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.  Google Scholar

[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.  Google Scholar

[3]

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

[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.   Google Scholar

[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.  Google Scholar

[6]

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

[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.   Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[12]

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

[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.  Google Scholar

[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.  Google Scholar

[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).   Google Scholar

[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.  Google Scholar

[17]

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

[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.   Google Scholar

[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.  Google Scholar

[20]

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

[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.  Google Scholar

[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).   Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[26]

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

[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.  Google Scholar

[28]

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

[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.  Google Scholar

[30]

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

[31]

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

[32]

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

[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.  Google Scholar

[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.   Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[38]

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

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.  Google Scholar

[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.  Google Scholar

[3]

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

[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.   Google Scholar

[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.  Google Scholar

[6]

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

[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.   Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[12]

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

[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.  Google Scholar

[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.  Google Scholar

[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).   Google Scholar

[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.  Google Scholar

[17]

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

[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.   Google Scholar

[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.  Google Scholar

[20]

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

[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.  Google Scholar

[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).   Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[26]

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

[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.  Google Scholar

[28]

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

[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.  Google Scholar

[30]

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

[31]

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

[32]

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

[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.  Google Scholar

[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.   Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[38]

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

[1]

Xin Guo, Lexin Li, Qiang Wu. Modeling interactive components by coordinate kernel polynomial models. Mathematical Foundations of Computing, 2020, 3 (4) : 263-277. doi: 10.3934/mfc.2020010

[2]

Juan Pablo Pinasco, Mauro Rodriguez Cartabia, Nicolas Saintier. Evolutionary game theory in mixed strategies: From microscopic interactions to kinetic equations. Kinetic & Related Models, , () : -. doi: 10.3934/krm.2020051

[3]

Ebraheem O. Alzahrani, Muhammad Altaf Khan. Androgen driven evolutionary population dynamics in prostate cancer growth. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020426

[4]

Shipra Singh, Aviv Gibali, Xiaolong Qin. Cooperation in traffic network problems via evolutionary split variational inequalities. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020170

[5]

Martin Kalousek, Joshua Kortum, Anja Schlömerkemper. Mathematical analysis of weak and strong solutions to an evolutionary model for magnetoviscoelasticity. Discrete & Continuous Dynamical Systems - S, 2021, 14 (1) : 17-39. doi: 10.3934/dcdss.2020331

[6]

Jun Zhou. Lifespan of solutions to a fourth order parabolic PDE involving the Hessian modeling epitaxial growth. Communications on Pure & Applied Analysis, 2020, 19 (12) : 5581-5590. doi: 10.3934/cpaa.2020252

2018 Impact Factor: 1.313

Metrics

  • PDF downloads (13)
  • HTML views (0)
  • Cited by (10)

Other articles
by authors

[Back to Top]