Department of Mathematics, University of California at Irvine, Irvine, CA 92697, USA.
J Biol Dyn. 2012;6 Suppl 1(0 1):54-71. doi: 10.1080/17513758.2011.590610. Epub 2011 Jun 27.
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.
神经胶质瘤是非常侵袭性的脑肿瘤，其中肿瘤细胞获得了穿透周围正常组织的能力。这种肿瘤的侵袭机制仍有待阐明。我们的工作受到迁移/增殖二分法（去或生长）假说的启发，即细胞群体中拮抗的迁移和增殖细胞行为，这可能在这些肿瘤中起核心作用。在本文中，我们提出了一个简单的去或生长模型，以研究神经胶质瘤细胞群体的动力学，其中从迁移表型向增殖表型的转变（反之亦然）取决于局部细胞密度。该模型由两个描述细胞迁移、增殖和表型转变的反应扩散方程组成。我们使用数值和分析技术的组合来描述我们模型产生的时空不稳定性和传播波解的发展。我们证明，密度依赖性的去或生长机制可以产生类似于与肿瘤异质性和侵袭相关的复杂动力学。
