An Analytic and Probabilistic Approach to the Problem of Matroid Representibility

We introduce various quantities that can be defined for an arbitrary matroid, and show that certain conditions on these quantities imply that a matroid is not representable over $\mathbb{F}_q$. Mostly, for a matroid of rank $r$, we examine the proportion of size-$(r-k)$ subsets that are dependent, and give bounds, in terms of the cardinality of the matroid and $q$ a prime power, for this proportion, below which the matroid is not representable over $\mathbb{F}_q$. We also explore connections between the defined quantities and demonstrate that they can be used to prove that random matrices have high proportions of subsets of columns independent

The decatenation checkpoint

The decatenation checkpoint delays entry into mitosis until the chromosomes have been disentangled. Deficiency in or bypass of the decatenation checkpoint can cause chromosome breakage and nondisjunction during mitosis, which results in aneuploidy and chromosome rearrangements in the daughter cells. A deficiency in the decatenation checkpoint has been reported in lung and bladder cancer cell lines and may contribute to the accumulation of chromosome aberrations that commonly occur during tumour progression. A checkpoint deficiency has also been documented in cultured stem and progenitor cells, and cancer stem cells are likely to be derived from stem and progenitor cells that lack an effective decatenation checkpoint. An inefficient decatenation checkpoint is likely to be a source of the chromosome aberrations that are common features of most tumours, but an inefficient decatenation checkpoint in cancer stem cells could also provide a potential target for chemotherapy

Point sets on the sphere S2\mathbb{S}^2 with small spherical cap discrepancy

In this paper we study the geometric discrepancy of explicit constructions of uniformly distributed points on the two-dimensional unit sphere. We show that the spherical cap discrepancy of random point sets, of spherical digital nets and of spherical Fibonacci lattices converges with order $N^{-1/2}$. Such point sets are therefore useful for numerical integration and other computational simulations. The proof uses an area-preserving Lambert map. A detailed analysis of the level curves and sets of the pre-images of spherical caps under this map is given

Rapid production of human liver scaffolds for functional tissue engineering by high shear stress oscillation-decellularization

The development of human liver scaffolds retaining their 3-dimensional structure and extra-cellular matrix (ECM) composition is essential for the advancement of liver tissue engineering. We report the design and validation of a new methodology for the rapid and accurate production of human acellular liver tissue cubes (ALTCs) using normal liver tissue unsuitable for transplantation. The application of high shear stress is a key methodological determinant accelerating the process of tissue decellularization while maintaining ECM protein composition, 3D-architecture and physico-chemical properties of the native tissue. ALTCs were engineered with human parenchymal and non-parenchymal liver cell lines (HepG2 and LX2 cells, respectively), human umbilical vein endothelial cells (HUVEC), as well as primary human hepatocytes and hepatic stellate cells. Both parenchymal and non-parenchymal liver cells grown in ALTCs exhibited markedly different gene expression when compared to standard 2D cell cultures. Remarkably, HUVEC cells naturally migrated in the ECM scaffold and spontaneously repopulated the lining of decellularized vessels. The metabolic function and protein synthesis of engineered liver scaffolds with human primary hepatocytes reseeded under dynamic conditions were maintained. These results provide a solid basis for the establishment of effective protocols aimed at recreating human liver tissue in vitro

The Chromatin Remodeler SPLAYED Regulates Specific Stress Signaling Pathways

Organisms are continuously exposed to a myriad of environmental stresses. Central to an organism's survival is the ability to mount a robust transcriptional response to the imposed stress. An emerging mechanism of transcriptional control involves dynamic changes in chromatin structure. Alterations in chromatin structure are brought about by a number of different mechanisms, including chromatin modifications, which covalently modify histone proteins; incorporation of histone variants; and chromatin remodeling, which utilizes ATP hydrolysis to alter histone-DNA contacts. While considerable insight into the mechanisms of chromatin remodeling has been gained, the biological role of chromatin remodeling complexes beyond their function as regulators of cellular differentiation and development has remained poorly understood. Here, we provide genetic, biochemical, and biological evidence for the critical role of chromatin remodeling in mediating plant defense against specific biotic stresses. We found that the Arabidopsis SWI/SNF class chromatin remodeling ATPase SPLAYED (SYD) is required for the expression of selected genes downstream of the jasmonate (JA) and ethylene (ET) signaling pathways. SYD is also directly recruited to the promoters of several of these genes. Furthermore, we show that SYD is required for resistance against the necrotrophic pathogen Botrytis cinerea but not the biotrophic pathogen Pseudomonas syringae. These findings demonstrate not only that chromatin remodeling is required for selective pathogen resistance, but also that chromatin remodelers such as SYD can regulate specific pathways within biotic stress signaling networks

Persistence of DNA threads in human anaphase cells suggests late completion of sister chromatid decatenation

PICH (Plk1-interacting checkpoint helicase) was recently identified as an essential component of the spindle assembly checkpoint and shown to localize to kinetochores, inner centromeres, and thin threads connecting separating chromosomes even during anaphase. In this paper, we have used immuno-fiber fluorescence in situ hybridization and chromatin-immunoprecipitation to demonstrate that PICH associates with centromeric chromatin during anaphase. Furthermore, by careful analysis of PICH-positive anaphase threads through FISH as well as bromo-deoxyurdine and CREST labeling, we strengthen the evidence that these threads comprise mainly alphoid centromere deoxyribonucleic acid. Finally, by timing the addition of ICRF-193 (a specific inhibitor of topoisomerase-II alpha) to cells synchronized in anaphase, we demonstrate that topoisomerase activity is required specifically to resolve PICH-positive threads during anaphase (as opposed to being required to prevent the formation of such threads during earlier cell cycle stages). These data indicate that PICH associates with centromeres during anaphase and that most PICH-positive threads evolve from inner centromeres as these stretch in response to tension. Moreover, they show that topoisomerase activity is required during anaphase for the resolution of PICH-positive threads, implying that the complete separation of sister chromatids occurs later than previously assumed

Chromosome 7 and 19 Trisomy in Cultured Human Neural Progenitor Cells

BACKGROUND:Stem cell expansion and differentiation is the foundation of emerging cell therapy technologies. The potential applications of human neural progenitor cells (hNPCs) are wide ranging, but a normal cytogenetic profile is important to avoid the risk of tumor formation in clinical trials. FDA approved clinical trials are being planned and conducted for hNPC transplantation into the brain or spinal cord for various neurodegenerative disorders. Although human embryonic stem cells (hESCs) are known to show recurrent chromosomal abnormalities involving 12 and 17, no studies have revealed chromosomal abnormalities in cultured hNPCs. Therefore, we investigated frequently occurring chromosomal abnormalities in 21 independent fetal-derived hNPC lines and the possible mechanisms triggering such aberrations. METHODS AND FINDINGS:While most hNPC lines were karyotypically normal, G-band karyotyping and fluorescent in situ hybridization (FISH) analyses revealed the emergence of trisomy 7 (hNPC(+7)) and trisomy 19 (hNPC(+19)), in 24% and 5% of the lines, respectively. Once detected, subsequent passaging revealed emerging dominance of trisomy hNPCs. DNA microarray and immunoblotting analyses demonstrate epidermal growth factor receptor (EGFR) overexpression in hNPC(+7) and hNPC(+19) cells. We observed greater levels of telomerase (hTERT), increased proliferation (Ki67), survival (TUNEL), and neurogenesis (beta(III)-tubulin) in hNPC(+7) and hNPC(+19), using respective immunocytochemical markers. However, the trisomy lines underwent replicative senescence after 50-60 population doublings and never showed neoplastic changes. Although hNPC(+7) and hNPC(+19) survived better after xenotransplantation into the rat striatum, they did not form malignant tumors. Finally, EGF deprivation triggered a selection of trisomy 7 cells in a diploid hNPC line. CONCLUSIONS:We report that hNPCs are susceptible to accumulation of chromosome 7 and 19 trisomy in long-term cell culture. These results suggest that micro-environmental cues are powerful factors in the selection of specific hNPC aneuploidies, with trisomy of chromosome 7 being the most common. Given that a number of stem cell based clinical trials are being conducted or planned in USA and a recent report in PLoS Medicine showing the dangers of grafting an inordinate number of cells, these data substantiate the need for careful cytogenetic evaluation of hNPCs (fetal or hESC-derived) before their use in clinical or basic science applications