title: Density-dependent quiescence in glioma invasion: instability in a simple reaction-diffusion model for the migration/proliferation dichotomy.
abstract: Gliomas are very aggressive brain tumours, in which tumour cells gain the ability to penetrate the surrounding normal tissue. The invasion mechanisms of this type of tumour remain to be elucidated. Our work is motivated by the migration/proliferation dichotomy (go-or-grow) hypothesis, i.e. the antagonistic migratory and proliferating cellular behaviours in a cell population, which may play a central role in these tumours. In this paper, we formulate a simple go-or-grow model to investigate the dynamics of a population of glioma cells for which the switch from a migratory to a proliferating phenotype (and vice versa) depends on the local cell density. The model consists of two reaction-diffusion equations describing cell migration, proliferation and a phenotypic switch. We use a combination of numerical and analytical techniques to characterize the development of spatio-temporal instabilities and travelling wave solutions generated by our model. We demonstrate that the density-dependent go-or-grow mechanism can produce complex dynamics similar to those associated with tumour heterogeneity and invasion.
authors.affiliation: Department of Mathematics, University of California at Irvine, Irvine, CA 92697, USA. karap@math.uci.edu
authors.forename: Kara
authors.initials: K
authors.lastname: Pham
authors.forename: Arnaud
authors.initials: A
authors.lastname: Chauviere
authors.forename: Haralambos
authors.initials: H
authors.lastname: Hatzikirou
authors.forename: Xiangrong
authors.initials: X
authors.lastname: Li
authors.forename: Helen M
authors.initials: HM
authors.lastname: Byrne
authors.forename: Vittorio
authors.initials: V
authors.lastname: Cristini
authors.forename: John
authors.initials: J
authors.lastname: Lowengrub
mesh_terms: D001932:Brain Neoplasms / Q000473:pathology*; D002452:Cell Count; D002453:Cell Cycle; D002465:Cell Movement; D049109:Cell Proliferation; D004058:Diffusion; D005910:Glioma / Q000473:pathology*; D006801:Humans; D008954:Models, Biological; D009361:Neoplasm Invasiveness; D013997:Time Factors