Density-dependent quiescence in glioma invasion: Instability in a simple reaction-diffusion model for the migration/proliferation dichotomy

Kara Pham, Arnaud Chauviere, Haralambos Hatzikirou, Xiangrong Li, Helen M. Byrne, Vittorio Cristini, John Lowengrub

Research output: Contribution to journalArticlepeer-review

41 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)54-71
Number of pages18
JournalJournal of Biological Dynamics
Volume6
Issue numberSUPPL. 1
DOIs
StatePublished - May 2012

Keywords

  • cell migration/proliferation
  • diffusion-driven instability
  • go-or-grow
  • spatio-temporal heterogeneity
  • travelling wave solutions
  • tumour invasion

ASJC Scopus subject areas

  • Ecology, Evolution, Behavior and Systematics
  • Ecology

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