Bach et al: An evolutionary-game model of tumour-cell interactions

L.A. Bach, S.M. Bentzen, J. Alsner and F.B. Christiansen. An evolutionary-game model of tumour-cell interactions: possible relevance to gene therapy. European Journal of Cancer 27 (2001) 2116-2120.

Bach et al have taken the work from Tomlinson and Bodmer (which I reviewed a few day ago) in which angiogenesis is studied with the help a Game Theory. In the previous case the game involved two players who could chose to produce angiogenic factors or to do nothing. As long as one of the players is willing to shoulder on the cost of producing the factor, both players get the benefit. As expected the result is a polymorphism in which both types of strategies coexist. I said that this polymorphism is to be expected since if there were only factor producing cells then non cooperating cells will have an advantage (since they get the benefits without paying the costs) whereas if the population is made of non cooperating cells then factor producing cells will have an advantage (as long as the benefit of producing the factor is higher than the cost).

The revision of the model proposed by Bach et al considers the implications of extending the game to three players if the benefits of angiogenesis appear only if two out of the three players cooperate to produce the factor.

The payoff table would look like this:

A+,A+ A+,A- A-, A-
A+ 1-i+j 1-i+j 1-i
A- 1+j 1+j 1

where A+ means factor producing and A- means that is not factor producing. Also i is the cost of producing the factor and j is the benefit.

Bach et al analyse how these cost and benefit parameters affect the equilibria and the existence of polymorphism. For this they use computer simulations and find that when the benefit is three times the cost something interesting happens. In that case the final composition of the tumour population would be a consequence of the composition of the original population. Most likely this finding has limited (if any) consequences in potential therapies since physicians have not got the ability to change the initial composition of phenotypes in a tumour. Still, the (qualitative) results can be used as a guide for gene therapies.

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