A. Anderson, A. Weaver, P. Cummings and V. Quaranta. Tumor morphology and phenotypics evolution driven by selective pressure from the microenvironment. Cell 127, 905-915, December 2006.
This is the paper I mentioned in my previous post. It is not that usual to find a mathematical model in a journal like Cell so I hope that this is part of a growing trend.
The paper investigates how the microenvironments helps to drive cancer evolution. To do so they use a hybrid cellular automata model in which cells live in the discrete lattice and the microenvironment (oxygen concentration, extra cellular matrix macromolecule concentration and matrix degrading enzyme) is modeled using continuous variables. The cells are characterised by a number of parameters that determine their behaviour with respect to proliferation, cell-cell adhesion, oxygen consumption, haptotaxis or production of matrix degradation enzymes. Cells follow a life cycle and only proliferate when they reach a certain age. That age depends on the cell's phenotype. During mitosis a cell might alter its phenotype and change the values of proliferation, adhesion, oxygen consumption, etc.
With heterogeneous microenvironment and cell behaviour you get different patterns of tumour growth, some of them favouring agressive invading phenotypes and some of them favouring the coexistance of all sorts of phenotypes. Having the model they described it is possible to study who different microenvironmental factors determine evolution. The results show that harsh environments (little oxygen) select for aggressive phenotypes whereas in milder environments allow for the coexistance of a much bigger range of phenotypes and that these tumours are unlikely to be invasive.
The model is very interesting and the conclusions seem pretty reasonable: Tough microenvironments lead to aggressive tumours. My intuition tells me that on the other hand, heterogeneous populations are more likely to be able to cope with an external aggression which would imply that a less aggressive but more diverse tumour would not respond well to therapies that target any specific kind of behaviour. The main problem with the paper is that the model is fairly complicated for clinical validation.