In this paper we study bifurcations in mass-action networks with two chemical species and reactant complexes of molecularity no more than two. We refer to these as planar, quadratic networks as they give rise to (at most) quadratic differential equations on the nonnegative quadrant of the plane. Our aim is to study bifurcations in networks in this class with the fewest possible reactions, and the lowest possible product molecularity.
View Article and Find Full Text PDFIt is known that rank-two bimolecular mass-action systems do not admit limit cycles. With a view to understanding which small mass-action systems admit oscillation, in this paper we study rank-two networks with bimolecular source complexes but allow target complexes with higher molecularities. As our goal is to find oscillatory networks of minimal size, we focus on networks with three reactions, the minimum number that is required for oscillation.
View Article and Find Full Text PDFWhereas the positive equilibrium of a planar mass-action system with deficiency zero is always globally stable, for deficiency-one networks there are many different scenarios, mainly involving oscillatory behaviour. We present several examples, with centers or multiple limit cycles.
View Article and Find Full Text PDFAntisense oligonucleotides (ASOs) represent an emerging therapeutic platform for targeting genetic diseases by influencing various aspects of (pre-)mRNA biology, such as splicing, stability, and translation. In this study, we investigated the potential of modulating the splicing pattern in recessive dystrophic epidermolysis bullosa (RDEB) patient cells carrying a frequent genomic variant (c.425A > G) that disrupts splicing in the gene by using short 2'-O-(2-Methoxyethyl) oligoribo-nucleotides (2'-MOE ASOs).
View Article and Find Full Text PDFMachine learning has been proven to be a powerful tool in the identification of diagnostic tumor biomarkers but is often impeded in rare cancers due to small patient numbers. In patients suffering from recessive dystrophic epidermolysis bullosa (RDEB), early-in-life development of particularly aggressive cutaneous squamous-cell carcinomas (cSCCs) represents a major threat and timely detection is crucial to facilitate prompt tumor excision. As miRNAs have been shown to hold great potential as liquid biopsy markers, we characterized miRNA signatures derived from cultured primary cells specific for the potential detection of tumors in RDEB patients.
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