On the multiple Borsuk numbers of sets

The Borsuk number of a set S of diameter d >0 in Euclidean n-space is the smallest value of m such that S can be partitioned into m sets of diameters less than d. Our aim is to generalize this notion in the following way: The k-fold Borsuk number of such a set S is the smallest value of m such that there is a k-fold cover of S with m sets of diameters less than d. In this paper we characterize the k-fold Borsuk numbers of sets in the Euclidean plane, give bounds for those of centrally symmetric sets, smooth bodies and convex bodies of constant width, and examine them for finite point sets in the Euclidean 3-space.Comment: 16 pages, 3 figure

Enhancement of glucosinolate and isothiocyanate profiles in brassicaceae crops: addressing challenges in breeding for cultivation, storage, and consumer-related traits

Glucosinolates (GSLs) and isothiocyanates (ITCs) produced by Brassicaceae plants are popular targets for analysis due to the health benefits associated with them. Breeders aim to increase the concentrations in commercial varieties; however, there are few examples of this. The most well-known is Beneforté broccoli, which has increased glucoraphanin/ sulforaphane concentrations compared to those of conventional varieties. It was developed through traditional breeding methods with considerations for processing, consumption, and health made throughout this process. Many studies presented in the literature do not take a holistic approach, and key points about breeding, cultivation methods, postharvest storage, sensory attributes, and consumer preferences are not properly taken into account. In this review, we draw together data for multiple species and address how such factors can influence GSL profiles. We encourage researchers and institutions to engage with industry and consumers to produce research that can be utilized in the improvement of Brassicaceae crops

Effect of diindolylmethane supplementation on low-grade cervical cytological abnormalities: double-blind, randomised, controlled trial

This work was supported by a Cancer Research UK project grant (C8162/A4609 project costs) and a programme grant (C8162/A10406)

Phenethyl isothiocyanate exhibits antileukemic activity in vitro and in vivo by inactivation of Akt and activation of JNK pathways

Effects of phenethyl isothiocyanate (PEITC) have been investigated in human leukemia cells (U937, Jurkat, and HL-60) as well as in primary human acute myeloid leukemia (AML) cells in relation to apoptosis and cell signaling events. Exposure of cells to PEITC resulted in pronounced increase in the activation of caspase-3, -8, -9, cleavage/degradation of PARP, and apoptosis in dose- and time-dependent manners. These events were accompanied by the caspase-independent downregulation of Mcl-1, inactivation of Akt, as well as activation of Jun N-terminal kinase (JNK). Inhibition of PI3K/Akt by LY294002 significantly enhanced PEITC-induced apoptosis. Conversely, enforced activation of Akt by a constitutively active Akt construct markedly abrogated PEITC-mediated JNK activation, Mcl-1 downregulation, caspase activation, and apoptosis, and also interruption of the JNK pathway by pharmacological or genetically (e.g., siRNA) attenuated PEITC-induced apoptosis. Finally, administration of PEITC markedly inhibited tumor growth and induced apoptosis in U937 xenograft model in association with inactivation of Akt, activation of JNK, as well as downregulation of Mcl-1. Taken together, these findings represent a novel mechanism by which agents targeting Akt/JNK/Mcl-1 pathway potentiate PEITC lethality in transformed and primary human leukemia cells and inhibitory activity of tumor growth of U937 xenograft model

Molecular Characterisation of Long-Acting Insulin Analogues in Comparison with Human Insulin, IGF-1 and Insulin X10

AIMS/HYPOTHESIS: There is controversy with respect to molecular characteristics of insulin analogues. We report a series of experiments forming a comprehensive characterisation of the long acting insulin analogues, glargine and detemir, in comparison with human insulin, IGF-1, and the super-mitogenic insulin, X10. METHODS: We measured binding of ligands to membrane-bound and solubilised receptors, receptor activation and mitogenicity in a number of cell types. RESULTS: Detemir and glargine each displayed a balanced affinity for insulin receptor (IR) isoforms A and B. This was also true for X10, whereas IGF-1 had a higher affinity for IR-A than IR-B. X10 and glargine both exhibited a higher relative IGF-1R than IR binding affinity, whereas detemir displayed an IGF-1R:IR binding ratio of ≤ 1. Ligands with high relative IGF-1R affinity also had high affinity for IR/IGF-1R hybrid receptors. In general, the relative binding affinities of the analogues were reflected in their ability to phosphorylate the IR and IGF-1R. Detailed analysis revealed that X10, in contrast to the other ligands, seemed to evoke a preferential phosphorylation of juxtamembrane and kinase domain phosphorylation sites of the IR. Sustained phosphorylation was only observed from the IR after stimulation with X10, and after stimulation with IGF-1 from the IGF-1R. Both X10 and glargine showed an increased mitogenic potency compared to human insulin in cells expressing many IGF-1Rs, whereas only X10 showed increased mitogenicity in cells expressing many IRs. CONCLUSIONS: Detailed analysis of receptor binding, activation and in vitro mitogenicity indicated no molecular safety concern with detemir

Minor Abnormalities of Testis Development in Mice Lacking the Gene Encoding the MAPK Signalling Component, MAP3K1

In mammals, the Y chromosome is a dominant male determinant, causing the bipotential gonad to develop as a testis. Recently, cases of familial and spontaneous 46,XY disorders of sex development (DSD) have been attributed to mutations in the human gene encoding mitogen-activated protein kinase kinase kinase 1, MAP3K1, a component of the mitogen-activated protein kinase (MAPK) signal transduction pathway. In individuals harbouring heterozygous mutations in MAP3K1, dysregulation of MAPK signalling was observed in lymphoblastoid cell lines, suggesting a causal role for these mutations in disrupting XY sexual development. Mice lacking the cognate gene, Map3k1, are viable and exhibit the eyes open at birth (EOB) phenotype on a mixed genetic background, but on the C57BL/6J genetic background most mice die at around 14.5 dpc due to a failure of erythropoiesis in the fetal liver. However, no systematic examination of sexual development in Map3k1-deficient mice has been described, an omission that is especially relevant in the case of C57BL/6J, a genetic background that is sensitized to disruptions to testis determination. Here, we report that on a mixed genetic background mice lacking Map3k1 are fertile and exhibit no overt abnormalities of testis development. On C57BL/6J, significant non-viability is observed with very few animals surviving to adulthood. However, an examination of development in Map3k1-deficient XY embryos on this genetic background revealed no significant defects in testis determination, although minor abnormalities were observed, including an increase in gonadal length. Based on these observations, we conclude that MAP3K1 is not required for mouse testis determination. We discuss the significance of these data for the functional interpretation of sex-reversing MAP3K1 mutations in humans

Synchronization in G0/G1 enhances the mitogenic response of cells overexpressing the human insulin receptor A isoform to insulin

Evaluating mitogenic signaling specifically through the human insulin receptor (IR) is relevant for the preclinical safety assessment of developmental insulin analogs. It is known that overexpression of IR sensitizes cells to the mitogenic effects of insulin, but it is essentially unknown how mitogenic responses can be optimized to allow practical use of such recombinant cell lines for preclinical safety testing. We constitutively overexpressed the short isoform of the human insulin receptor (hIR-A, exon 11-negative) in L6 rat skeletal myoblasts. Because the mitogenic effect of growth factors such as insulin is expected to act in G0/G1, promoting S-phase entry, we developed a combined topoinhibition + serum deprivation strategy to explore the effect of G0/G1 synchronization as an independent parameter in the context of serum deprivation, the latter being routinely used to reduce background in mitogenicity assays. G0/G1 synchronization significantly improved the mitogenic responses of L6-hIR cells to insulin, measured by 3H-thymidine incorporation. Comparison with the parental L6 cells using phospho-mitogen-activated protein kinase, phospho-AKT, as well as 3H-thymidine incorporation end points supported that the majority of the mitogenic effect of insulin in L6-hIR cells was mediated by the overexpressed hIR-A. Using the optimized L6-hIR assay, we found that the X-10 insulin analog was more mitogenic than native human insulin, supporting that X-10 exhibits increased mitogenic signaling through the hIR-A. In summary, this study provides the first demonstration that serum deprivation may not be sufficient, and G0/G1 synchronization may be required to obtain optimal responsiveness of hIR-overexpressing cell lines for preclinical safety testing

Glucosinolates, myrosinase hydrolysis products, and flavonols found in rocket (Eruca sativa and Diplotaxis tenuifolia)

Rocket species have been shown to have very high concentrations of glucosinolates and flavonols, which have numerous positive health benefits with regular consumption. In this review we highlight how breeders and processors of rocket species can utilize genomic and phytochemical research to improve varieties and enhance the nutritive benefits to consumers. Plant breeders are increasingly looking to new technologies such as HPLC, UPLC, LC-MS and GC-MS to screen populations for their phytochemical content to inform plant selections. Here we collate the research that has been conducted to-date in rocket, and summarise all glucosinolate and flavonol compounds identified in the species. We emphasize the importance of the broad screening of populations for phytochemicals and myrosinase degradation products, as well as unique traits that may be found in underutilized gene bank resources. We also stress that collaboration with industrial partners is becoming essential for long-term plant breeding goals through research