Theoretical predictions of lactate and hydrogen ion distributions in tumours

High levels of lactate and H(+)-ions play an important role in the invasive and metastatic cascade of some tumours. We develop a mathematical model of cellular pH regulation focusing on the activity of the Na(+)/H(+) exchanger (NHE) and the lactate/H(+) symporter (MCT) to investigate the spatial correlations of extracellular lactate and H(+)-ions. We highlight a crucial role for blood vessel perfusion rates in determining the spatial correlation between these two cations. We also predict critical roles for blood lactate, the activity of the MCTs and NHEs on the direction of the cellular pH gradient in the tumour. We also incorporate experimentally determined heterogeneous distributions of the NHE and MCT transporters. We show that this can give rise to a higher intracellular pH and a lower intracellular lactate but does not affect the direction of the reversed cellular pH gradient or redistribution of protons away from the glycolytic source. On the other hand, including intercellular gap junction communication in our model can give rise to a reversed cellular pH gradient and can influence the levels of pH.