A glimpse into the differential topology and geometry of optimal transport

This note exposes the differential topology and geometry underlying some of the basic phenomena of optimal transportation. It surveys basic questions concerning Monge maps and Kantorovich measures: existence and regularity of the former, uniqueness of the latter, and estimates for the dimension of its support, as well as the associated linear programming duality. It shows the answers to these questions concern the differential geometry and topology of the chosen transportation cost. It also establishes new connections --- some heuristic and others rigorous --- based on the properties of the cross-difference of this cost, and its Taylor expansion at the diagonal.Comment: 27 page

Transoceanic Dispersal and Plate Tectonics Shaped Global Cockroach Distributions: Evidence from Mitochondrial Phylogenomics

Following the acceptance of plate tectonics theory in the latter half of the 20th century, vicariance became the dominant explanation for the distributions of many plant and animal groups. In recent years, however, molecular-clock analyses have challenged a number of well-accepted hypotheses of vicariance. As a widespread group of insects with a fossil record dating back 300 My, cockroaches provide an ideal model for testing hypotheses of vicariance through plate tectonics versus transoceanic dispersal. However, their evolutionary history remains poorly understood, in part due to unresolved relationships among the nine recognized families. Here, we present a phylogenetic estimate of all extant cockroach families, as well as a timescale for their evolution, based on the complete mitochondrial genomes of 119 cockroach species. Divergence dating analyses indicated that the last common ancestor of all extant cockroaches appeared ∼235 Ma, ∼95 My prior to the appearance of fossils that can be assigned to extant families, and before the breakup of Pangaea began. We reconstructed the geographic ranges of ancestral cockroaches and found tentative support for vicariance through plate tectonics within and between several major lineages. We also found evidence of transoceanic dispersal in lineages found across the Australian, Indo-Malayan, African, and Madagascan regions. Our analyses provide evidence that both vicariance and dispersal have played important roles in shaping the distribution and diversity of these insects

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)

Regulatory domain selectivity in the cell-type specific PKN-dependence of cell migration

The mammalian protein kinase N (PKN) family of Serine/Threonine kinases comprises three isoforms, which are targets for Rho family GTPases. Small GTPases are major regulators of the cellular cytoskeleton, generating interest in the role(s) of specific PKN isoforms in processes such as cell migration and invasion. It has been reported that PKN3 is required for prostate tumour cell invasion but not PKN1 or 2. Here we employ a cell model, the 5637 bladder tumour cell line where PKN2 is relatively highly expressed, to assess the potential redundancy of these isoforms in migratory responses. It is established that PKN2 has a critical role in the migration and invasion of these cells. Furthermore, using a PKN wild-type and chimera rescue strategy, it is shown that PKN isoforms are not simply redundant in supporting migration, but appear to be linked through isoform specific regulatory domain properties to selective upstream signals. It is concluded that intervention in PKNs may need to be directed at multiple isoforms to be effective in different cell types

Endothelial dysfunction of bypass graft: Direct comparison of In Vitro and In Vivo models of ischemia-reperfusion injury

BACKGROUND: Although, ischemia/reperfusion induced vascular dysfunction has been widely described, no comparative study of in vivo- and in vitro-models exist. In this study, we provide a direct comparison between models (A) ischemic storage and in-vitro reoxygenation (B) ischemic storage and in vitro reperfusion (C) ischemic storage and in-vivo reperfusion. METHODS AND RESULTS: Aortic arches from rats were stored for 2 hours in saline. Arches were then (A) in vitro reoxygenated (B) in vitro incubated in hypochlorite for 30 minutes (C) in vivo reperfused after heterotransplantation (2, 24 hours and 7 days reperfusion). Endothelium-dependent and independent vasorelaxations were assessed in organ bath. DNA strand breaks were assessed by TUNEL-method, mRNA expressions (caspase-3, bax, bcl-2, eNOS) by quantitative real-time PCR, proteins by Western blot analysis and the expression of CD-31 by immunochemistry. Endothelium-dependent maximal relaxation was drastically reduced in the in-vivo models compared to ischemic storage and in-vitro reperfusion group, and no difference showed between ischemic storage and control group. CD31-staining showed significantly lower endothelium surface ratio in-vivo, which correlated with TUNEL-positive ratio. Increased mRNA and protein levels of pro- and anti-apoptotic gens indicated a significantly higher damage in the in-vivo models. CONCLUSION: Even short-period of ischemia induces severe endothelial damage (in-vivo reperfusion model). In-vitro models of ischemia-reperfusion injury can be limitedly suited for reliable investigations. Time course of endothelial stunning is also described

Interstitial cell migration: integrin-dependent and alternative adhesion mechanisms

Adhesion and migration are integrated cell functions that build, maintain and remodel the multicellular organism. In migrating cells, integrins are the main transmembrane receptors that provide dynamic interactions between extracellular ligands and actin cytoskeleton and signalling machineries. In parallel to integrins, other adhesion systems mediate adhesion and cytoskeletal coupling to the extracellular matrix (ECM). These include multifunctional cell surface receptors (syndecans and CD44) and discoidin domain receptors, which together coordinate ligand binding with direct or indirect cytoskeletal coupling and intracellular signalling. We review the way that the different adhesion systems for ECM components impact cell migration in two- and three-dimensional migration models. We further discuss the hierarchy of these concurrent adhesion systems, their specific tasks in cell migration and their contribution to migration in three-dimensional multi-ligand tissue environments

Small Non-coding RNAs Govern Mammary Gland Tumorigenesis

Small non-coding RNAs include siRNA, miRNA, piRNA and snoRNA. The involvement of miRNAs in the regulation of mammary gland tumorigenesis has been widely studied while the role for other small non-coding RNAs remains unclear. Here we summarize the involvement of miRNA in breast cancer onset and progression through regulating the cell cycle and cellular proliferation. The regulation of breast cancer stem cells and tumor regeneration by miRNA is reviewed. In addition, the emerging evidence demonstrating the involvement of piRNA and snoRNA in breast cancer is briefly described

In Vitro and In Vivo High-Throughput Assays for the Testing of Anti-Trypanosoma cruzi Compounds

The treatment of Trypanosoma cruzi infection (the cause of human Chagas disease) remains a significant challenge. Only two drugs, both with substantial toxicity, are available and the efficacy of these dugs is often questioned – in many cases due to the limitations of the methods for assessing efficacy rather than to true lack of efficacy. For these reasons relatively few individuals infected with T. cruzi actually have their infections treated. In this study, we report on innovative methods that will facilitate the discovery of new compounds for the treatment of T. cruzi infection and Chagas disease. Utilizing fluorescent and bioluminescent parasite lines, we have developed in vitro tests that are reproducible and facile and can be scaled for high-throughput screening of large compound libraries. We also validate an in vivo screening test that monitors parasite replication at the site of infection and determines the effectiveness of drug treatment in less than two weeks. More importantly, results in this rapid in vivo test show strong correlations with those obtained in long-term (e.g. 40 day or more) treatment assays. The results of this study remove one of the obstacles for identification of effective and safe compounds to treat Chagas disease

Induction of Bcl-2 Expression by Hepatitis B Virus Pre-S2 Mutant Large Surface Protein Resistance to 5-Fluorouracil Treatment in Huh-7 Cells

BACKGROUND: Hepatocellular carcinoma (HCC) is one of the most common malignancies worldwide with poor prognosis due to resistance to conventional chemotherapy and limited efficacy of radiotherapy. Our previous studies have indicated that expression of Hepatitis B virus pre-S2 large mutant surface antigen (HBV pre-S2Δ) is associated with a significant risk of developing HCC. However, the relationship between HBV pre-S2Δ protein and the resistance of chemotherapeutic drug treatment is still unclear. METHODOLOGY/PRINCIPAL FINDINGS: Here, we show that the expression of HBV pre-S2Δ mutant surface protein in Huh-7 cell significantly promoted cell growth and colony formation. Furthermore, HBV pre-S2Δ protein increased both mRNA (2.7±0.5-fold vs. vehicle, p=0.05) and protein (3.2±0.3-fold vs. vehicle, p=0.01) levels of Bcl-2 in Huh-7 cells. HBV pre-S2Δ protein also enhances Bcl-2 family, Bcl-xL and Mcl-1, expression in Huh-7 cells. Meanwhile, induction of NF-κB p65, ERK, and Akt phosphorylation, and GRP78 expression, an unfolded protein response chaperone, were observed in HBV pre-S2Δ and HBV pre-S-expressing cells. Induction of Bcl-2 expression by HBV pre-S2Δ protein resulted in resistance to 5-fluorouracil treatment in colony formation, caspase-3 assay, and cell apoptosis, and can enhance cell death by co-incubation with Bcl-2 inhibitor. Similarly, transgenic mice showed higher expression of Bcl-2 in liver tissue expressing HBV pre-S2Δ large surface protein in vivo. CONCLUSION/SIGNIFICANCE: Our result demonstrates that HBV pre-S2Δ increased Bcl-2 expression which plays an important role in resistance to 5-fluorouracil-caused cell death. Therefore, these data provide an important chemotherapeutic strategy in HBV pre-S2Δ-associated tumor