2014/08/06 by Tang Quoc Bao, Bao, Tang Quoc, Klemens Fellner +5
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #35B40 #35K57 #92C45 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Cellular Mechanics and Interactions #FOS: Mathematics #Mathematical Biology Tumor Growth
paper · pdf · doi:10.48550/arxiv.1408.1303
openalex publication_date 2014/08/06 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
The asymmetric stem-cell division of Drosophila SOP precursor cells is driven\nby the asymmetric localisation of the key protein Lgl (Lethal giant larvae)\nduring mitosis, when Lgl is phosphorylated by the kinase aPKC on a subpart of\nthe cortex and subsequently released into the cytoplasm.\n In this paper, we present a volume-surface reaction-diffusion system, which\nmodels the localisation of Lgl within the cell cytoplasm and on the cell\ncortex. We prove well-posedness of global solutions as well as regularity of\nthe solutions. Moreover, we rigorously perform the fast reaction limit to a\nreduced quasi-steady-state approximation system, when phosphorylated Lgl is\ninstantaneously expelled from the cortex. Finally, we apply a suitable first\norder finite element scheme to simulate and discuss interesting numerical\nexamples, which illustrate i) the influence of the presence/absence of\nsurface-diffusion to the behaviour of the system and the complex balance steady\nstate and ii) the dependency on the release rate of phosphorylated cortical\nLgl.\n