Theorems on existence and global dynamics for the Einstein equations

This article is a guide to theorems on existence and global dynamics of solutions of the Einstein equations. It draws attention to open questions in the field. The local-in-time Cauchy problem, which is relatively well understood, is surveyed. Global results for solutions with various types of symmetry are discussed. A selection of results from Newtonian theory and special relativity that offer useful comparisons is presented. Treatments of global results in the case of small data and results on constructing spacetimes with prescribed singularity structure or late-time asymptotics are given. A conjectural picture of the asymptotic behaviour of general cosmological solutions of the Einstein equations is built up. Some miscellaneous topics connected with the main theme are collected in a separate section.Comment: Submitted to Living Reviews in Relativity, major update of Living Rev. Rel. 5 (2002)

Theorems on existence and global dynamics for the Einstein equations

This article is a guide to theorems on existence and global dynamics of solutions of the Einstein equations. It draws attention to open questions in the field. The local in time Cauchy problem, which is relatively well understood, is surveyed. Global results for solutions with various types of symmetry are discussed. A selection of results from Newtonian theory and special relativity which offer useful comparisons is presented. Treatments of global results in the case of small data and results on constructing spacetimes with prescribed singularity structure are given. A conjectural picture of the asymptotic behaviour of general cosmological solutions of the Einstein equations is built up. Some miscellaneous topics connected with the main theme are collected in a separate section.Comment: 54 pages, submitted to Living Reviews in Relativit

Effects of the Histone Deacetylase Inhibitor Valproic Acid on Human Pericytes In Vitro

Microvascular pericytes are of key importance in neoformation of blood vessels, in stabilization of newly formed vessels as well as maintenance of angiostasis in resting tissues. Furthermore, pericytes are capable of differentiating into pro-fibrotic collagen type I producing fibroblasts. The present study investigates the effects of the histone deacetylase (HDAC) inhibitor valproic acid (VPA) on pericyte proliferation, cell viability, migration and differentiation. The results show that HDAC inhibition through exposure of pericytes to VPA in vitro causes the inhibition of pericyte proliferation and migration with no effect on cell viability. Pericyte exposure to the potent HDAC inhibitor Trichostatin A caused similar effects on pericyte proliferation, migration and cell viability. HDAC inhibition also inhibited pericyte differentiation into collagen type I producing fibroblasts. Given the importance of pericytes in blood vessel biology a qPCR array focusing on the expression of mRNAs coding for proteins that regulate angiogenesis was performed. The results showed that HDAC inhibition promoted transcription of genes involved in vessel stabilization/maturation in human microvascular pericytes. The present in vitro study demonstrates that VPA influences several aspects of microvascular pericyte biology and suggests an alternative mechanism by which HDAC inhibition affects blood vessels. The results raise the possibility that HDAC inhibition inhibits angiogenesis partly through promoting a pericyte phenotype associated with stabilization/maturation of blood vessels

What is damaging the kidney in lupus nephritis?

Despite marked improvements in the survival of patients with severe lupus nephritis over the past 50 years, the rate of complete clinical remission after immune suppression therapy i

Modeling CICR in rat ventricular myocytes: voltage clamp studies

<p>Abstract</p> <p>Background</p> <p>The past thirty-five years have seen an intense search for the molecular mechanisms underlying calcium-induced calcium-release (CICR) in cardiac myocytes, with voltage clamp (VC) studies being the leading tool employed. Several VC protocols including lowering of extracellular calcium to affect <it>Ca</it>²⁺loading of the sarcoplasmic reticulum (SR), and administration of blockers caffeine and thapsigargin have been utilized to probe the phenomena surrounding SR <it>Ca</it>²⁺release. Here, we develop a deterministic mathematical model of a rat ventricular myocyte under VC conditions, to better understand mechanisms underlying the response of an isolated cell to calcium perturbation. Motivation for the study was to pinpoint key control variables influencing CICR and examine the role of CICR in the context of a physiological control system regulating cytosolic <it>Ca</it>²⁺concentration ([<it>Ca</it>²⁺]<it>_myo</it>).</p> <p>Methods</p> <p>The cell model consists of an electrical-equivalent model for the cell membrane and a fluid-compartment model describing the flux of ionic species between the extracellular and several intracellular compartments (cell cytosol, SR and the dyadic coupling unit (DCU), in which resides the mechanistic basis of CICR). The DCU is described as a controller-actuator mechanism, internally stabilized by negative feedback control of the unit's two diametrically-opposed <it>Ca</it>²⁺channels (trigger-channel and release-channel). It releases <it>Ca</it>²⁺flux into the cyto-plasm and is in turn enclosed within a negative feedback loop involving the SERCA pump, regulating[<it>Ca</it>²⁺]<it>_myo</it>.</p> <p>Results</p> <p>Our model reproduces measured VC data published by several laboratories, and generates graded <it>Ca</it>²⁺release at high <it>Ca</it>²⁺gain in a homeostatically-controlled environment where [<it>Ca</it>²⁺]<it>_myo</it>is precisely regulated. We elucidate the importance of the DCU elements in this process, particularly the role of the ryanodine receptor in controlling SR <it>Ca</it>²⁺release, its activation by trigger <it>Ca</it>²⁺, and its refractory characteristics mediated by the luminal SR <it>Ca</it>²⁺sensor. Proper functioning of the DCU, sodium-calcium exchangers and SERCA pump are important in achieving negative feedback control and hence <it>Ca</it>²⁺homeostasis.</p> <p>Conclusions</p> <p>We examine the role of the above <it>Ca</it>²⁺regulating mechanisms in handling various types of induced disturbances in <it>Ca</it>²⁺levels by quantifying cellular <it>Ca</it>²⁺balance. Our model provides biophysically-based explanations of phenomena associated with CICR generating useful and testable hypotheses.</p

The Einstein-Vlasov System/Kinetic Theory

The main purpose of this article is to provide a guide to theorems on global properties of solutions to the Einstein--Vlasov system. This system couples Einstein's equations to a kinetic matter model. Kinetic theory has been an important field of research during several decades in which the main focus has been on non-relativistic and special relativistic physics, i.e., to model the dynamics of neutral gases, plasmas, and Newtonian self-gravitating systems. In 1990, Rendall and Rein initiated a mathematical study of the Einstein--Vlasov system. Since then many theorems on global properties of solutions to this system have been established.Comment: Published version http://www.livingreviews.org/lrr-2011-

FcγRIIb differentially regulates pre-immune and germinal center B cell tolerance in mouse and human.

Several tolerance “checkpoints” exist throughout B cell development to control autoreactive B cells and prevent the generation of pathogenic autoantibodies. FcγRIIb is an Fc receptor that inhibits B cell activation and, if defective, is associated with autoimmune disease. Its impact on specific B cell tolerance checkpoints is unknown. Here we show that reduced expression of FcγRIIb leads to increased deletion and anergy of autoreactive immature B cells, but despite this autoreactive B cells expand in the germinal center and serum autoantibodies are produced, even in response to exogenous non-self antigen. Thus, we show FcγRIIb has opposing effects on pre- and post-immune tolerance checkpoints, and suggest B cell tolerance requires the control of “bystander” germinal center B cells with low or no affinity for the immunization antigen.This work was funded by the Wellcome Trust (Programme Grant Number 083650/Z/07/Z to KGCS) and supported by the NIHR Cambridge Biomedical Research Centre. ME was funded by the Wellcome Trust (Programme Grant Number 083650/Z/07/Z), by a Junior Team Leader starting grant from the Laboratory of Excellence in Research on Medication and Innovative Therapeutics (LabEx LERMIT) supported by a grant from ANR (ANR-10-LABX-33) under the program “Investissements d'Avenir” (ANR-11-IDEX-0003-01) and by an ANR @RAction starting grant (ANR-14-ACHN- 0008). KGCS is an NIHR Senior Clinical Investigator and a Distinguished Innovator of the Lupus Research Institute