Centre for Mathematical Biology, Mathematical Institute, Oxford University, 24-29 St Giles', Oxford OX1 3LB, UK.
J Theor Biol. 2010 Dec 7;267(3):461-70. doi: 10.1016/j.jtbi.2010.08.028. Epub 2010 Sep 8.
It is well established that the tumour microenvironment can both promote and suppress tumour growth and invasion, however, most mathematical models of invasion view the normal tissue as inhibiting tumour progression via immune modulation or spatial constraint. In particular, the production of acid by tumour cells and the subsequent creation of a low extracellular pH environment has been explored in several 'acid-mediated tumour invasion' models where the acidic environment facilitates normal cell death and permits tumour invasion. In this paper, we extend the acid-invasion model developed by Gatenby and Gawlinski (1996) to include both the competitive and cooperative interactions between tumour and normal cells, by incorporating the influence of extracellular matrix and protease production at the tumour-stroma interface. Our model predicts an optimal level of tumour acidity which produces both cell death and matrix degradation. Additionally, very aggressive tumours prevent protease production and matrix degradation by excessive normal cell destruction, leading to an acellular (but matrix filled) gap between the tumour and normal tissue, a feature seen in encapsulated tumours. These results suggest, counterintuitively, that increasing tumour acidity may, in some cases, prevent tumour invasion.
肿瘤微环境既能促进又能抑制肿瘤的生长和侵袭，这一点已得到充分证实，然而，大多数侵袭性数学模型认为，正常组织通过免疫调节或空间限制来抑制肿瘤进展。特别是，肿瘤细胞产生的酸以及随后形成的低细胞外 pH 环境已在几种“酸介导的肿瘤侵袭”模型中得到了探索，在这些模型中，酸性环境促进正常细胞死亡并允许肿瘤侵袭。在本文中，我们通过在肿瘤-基质界面处包含细胞外基质和蛋白酶产生的影响，将 Gatenby 和 Gawlinski（1996 年）开发的酸侵袭模型扩展到包括肿瘤细胞和正常细胞之间的竞争和合作相互作用。我们的模型预测了一种最佳的肿瘤酸度水平，既能产生细胞死亡又能产生基质降解。此外，非常侵袭性的肿瘤通过过度破坏正常细胞来阻止蛋白酶的产生和基质的降解，导致肿瘤和正常组织之间存在无细胞（但充满基质）的间隙，这种特征在囊状肿瘤中可见。这些结果表明，反直觉的是，增加肿瘤酸度在某些情况下可能会阻止肿瘤侵袭。
