2013, 10(3): 873-911. doi: 10.3934/mbe.2013.10.873

Application of evolutionary games to modeling carcinogenesis

1. 

Department of Automatic Control, Silesian University of Technology, 44-101 Gliwice, Poland, Poland

Received  June 2012 Revised  February 2013 Published  April 2013

We review a quite large volume of literature concerning mathematical modelling of processes related to carcinogenesis and the growth of cancer cell populations based on the theory of evolutionary games. This review, although partly idiosyncratic, covers such major areas of cancer-related phenomena as production of cytotoxins, avoidance of apoptosis, production of growth factors, motility and invasion, and intra- and extracellular signaling. We discuss the results of other authors and append to them some additional results of our own simulations dealing with the possible dynamics and/or spatial distribution of the processes discussed.
Citation: Andrzej Swierniak, Michal Krzeslak. Application of evolutionary games to modeling carcinogenesis. Mathematical Biosciences & Engineering, 2013, 10 (3) : 873-911. doi: 10.3934/mbe.2013.10.873
References:
[1]

A. R. Anderson, M. Hassanein, K. M. Branch, J. Lu, N. A. Lobdell, J. Maier, D. Basanta, B. Weidow, A. Narasanna, C. L. Arteaga, A. B. Reynolds, V. Quaranta, L. Estrada and A. M. Weaver, Microenvironmental independence associated with tumor progression,, Cancer Res., 69 (2009), 8797. doi: 10.1158/0008-5472.CAN-09-0437.

[2]

D. Albino, P. Scaruffi, S. Moretti, S. Coco, M. Truini, C. Di Cristofano, A. Cavazzana, S. Stigliani, S. Bonassi and G. P. Tonini, Identification of low intratumoral gene expression heterogeneity in neuroblastic tumors by genome-wide expression analysis and game theory,, Cancer, 113 (2008), 1412. doi: 10.1002/cncr.23720.

[3]

R. Axelrod, D. Axelrod and K. J. Pienta, Evolution of cooperation among tumor cells,, PNAS, 103 (2006), 13474. doi: 10.1073/pnas.0606053103.

[4]

L. A. Bach, S. M. Bentzen, J. Alsner and F. B. Christiansen, An evolutionary-game model of tumour-cell interactions: Possible relevance do gene therapy,, European Journal of Cancer, 37 (2001), 2116.

[5]

L. A. Bach, D. J. T. Sumpter, J. Alsner and V. Loeschcke, Spatial evolutionary games of interaction among generic cancer cells,, Journal of Theoretical Medicin, 5 (2003), 47. doi: 10.1080/10273660310001630443.

[6]

D. Basanta and A. Deutsch, A game theoretical perspective on the somatic evolution of cancer,, in, (2008), 1.

[7]

D. Basanta, R. A. Gatenby and A. R. A. Anderson, Exploiting evolution to treat drug resistance: Combination therapy and the double bind,, Mol. Pharmaceutics, 9 (2012), 917.

[8]

D. Basanta, H. Hatzikirou and A. Deutsch, Studying the emergency of invasiveness in tumours using game theory,, Eur. Phys. J. B., 63 (2008), 393. doi: 10.1140/epjb/e2008-00249-y.

[9]

D. Basanta, J. G. Scott, R. Rockne, K. R. Swanson and A. R. A. Anderson, The role of IDH1 mutated tumour cells in secondary glioblastomas: An evolutionary game theoretical view,, Phys. Biol., 8 (2011). doi: 10.1088/1478-3975/8/1/015016.

[10]

D. Basanta, M. Simon, H. Hatzikirou and A. Deutsch, Evolutionary game theory elucidates the role of glycolysis in glioma progression and invasion,, Cell Proliferation, 41 (2008), 980. doi: 10.1111/j.1365-2184.2008.00563.x.

[11]

D. Basanta, J. G. Scott, M. N. Fishman, G. Ayala, S. W. Hayward and A. R. A. Anderson, Investigating prostate cancer tumout-stroma interactions: clinical and biological insights from an evolutionary game,, British Journal of Cancer, 106 (2012), 174. doi: 10.1038/bjc.2011.517.

[12]

D. T. Bishop and C. Cannings, Models of animal conflict,, Advances in Applied Probability, 8 (1976), 616. doi: 10.2307/1425917.

[13]

C. Cleveland, D. Liao and R. Austin, Physics of cancer propagation: A game theory perspective,, AIP Advances, 2 (2012). doi: 10.1063/1.3699043.

[14]

B. Crespi and K. Summers, Evolutionary biology of cancer,, Trends in Ecology and Evolution, 20 (2005), 545. doi: 10.1016/j.tree.2005.07.007.

[15]

F. Delaplace, A. Petrovna, M. Malo, F. Maquerlot, R. Fodil, D. Lawrence and G. Barlovatz-Meimon, "The PAI-1 game": Towards modelling the Plasminogen Activation system (Pas) dependent migration of cancer cells with the game theory,, Integrative Post-Genomics, (2004).

[16]

D. Dingli, F. A. C. C. Chalub, F. C. Santos, S. Van Segbroeck and J. M. Pacheco, Cancer phenotype as the outcome of an evolutionary game between normal and malignant cells,, British Journal of Cancer, 20 (2005), 545. doi: 10.1038/sj.bjc.6605288.

[17]

R. A. Gatenby and T. L Vincent, An evolutionary model of carcinogenesis,, Cancer Res., 63 (2003), 6212.

[18]

R. A. Gatenby and T. L Vincent, Application of quantitative models from population biology and evolutionary game theory to tumor therapeutic strategies,, Mol. Cancer Ther., 2 (2003), 919.

[19]

M. Gerstung, H. Nakhoul and N. Beerenwinkel, Evolutionary Games with Affine Fitness functions: Applications to cancer,, Dynamic Games and Applications, 1 (2011), 370. doi: 10.1007/s13235-011-0029-0.

[20]

J. Hofbauer and K. Sigmund, Evolutionary game dynamics,, Bull. Amer. Math. Soc., 40 (2003), 479. doi: 10.1090/S0273-0979-03-00988-1.

[21]

N. L. Komarova, Mathematical modeling of tumorigenesis: mission possible,, Curr. Opin. Oncol. January, 17 (2005), 39. doi: 10.1097/01.cco.0000143681.37692.32.

[22]

M. Krzeslak and A. Swierniak, Extended game-theoretic model of interaction between tumour cells,, Proc of the 18 Nat. Conf. On Applications of Mathematics in Biology and Medicine, (2012).

[23]

M. Krzeslak and A. Swierniak, Spatial evolutionary games and radiation induced bystander effect,, Archives of Control Science, 21 (2011), 135. doi: 10.2478/v10170-010-0036-1.

[24]

Y. Mansury and T. S Deisboeck, The impact of "search precision" in an agent-based tumor model,, Journal of Theoretical Biology, 224 (2003), 325. doi: 10.1016/S0022-5193(03)00169-3.

[25]

Y. Mansury, M. Diggory and T. S Deisboeck, Evolutionary game theory in an agent based brain tumor model: Exploring the genotype phenotype link,, Jour. Theo. Biol., 238 (2006), 146. doi: 10.1016/j.jtbi.2005.05.027.

[26]

J. Maynard Smith, "Evolution and the Theory of Games,", Cambridge: Cambridge University Press, (1982).

[27]

J. Maynard Smith, The theory of games and the evolution of animal conflicts,, J. Theor. Biol., 47 (1974), 209. doi: 10.1016/0022-5193(74)90110-6.

[28]

J. Maynard Smith and G. R. Price, The Logic of Animal Conflict,, Nature, 246 (1973), 16. doi: 10.1038/246015a0.

[29]

J. W. McEvoy, Evolutionary game theory: Lessons and limitations, a cancer perspective,, British Journal of Cancer, 101 (2009), 2060. doi: 10.1038/sj.bjc.6605444.

[30]

M. A. Nowak, "Evolutionary Dynamics,", 2004. Available from: \url{http://athome.harvard.edu/programs/evd/index.html}, (). doi: 10.1007/BF02985382.

[31]

M. A. Nowak and R. M. May, Evolutionary games and spatial chaos,, Nature, 18 (1992), 826. doi: 10.1038/359826a0.

[32]

K. Sigmund and M. A. Nowak, Evolutionary game theory,, Curr. Biol., 9 (1999), 503.

[33]

P. F Stadler, Dynamics of autocatalytic reaction networks. IV: Inhomogeneous replicator networks,, Biosystems, 26 (1991), 1. doi: 10.1016/0303-2647(91)90033-H.

[34]

A. Swierniak and M. Krzeslak, Game theoretic approach to mathematical modeling of radiation induced bystander effect,, Proc of the 16 Nat. Conf. On Applications of Mathematics in Biology and Medicine, (2010), 99.

[35]

P. D. Taylor and L. B. Jonker, Evolutionarily stable strategies and game dynamics,, Mathematical Biosciences, 40 (1978), 145. doi: 10.1016/0025-5564(78)90077-9.

[36]

I. P. M. Tomlinson, Game-theory models of interactions between tumour cells,, European Journal of Cancer, 33 (1997), 1495. doi: 10.1016/S0959-8049(97)00170-6.

[37]

I. P. M. Tomlinson and W. F. Bodmer, Modeling the consequences of interactions between tumour cells,, British Journal of Cancer, 75 (1997), 157. doi: 10.1038/bjc.1997.26.

[38]

J. von Neuman, "Theory of Self Reproducing Automata,", University of Illinois Press, (1966).

show all references

References:
[1]

A. R. Anderson, M. Hassanein, K. M. Branch, J. Lu, N. A. Lobdell, J. Maier, D. Basanta, B. Weidow, A. Narasanna, C. L. Arteaga, A. B. Reynolds, V. Quaranta, L. Estrada and A. M. Weaver, Microenvironmental independence associated with tumor progression,, Cancer Res., 69 (2009), 8797. doi: 10.1158/0008-5472.CAN-09-0437.

[2]

D. Albino, P. Scaruffi, S. Moretti, S. Coco, M. Truini, C. Di Cristofano, A. Cavazzana, S. Stigliani, S. Bonassi and G. P. Tonini, Identification of low intratumoral gene expression heterogeneity in neuroblastic tumors by genome-wide expression analysis and game theory,, Cancer, 113 (2008), 1412. doi: 10.1002/cncr.23720.

[3]

R. Axelrod, D. Axelrod and K. J. Pienta, Evolution of cooperation among tumor cells,, PNAS, 103 (2006), 13474. doi: 10.1073/pnas.0606053103.

[4]

L. A. Bach, S. M. Bentzen, J. Alsner and F. B. Christiansen, An evolutionary-game model of tumour-cell interactions: Possible relevance do gene therapy,, European Journal of Cancer, 37 (2001), 2116.

[5]

L. A. Bach, D. J. T. Sumpter, J. Alsner and V. Loeschcke, Spatial evolutionary games of interaction among generic cancer cells,, Journal of Theoretical Medicin, 5 (2003), 47. doi: 10.1080/10273660310001630443.

[6]

D. Basanta and A. Deutsch, A game theoretical perspective on the somatic evolution of cancer,, in, (2008), 1.

[7]

D. Basanta, R. A. Gatenby and A. R. A. Anderson, Exploiting evolution to treat drug resistance: Combination therapy and the double bind,, Mol. Pharmaceutics, 9 (2012), 917.

[8]

D. Basanta, H. Hatzikirou and A. Deutsch, Studying the emergency of invasiveness in tumours using game theory,, Eur. Phys. J. B., 63 (2008), 393. doi: 10.1140/epjb/e2008-00249-y.

[9]

D. Basanta, J. G. Scott, R. Rockne, K. R. Swanson and A. R. A. Anderson, The role of IDH1 mutated tumour cells in secondary glioblastomas: An evolutionary game theoretical view,, Phys. Biol., 8 (2011). doi: 10.1088/1478-3975/8/1/015016.

[10]

D. Basanta, M. Simon, H. Hatzikirou and A. Deutsch, Evolutionary game theory elucidates the role of glycolysis in glioma progression and invasion,, Cell Proliferation, 41 (2008), 980. doi: 10.1111/j.1365-2184.2008.00563.x.

[11]

D. Basanta, J. G. Scott, M. N. Fishman, G. Ayala, S. W. Hayward and A. R. A. Anderson, Investigating prostate cancer tumout-stroma interactions: clinical and biological insights from an evolutionary game,, British Journal of Cancer, 106 (2012), 174. doi: 10.1038/bjc.2011.517.

[12]

D. T. Bishop and C. Cannings, Models of animal conflict,, Advances in Applied Probability, 8 (1976), 616. doi: 10.2307/1425917.

[13]

C. Cleveland, D. Liao and R. Austin, Physics of cancer propagation: A game theory perspective,, AIP Advances, 2 (2012). doi: 10.1063/1.3699043.

[14]

B. Crespi and K. Summers, Evolutionary biology of cancer,, Trends in Ecology and Evolution, 20 (2005), 545. doi: 10.1016/j.tree.2005.07.007.

[15]

F. Delaplace, A. Petrovna, M. Malo, F. Maquerlot, R. Fodil, D. Lawrence and G. Barlovatz-Meimon, "The PAI-1 game": Towards modelling the Plasminogen Activation system (Pas) dependent migration of cancer cells with the game theory,, Integrative Post-Genomics, (2004).

[16]

D. Dingli, F. A. C. C. Chalub, F. C. Santos, S. Van Segbroeck and J. M. Pacheco, Cancer phenotype as the outcome of an evolutionary game between normal and malignant cells,, British Journal of Cancer, 20 (2005), 545. doi: 10.1038/sj.bjc.6605288.

[17]

R. A. Gatenby and T. L Vincent, An evolutionary model of carcinogenesis,, Cancer Res., 63 (2003), 6212.

[18]

R. A. Gatenby and T. L Vincent, Application of quantitative models from population biology and evolutionary game theory to tumor therapeutic strategies,, Mol. Cancer Ther., 2 (2003), 919.

[19]

M. Gerstung, H. Nakhoul and N. Beerenwinkel, Evolutionary Games with Affine Fitness functions: Applications to cancer,, Dynamic Games and Applications, 1 (2011), 370. doi: 10.1007/s13235-011-0029-0.

[20]

J. Hofbauer and K. Sigmund, Evolutionary game dynamics,, Bull. Amer. Math. Soc., 40 (2003), 479. doi: 10.1090/S0273-0979-03-00988-1.

[21]

N. L. Komarova, Mathematical modeling of tumorigenesis: mission possible,, Curr. Opin. Oncol. January, 17 (2005), 39. doi: 10.1097/01.cco.0000143681.37692.32.

[22]

M. Krzeslak and A. Swierniak, Extended game-theoretic model of interaction between tumour cells,, Proc of the 18 Nat. Conf. On Applications of Mathematics in Biology and Medicine, (2012).

[23]

M. Krzeslak and A. Swierniak, Spatial evolutionary games and radiation induced bystander effect,, Archives of Control Science, 21 (2011), 135. doi: 10.2478/v10170-010-0036-1.

[24]

Y. Mansury and T. S Deisboeck, The impact of "search precision" in an agent-based tumor model,, Journal of Theoretical Biology, 224 (2003), 325. doi: 10.1016/S0022-5193(03)00169-3.

[25]

Y. Mansury, M. Diggory and T. S Deisboeck, Evolutionary game theory in an agent based brain tumor model: Exploring the genotype phenotype link,, Jour. Theo. Biol., 238 (2006), 146. doi: 10.1016/j.jtbi.2005.05.027.

[26]

J. Maynard Smith, "Evolution and the Theory of Games,", Cambridge: Cambridge University Press, (1982).

[27]

J. Maynard Smith, The theory of games and the evolution of animal conflicts,, J. Theor. Biol., 47 (1974), 209. doi: 10.1016/0022-5193(74)90110-6.

[28]

J. Maynard Smith and G. R. Price, The Logic of Animal Conflict,, Nature, 246 (1973), 16. doi: 10.1038/246015a0.

[29]

J. W. McEvoy, Evolutionary game theory: Lessons and limitations, a cancer perspective,, British Journal of Cancer, 101 (2009), 2060. doi: 10.1038/sj.bjc.6605444.

[30]

M. A. Nowak, "Evolutionary Dynamics,", 2004. Available from: \url{http://athome.harvard.edu/programs/evd/index.html}, (). doi: 10.1007/BF02985382.

[31]

M. A. Nowak and R. M. May, Evolutionary games and spatial chaos,, Nature, 18 (1992), 826. doi: 10.1038/359826a0.

[32]

K. Sigmund and M. A. Nowak, Evolutionary game theory,, Curr. Biol., 9 (1999), 503.

[33]

P. F Stadler, Dynamics of autocatalytic reaction networks. IV: Inhomogeneous replicator networks,, Biosystems, 26 (1991), 1. doi: 10.1016/0303-2647(91)90033-H.

[34]

A. Swierniak and M. Krzeslak, Game theoretic approach to mathematical modeling of radiation induced bystander effect,, Proc of the 16 Nat. Conf. On Applications of Mathematics in Biology and Medicine, (2010), 99.

[35]

P. D. Taylor and L. B. Jonker, Evolutionarily stable strategies and game dynamics,, Mathematical Biosciences, 40 (1978), 145. doi: 10.1016/0025-5564(78)90077-9.

[36]

I. P. M. Tomlinson, Game-theory models of interactions between tumour cells,, European Journal of Cancer, 33 (1997), 1495. doi: 10.1016/S0959-8049(97)00170-6.

[37]

I. P. M. Tomlinson and W. F. Bodmer, Modeling the consequences of interactions between tumour cells,, British Journal of Cancer, 75 (1997), 157. doi: 10.1038/bjc.1997.26.

[38]

J. von Neuman, "Theory of Self Reproducing Automata,", University of Illinois Press, (1966).

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