Uniqueness and Non-uniqueness in the Einstein Constraints

The conformal thin sandwich (CTS) equations are a set of four of the Einstein equations, which generalize the Laplace-Poisson equation of Newton's theory. We examine numerically solutions of the CTS equations describing perturbed Minkowski space, and find only one solution. However, we find {\em two} distinct solutions, one even containing a black hole, when the lapse is determined by a fifth elliptic equation through specification of the mean curvature. While the relationship of the two systems and their solutions is a fundamental property of general relativity, this fairly simple example of an elliptic system with non-unique solutions is also of broader interest.Comment: 4 pages, 4 figures; abstract and introduction rewritte

FGF Signaling Inhibition in ESCs Drives Rapid Genome-wide Demethylation to the Epigenetic Ground State of Pluripotency

SummaryGenome-wide erasure of DNA methylation takes place in primordial germ cells (PGCs) and early embryos and is linked with pluripotency. Inhibition of Erk1/2 and Gsk3β signaling in mouse embryonic stem cells (ESCs) by small-molecule inhibitors (called 2i) has recently been shown to induce hypomethylation. We show by whole-genome bisulphite sequencing that 2i induces rapid and genome-wide demethylation on a scale and pattern similar to that in migratory PGCs and early embryos. Major satellites, intracisternal A particles (IAPs), and imprinted genes remain relatively resistant to erasure. Demethylation involves oxidation of 5-methylcytosine (5mC) to 5-hydroxymethylcytosine (5hmC), impaired maintenance of 5mC and 5hmC, and repression of the de novo methyltransferases (Dnmt3a and Dnmt3b) and Dnmt3L. We identify a Prdm14- and Nanog-binding cis-acting regulatory region in Dnmt3b that is highly responsive to signaling. These insights provide a framework for understanding how signaling pathways regulate reprogramming to an epigenetic ground state of pluripotency

A Survey of the Humoral Immune Response of Cancer Patients to a Panel of Human Tumor Antigens

Evidence is growing for both humoral and cellular immune recognition of human tumor antigens. Antibodies with specificity for antigens initially recognized by cytotoxic T lymphocytes (CTLs), e.g., MAGE and tyrosinase, have been detected in melanoma patient sera, and CTLs with specificity for NY-ESO-1, a cancer-testis (CT) antigen initially identified by autologous antibody, have recently been identified. To establish a screening system for the humoral response to autoimmunogenic tumor antigens, an enzyme-linked immunosorbent assay (ELISA) was developed using recombinant NY-ESO-1, MAGE-1, MAGE-3, SSX2, Melan-A, and tyrosinase proteins. A survey of sera from 234 cancer patients showed antibodies to NY-ESO-1 in 19 patients, to MAGE-1 in 3, to MAGE-3 in 2, and to SSX2 in 1 patient. No reactivity to these antigens was found in sera from 70 normal individuals. The frequency of NY-ESO-1 antibody was 9.4% in melanoma patients and 12.5% in ovarian cancer patients. Comparison of tumor NY-ESO-1 phenotype and NY-ESO-1 antibody response in 62 stage IV melanoma patients showed that all patients with NY-ESO-1+ antibody had NY-ESO-1+ tumors, and no patients with NY-ESO-1− tumors had NY-ESO-1 antibody. As the proportion of melanomas expressing NY-ESO-1 is 20–40% and only patients with NY-ESO-1+ tumors have antibody, this would suggest that a high percentage of patients with NY-ESO-1+ tumors develop an antibody response to NY-ESO-1

Gene evolution of epoxide hydrolases and recommended nomenclature

We have analyzed amino acid sequence relationships among soluble and microsomal epoxide hydrolases, haloacid dehalogenases, and a haloalkane dehalogenase. The amino-terminal residues (1-229) of mammalian soluble epoxide hydrolase are homologous to a haloacid dehalogenase. The carboxy-terminal residues (230-554) of mammalian soluble epoxide hydrolase are homologous to haloalkane dehalogenase, to plant soluble epoxide hydrolase, and to microsomal epoxide hydrolase. The shared identity between the haloacid and haloalkane dehalogenases does not indicate relatedness between these two types of dehalogenases. The amino-terminal and carboxy-terminal homologies of mammalian soluble epoxide hydrolase to the respective dehalogenases suggests that this epoxide hydrolase, but not the soluble epoxide hydrolase of plant or the microsomal epoxide hydrolase, derives from a gene fusion. The homology of microsomal to soluble epoxide hydrolase suggests they derive from a gene duplication, probably of an ancestral bacterial (epoxide) hydrolase gene. Based on homology to haloalkane dehalogenase, the catalytic residues for the soluble and microsomal epoxide hydrolases are predicted. A nomenclature system based on divergent molecular evolution is proposed for these epoxide hydrolases