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 Adrenomedullin on the Glomerular Adrenomedullin System in a Rat Model of Anti-Thy1 Glomerulonephritis

Background: Adrenomedullin (ADM) has antiproliferative effects on glomerular mesangial cells. The study was performed to determine changes in glomerular gene expression of the ADM system by ADM treatment in anti-Thy1 glomerulonephritis (GN). Methods: GN in rats was induced by injecting anti-Thy-1 antibody. To show the effect of ADM treatment, rats received ADM from day 3 to day 6 of GN. Supplemental rats were sacrificed on day 3, 7 and 14 of GN to show the expression pattern of adrenomedullin and its receptors. Glomeruli were prepared by sieving or laser-assisted microdissection. Expression of ADM, calcitonin receptor-like receptor (CLR), receptor activity-modifying proteins (RAMP) 1–3, CD34, Thy1 and nephrin was analyzed using real-time PCR. Results: During GN a reduction of CLR and RAMP 2 + 3 expressions was detected on days 3, 7 and 14, while RAMP 1 rose. ADM mRNA decreased on days 3 and 7. Thy1 expression as a surrogate of mesangial cell number was downregulated during GN. A significant reduction of CD34 expression, as a surrogate for endothelial cell number, was detected on day 7. A tendency towards reduction of nephrin gene expression, as a surrogate for number of podocytes, was seen. The administration of ADM during GN did not change the expression on Thy1, CD34 or nephrin. The results were similar for microdissected and sieved glomeruli. In ADM-treated GN animals ADM gene expression rose compared to untreated GN animals on day 6. These effects were detected both in sieved and microdissected glomeruli. ADM administration did not change the expression of the receptors. Conclusion: The downregulation of adrenomedullin during GN at the gene level can be improved by ADM application

Quantifying the heterogeneity of macromolecular machines by mass photometry

Sample purity is central to in vitro studies of protein function and regulation, and to the efficiency and success of structural studies using techniques such as x-ray crystallography and cryo-electron microscopy (cryo-EM). Here, we show that mass photometry (MP) can accurately characterize the heterogeneity of a sample using minimal material with high resolution within a matter of minutes. To benchmark our approach, we use negative stain electron microscopy (nsEM), a popular method for EM sample screening. We include typical workflows developed for structure determination that involve multi-step purification of a multi-subunit ubiquitin ligase and chemical cross-linking steps. When assessing the integrity and stability of large molecular complexes such as the proteasome, we detect and quantify assemblies invisible to nsEM. Our results illustrate the unique advantages of MP over current methods for rapid sample characterization, prioritization and workflow optimization

Quantifying the heterogeneity of macromolecular machines by mass photometry

© 2020, The Author(s). Sample purity is central to in vitro studies of protein function and regulation, and to the efficiency and success of structural studies using techniques such as x-ray crystallography and cryo-electron microscopy (cryo-EM). Here, we show that mass photometry (MP) can accurately characterize the heterogeneity of a sample using minimal material with high resolution within a matter of minutes. To benchmark our approach, we use negative stain electron microscopy (nsEM), a popular method for EM sample screening. We include typical workflows developed for structure determination that involve multi-step purification of a multi-subunit ubiquitin ligase and chemical cross-linking steps. When assessing the integrity and stability of large molecular complexes such as the proteasome, we detect and quantify assemblies invisible to nsEM. Our results illustrate the unique advantages of MP over current methods for rapid sample characterization, prioritization and workflow optimization

Expression, Purification, and Biochemical Characterization of Human Afamin

Afamin is an 87 kDa glycoprotein with five predicted N-glycosylation sites. Afamin's glycan abundance contributes to conformational and chemical inhomogeneity presenting great challenges for molecular structure determination. For the purpose of studying the structure of afamin, various forms of recombinantly expressed human afamin (rhAFM) with different glycosylation patterns were thus created. Wild-type rhAFM and various hypoglycosylated forms were expressed in CHO, CHO-Lec1, and HEK293T cells. Fully nonglycosylated rhAFM was obtained by transfection of point-mutated cDNA to delete all N-glycosylation sites of afamin. Wild-type and hypo/nonglycosylated rhAFM were purified from cell culture supernatants by immobilized metal ion affinity and size exclusion chromatography. Glycan analysis of purified proteins demonstrated differences in micro- and macro-heterogeneity of glycosylation enabling the comparison between hypoglycosylated, wild- type rhAFM, and native plasma afamin. Because antibody fragments can work as artificial chaperones by stabilizing the structure of proteins and consequently enhance the chance for successful crystallization, we incubated a Fab fragment of the monoclonal anti-afamin antibody N14 with human afamin and obtained a stoichiometric complex. Subsequent results showed sufficient expression of various partially or nonglycosylated forms of rhAFM in HEK293T and CHO cells and revealed that glycosylation is not necessary for expression and secretio

Expression, Purification, and Biochemical Characterization of Human Afamin

Afamin is an 87 kDa glycoprotein with five predicted N-glycosylation sites. Afamin's glycan abundance contributes to conformational and chemical inhomogeneity presenting great challenges for molecular structure determination. For the purpose of studying the structure of afamin, various forms of recombinantly expressed human afamin (rhAFM) with different glycosylation patterns were thus created. Wild-type rhAFM and various hypoglycosylated forms were expressed in CHO, CHO-Lec1, and HEK293T cells. Fully nonglycosylated rhAFM was obtained by transfection of point-mutated cDNA to delete all N-glycosylation sites of afamin. Wild-type and hypo/nonglycosylated rhAFM were purified from cell culture supernatants by immobilized metal ion affinity and size exclusion chromatography. Glycan analysis of purified proteins demonstrated differences in micro- and macro-heterogeneity of glycosylation enabling the comparison between hypoglycosylated, wild- type rhAFM, and native plasma afamin. Because antibody fragments can work as artificial chaperones by stabilizing the structure of proteins and consequently enhance the chance for successful crystallization, we incubated a Fab fragment of the monoclonal anti-afamin antibody N14 with human afamin and obtained a stoichiometric complex. Subsequent results showed sufficient expression of various partially or nonglycosylated forms of rhAFM in HEK293T and CHO cells and revealed that glycosylation is not necessary for expression and secretio