Tumour–stromal interactions in acid-mediated invasion: A mathematical model

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.