Why do cancers have high aerobic glycolysis? R Gatenby, R. Gillies. Nature reviews cancer, Vol. 4, November 2004, pp 891-899.
The role of acidity in solid tumour growth and invasion. K. Smallbone, D. Gavaghan, R. Gatenby and P. Maini. Journal of Theoretical Biology 235 (2005) pp 476-484.
In the second paper, Smallbone and colleagues introduce a mathematical model to study the possibility that tumour invasion and growth could be the result, not of genetic changes, but of changes in the tumour environment. This is, of course, a mathematical formalisation of the hypothesis presented in the other paper. They decided to take multicellular spheroids and produce an ODE model that describes tumour growth and progression as travelling waves: the one for the increased microenvironmental acidity and the second one with the tumour cells invading normal tissue. This is a clearly a quantitative model that, unfortunately, has not yet been validated by in vitro experiments although it looks to me that its design has been done with care so it would be feasible to do so. The model predicts among other things that avascular tumours will have higher acidity than vascular ones (which makes sense since blood vessels can be used to take part of this acidity out of the microenvironment) and that tumour necrosis could potentially be explained without the need to talk about cell starvation or overcrowding but by the acidification of the environment. They make a good case for antiangiogenic therapies since blood vessels can contribute to a decrease of microenvironment acidity that could be sufficient for tumour cells to survive but not for healthy cells that have a lower threshold of acidity resistance. They also suggest a treatment in which the membrane pumps that transport the acidity from within the cell to the outside environment, would be somehow blocked so glycolytic cells would literally poison themselves to death without changing the microenvironment for the healthy tissue cells.