Tomlinson and Bodmer: Modelling the consequences of interactions between tumour cells

I.P.M. Tomlinson and W.F. Bodmer. British Journal of Cancer 75 (2) 157-160, 1997.

Again Tomlinson, this time working with Bodmer, taking a couple of simple but interesting examples of the use of game theory for cancer research. This time they work on two different games: angiogenesis and apoptosis. In the first game angiogenic factors might be produced by tumour cells with the result that the cell producing and its neighbours reap the benefits of increased access to nutrients. In the second game cells might produce factors to escape angiogenesis which might or might not benefit the neighbours.

As it is usual in these cases the model assumes a large population of tumour cells, asexual reproduction and a population site that does not need to be constant since the object of the study is the frequency of particular phenotypes, not their absolute number. Further assumptions: the population of tumour cells is genetically diverse and this diversity is distributed homogeneously.

In the first game: angiogenesis, there are two strategies: either to produce or not to produce angiogenic factors. There is a cost associated to producing then and also a payoff. If you are a non producing tumour cell and you interact with a producing tumour cell you get the same benefits but none of the costs of a factor producing tumour cell. The result is that there are equilibria in which both phenotypes coexist as long as the cost of producing angiogenic factors is outweighed by the benefit.

The second game is more sophisticated. In this case we have three different strategies: either we produce factors to help neighbouring cells avoid apoptosis (paracrine factors), or we produce autocrine factors that help us avoid apoptosis or, alternatively, we might save ourselves all that trouble and do nothing. As usual there is a payoff table in which the different parameters represent the costs of producing paracrine and autocrine factors and the benefits they provide to whoever is the target of the factor. Tomlinson and Bodmer use GT to study different types of equilibria.

In this case it is easy to see that the first strategy is not viable since any group of cells doing nothing and reaping the benefits of endocrine factor producing cells would drive them to extintion. On the other hand if the cost of producing autocrine factors is smaller than the benefit of avoiding apoptosis then there will be a selection for cells capable of producing those autocrine factors.

The conclusion of the paper is that a tumour cell population might not adopt a strategy that would help the whole but does not confer any advantage to the individual that brings it (which is a reasonably safe proposition to make to people studying evolution). The question is again if there could be therapies designed to exploit the fact that tumour cells can stop cooperating among each other.