2.5- to 3.4-fold increase in quinidine levels of brain dialysate samples in anesthetized or awake animals, after single or repeated administration of PSC-833. In pMBMEC, a 2.0- to 2.5-fold efflux ratio was observed in the transcellular transport of quinidine. The P-gp-mediated vectorial transport of quinidine was eliminated by PSC-833. These results indicate that quinidine with PSC-833 is a good probe substrate-reference inhibitor combination for testing drug-drug interactions with P-gp in the in vivo and in vitro mouse systems. With increasing number of humanized transgenic mice, a test system with mouse microdialysis experimentation becomes more important to predict drug-drug interactions in humans

Physiological blood–brain transport is impaired with age by a shift in transcytosis

The vascular interface of the brain, known as the blood-brain barrier (BBB), is understood to maintain brain function in part via its low transcellular permeability1-3. Yet, recent studies have demonstrated that brain ageing is sensitive to circulatory proteins4,5. Thus, it is unclear whether permeability to individually injected exogenous tracers-as is standard in BBB studies-fully represents blood-to-brain transport. Here we label hundreds of proteins constituting the mouse blood plasma proteome, and upon their systemic administration, study the BBB with its physiological ligand. We find that plasma proteins readily permeate the healthy brain parenchyma, with transport maintained by BBB-specific transcriptional programmes. Unlike IgG antibody, plasma protein uptake diminishes in the aged brain, driven by an age-related shift in transport from ligand-specific receptor-mediated to non-specific caveolar transcytosis. This age-related shift occurs alongside a specific loss of pericyte coverage. Pharmacological inhibition of the age-upregulated phosphatase ALPL, a predicted negative regulator of transport, enhances brain uptake of therapeutically relevant transferrin, transferrin receptor antibody and plasma. These findings reveal the extent of physiological protein transcytosis to the healthy brain, a mechanism of widespread BBB dysfunction with age and a strategy for enhanced drug delivery