McGillen Jessica B, Gaffney Eamonn A, Martin Natasha K, Maini Philip K
Centre for Mathematical Biology, Mathematical Institute, Oxford University, 24-29 St Giles', Oxford, OX1 3LB, UK.
J Math Biol. 2014 Apr;68(5):1199-224. doi: 10.1007/s00285-013-0665-7. Epub 2013 Mar 28.
We model the metabolism and behaviour of a developing cancer tumour in the context of its microenvironment, with the aim of elucidating the consequences of altered energy metabolism. Of particular interest is the Warburg Effect, a widespread preference in tumours for cytosolic glycolysis rather than oxidative phosphorylation for glucose breakdown, as yet incompletely understood. We examine a candidate explanation for the prevalence of the Warburg Effect in tumours, the acid-mediated invasion hypothesis, by generalising a canonical non-linear reaction-diffusion model of acid-mediated tumour invasion to consider additional biological features of potential importance. We apply both numerical methods and a non-standard asymptotic analysis in a travelling wave framework to obtain an explicit understanding of the range of tumour behaviours produced by the model and how fundamental parameters govern the speed and shape of invading tumour waves. Comparison with conclusions drawn under the original system--a special case of our generalised system--allows us to comment on the structural stability and predictive power of the modelling framework.
我们在发育中的癌症肿瘤微环境背景下对其代谢和行为进行建模，目的是阐明能量代谢改变的后果。特别令人感兴趣的是瓦伯格效应，即肿瘤中普遍存在的偏好通过胞质糖酵解而非氧化磷酸化来分解葡萄糖的现象，目前对此尚未完全理解。我们通过推广酸介导肿瘤侵袭的经典非线性反应扩散模型以考虑其他潜在重要的生物学特征，来研究肿瘤中瓦伯格效应普遍存在的一种候选解释——酸介导侵袭假说。我们在行波框架中应用数值方法和非标准渐近分析，以明确了解该模型产生的肿瘤行为范围，以及基本参数如何控制侵袭性肿瘤波的速度和形状。与在原始系统（我们广义系统的一个特殊情况）下得出的结论进行比较，使我们能够对建模框架的结构稳定性和预测能力进行评论。
