The existence of an inverse limit of inverse system of measure spaces - a purely measurable case

The existence of an inverse limit of an inverse system of (probability) measure spaces has been investigated since the very beginning of the birth of the modern probability theory. Results from Kolmogorov [10], Bochner [2], Choksi [5], Metivier [14], Bourbaki [3] among others have paved the way of the deep understanding of the problem under consideration. All the above results, however, call for some topological concepts, or at least ones which are closely related topological ones. In this paper we investigate purely measurable inverse systems of (probability) measure spaces, and give a sucient condition for the existence of a unique inverse limit. An example for the considered purely measurable inverse systems of (probability) measure spaces is also given

Exponential martingales and changes of measure for counting processes

We give sufficient criteria for the Dol\'eans-Dade exponential of a stochastic integral with respect to a counting process local martingale to be a true martingale. The criteria are adapted particularly to the case of counting processes and are sufficiently weak to be useful and verifiable, as we illustrate by several examples. In particular, the criteria allow for the construction of for example nonexplosive Hawkes processes as well as counting processes with stochastic intensities depending on diffusion processes

Preservation of Piecewise Constancy under TV Regularization with Rectilinear Anisotropy

A recent result by Lasica, Moll and Mucha about the $\ell^1$-anisotropic Rudin-Osher-Fatemi model in $\mathbb{R}^2$ asserts that the solution is piecewise constant on a rectilinear grid, if the datum is. By means of a new proof we extend this result to $\mathbb{R}^n$. The core of our proof consists in showing that averaging operators associated to certain rectilinear grids map subgradients of the $\ell^1$-anisotropic total variation seminorm to subgradients

Cosmos 2044

The effects of microgravity and hind limb suspension on the enzyme patterns are assessed within a slow twitch muscle (soleus) and a fast twitch muscle (tibialis anterior). Studies were made on 95 soleus fibers and about 300 tibialis anterior (TA) fibers. Over 2200 individual enzyme measurements were made. Six key metabolic enzymes (hexokinase, pyruvate kinease, citrate kinase, beta-hydroxyacyl CoA dehydrogenase, glucose-6-P dehydrogenase, and aspartate aminotransferase) plus glutaminase and glutamate decarboxylase, as well as glutamate, aspartate, and GABA, were measured in 11 regions of the hippocampal formation of synchronous, flight, and tail suspension rats. Major differences were observed in the normal distribution of each enzyme and amine acid, but no substantive effects of either microgravity or tail suspension on these patterns were clearly demonstrated

The Glial Regenerative Response to Central Nervous System Injury Is Enabled by Pros-Notch and Pros-NFκB Feedback

Organisms are structurally robust, as cells accommodate changes preserving structural integrity and function. The molecular mechanisms underlying structural robustness and plasticity are poorly understood, but can be investigated by probing how cells respond to injury. Injury to the CNS induces proliferation of enwrapping glia, leading to axonal re-enwrapment and partial functional recovery. This glial regenerative response is found across species, and may reflect a common underlying genetic mechanism. Here, we show that injury to the Drosophila larval CNS induces glial proliferation, and we uncover a gene network controlling this response. It consists of the mutual maintenance between the cell cycle inhibitor Prospero (Pros) and the cell cycle activators Notch and NFκB. Together they maintain glia in the brink of dividing, they enable glial proliferation following injury, and subsequently they exert negative feedback on cell division restoring cell cycle arrest. Pros also promotes glial differentiation, resolving vacuolization, enabling debris clearance and axonal enwrapment. Disruption of this gene network prevents repair and induces tumourigenesis. Using wound area measurements across genotypes and time-lapse recordings we show that when glial proliferation and glial differentiation are abolished, both the size of the glial wound and neuropile vacuolization increase. When glial proliferation and differentiation are enabled, glial wound size decreases and injury-induced apoptosis and vacuolization are prevented. The uncovered gene network promotes regeneration of the glial lesion and neuropile repair. In the unharmed animal, it is most likely a homeostatic mechanism for structural robustness. This gene network may be of relevance to mammalian glia to promote repair upon CNS injury or disease

MTG16 regulates colonic epithelial differentiation, colitis, and tumorigenesis by repressing E protein transcription factors

Aberrant epithelial differentiation and regeneration contribute to colon pathologies, including inflammatory bowel disease (iBD) and colitis-associated cancer (CAC). Myeloid translocation gene 16 (MTG16, also known as CBFA2T3) is a transcriptional corepressor expressed in the colonic epithelium. MTG16 deficiency in mice exacerbates colitis and increases tumor burden in CAC, though the underlying mechanisms remain unclear. Here, we identified MTG16 as a central mediator of epithelial differentiation, promoting goblet and restraining enteroendocrine cell development in homeostasis and enabling regeneration following dextran sulfate sodium-induced (DSS-induced) colitis. Transcriptomic analyses implicated increased Ephrussi box-binding transcription factor (E protein) activity in MTG16-deficient colon crypts. Using a mouse model with a point mutation that attenuates MTG16:E protein interactions (Mtg16(P20ST)), we showed that MTG16 exerts control over colonic epithelial differentiation and regeneration by repressing E protein-mediated transcription. Mimicking murine colitis, MTG16 expression was increased in biopsies from patients with active IBD compared with unaffected controls. Finally, uncoupling MTG16:E protein interactions partially phenocopied the enhanced tumorigenicity of Mtg16(-/)(-) colon in the azoxymethane/DSS-induced model of CAC, indicating that MTG16 protects from tumorigenesis through additional mechanisms. Collectively, our results demonstrate that MTG16, via its repression of E protein targets. is a key regulator of cell fate decisions during colon homeostasis, colitis, and cancer.Peer reviewe

Notch and Prospero Repress Proliferation following Cyclin E Overexpression in the Drosophila Bristle Lineage

Understanding the mechanisms that coordinate cell proliferation, cell cycle arrest, and cell differentiation is essential to address the problem of how “normal” versus pathological developmental processes take place. In the bristle lineage of the adult fly, we have tested the capacity of post-mitotic cells to re-enter the cell cycle in response to the overexpression of cyclin E. We show that only terminal cells in which the identity is independent of Notch pathway undergo extra divisions after CycE overexpression. Our analysis shows that the responsiveness of cells to forced proliferation depends on both Prospero, a fate determinant, and on the level of Notch pathway activity. Our results demonstrate that the terminal quiescent state and differentiation are regulated by two parallel mechanisms acting simultaneously on fate acquisition and cell cycle progression

Possible Existence of Lysosome-Like Organella within Mitochondria and Its Role in Mitochondrial Quality Control

The accumulation of unhealthy mitochondria results in mitochondrial dysfunction, which has been implicated in aging, cancer, and a variety of degenerative diseases. However, the mechanism by which mitochondrial quality is regulated remains unclear. Here, we show that Mieap, a novel p53-inducible protein, induces intramitochondrial lysosome-like organella that plays a critical role in mitochondrial quality control. Mieap expression is directly regulated by p53 and is frequently lost in human cancer as result of DNA methylation. Mieap dramatically induces the accumulation of lysosomal proteins within mitochondria and mitochondrial acidic condition without destroying the mitochondrial structure (designated MALM, for Mieap-induced accumulation of lysosome-like organelles within mitochondria) in response to mitochondrial damage. MALM was not related to canonical autophagy. MALM is involved in the degradation of oxidized mitochondrial proteins, leading to increased ATP synthesis and decreased reactive oxygen species generation. These results suggest that Mieap induces intramitochondrial lysosome-like organella that plays a critical role in mitochondrial quality control by eliminating oxidized mitochondrial proteins. Cancer cells might accumulate unhealthy mitochondria due to p53 mutations and/or Mieap methylation, representing a potential cause of the Warburg effect