2020/05/04 by Niklas Kolbe, Kolbe, Niklas, Nikolaos Sfakianakis +7 · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · #35Q92 (Primary) #92C17 #92C50 (Secondary) #Analysis of PDEs (math.AP) #Cell Behavior (q-bio.CB) #FOS: Biological sciences #FOS: Mathematics #Gene Regulatory Network Analysis #Mathematical Biology Tumor Growth #Mathematical and Theoretical Epidemiology and Ecology Models
paper · pdf · doi:10.48550/arxiv.2005.01444
openalex publication_date 2020/05/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We provide a short review of existing models with multiple taxis performed by\n(at least) one species and consider a new mathematical model for tumor invasion\nfeaturing two mutually exclusive cell phenotypes (migrating and proliferating).\nThe migrating cells perform nonlinear diffusion and two types of taxis in\nresponse to non-diffusing cues: away from proliferating cells and up the\ngradient of surrounding tissue. Transitions between the two cell subpopulations\nare influenced by subcellular (receptor binding) dynamics, thus conferring the\nsetting a multiscale character.\n We prove global existence of weak solutions to a simplified model version and\nperform numerical simulations for the full setting under several phenotype\nswitching and motility scenarios. We also compare (via simulations) this model\nwith the corresponding haptotaxis-chemotaxis one featuring indirect\nchemorepellent production and provide a discussion about possible model\nextensions and mathematical challenges.\n