Acid-mediated tumour cell invasion: a discrete modelling approach using the extended Potts model

Acidic extracellular pH has been shown to play a crucial part in the invasive and metastatic cascade of some tumours. In this study, we examine the effect of extracellular acidity on tumour invasion focusing, in particular, on cellular adhesion, proteolytic enzyme activity and cellular proliferation. Our numerical simulations using a cellular Potts model show that, under acidic extracellular pH, changes in cell–matrix adhesion strength has a comparable effect on tumour invasiveness as the increase in proteolytic enzyme activity. We also show that tumour cells cultured under physiological pH tend to be large and the tumours develop a "diffuse" morphology compared to those cultured at acidic pH, which display protruding "fingers" at the advancing front. A key model prediction is the observation that the main effect on invasion from culturing cells at low extracellular pH stems from changes in the intercellular and cell–matrix adhesion strengths and proteolytic enzyme secretion rate. However, we show that the effects of proteolysis needs to be significant as low to moderate changes only has nominal effects on cell invasiveness. We find that the low pH _e effects on cell size and proliferation rate have much lower influence on cell invasiveness.