Mathematical modelling of tumour acidity: Regulation of intracellular pH

Measurements of extracellular pH (pH(e)) in vivo have shown that the microenvironment in tumours is more acidic than in normal tissue. However, both human and animal tumour cells have been shown to have an intracellular pH (pH(i)) on the alkaline side of neutrality (pH 7.1-7.2). This gives rise to a reversed pH gradient between tumours and normal tissue which implies that cells within solid tumours are capable of maintaining their level of pH(i) at physiological levels, despite lower than normal levels of pH(e). In this paper the authors describe a mathematical model that provides a possible explanation for the altered pH gradient observed in tumours. The authors examine the influence of changes in the microenvironment on the activity of several membrane based ion transport systems. Using qualitative analysis the authors show that the pH(i) of tumour cells is less sensitive to external pH than for normal cells, because of their increased reliance on the inefficient glycolytic pathway for energy production. It is shown that under aerobic conditions the lactate-/H⁺ symporter could be the most active exchanger in the regulation of pH(i) in tumour cells. However, under more hypoxic conditions lactate extrusion is reduced, and so this exchanger has little effect on resting pH(i) in these regions. The authors also consider an extended model which incorporates the transfer of acids from the cytosol into acidic organelles. The model demonstrates that one of the major factors involved in the maintenance of cytosolic pH to physiological levels, despite an acidic extracellular pH in hypoxic areas of tumour tissue (median, 6.9-7.0), is enhanced sequestration of cytosolic protons into acidic cellular vesicles such as endoplasmic reticulum, golgi, endosomes, and lysosomes.