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

51 Scopus citations


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
Issue numbersup1
StatePublished - Jan 2012
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-C1-013-04
Acknowledgements: J.L., K.P. and X.L. acknowledge support from the National Science Foundation Division of Mathematical Sciences (DMS) and from the National Institutes of Health through grant P50GM76516 for a Centre of Excellence in Systems Biology at the University of California, Irvine. A. C., H. H. and V. C. acknowledge support from The Cullen Trust for Health Care and the National Institute for Health, Integrative Cancer Biology Program: 1U54CA149196, for the Center for Systematic Modeling of Cancer Development. V. C. also acknowledges the National Science Foundation, Division of Mathematical Sciences for grant DMS-0818104. H. B. acknowledges partial support by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.


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