Skip to main content
SpringerLink
Log in
Book cover

New Challenges for Cancer Systems Biomedicine pp 3–18Cite as

Combining Game Theory and Graph Theory to Model Interactions between Cells in the Tumor Microenvironment

  • Chapter

Part of the book series: SIMAI Springer Series ((SEMA SIMAI))

Abstract

Mathematical concepts of graph theory and game theory both influence models of biological systems. We combine these two approaches to understand how game-like interactions influence the cellular topology of a planar tissue. We review the literature on the role of cell to cell interactions in tumourigenesis and survey the mathematical approaches that have been used to simulate such cell-cell interactions. We present how this game-graph approach can be used to simulate epithelial tissue growth and how it can foster our understanding of the role of cell-cell communication in the early stages of cancer development. We present computational models that we use to test how cooperating and non-cooperating cells build planar tissues and compare the simulated tissue topologies with literature data. We further discuss how such system could be used to model microenviromental communications between cancer cells and the surrounding tissue.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   119.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. Adra, S., Sun, T., MacNeil, S., Holcombe, M., Smallwood, R.: Development of a Three Dimensional Multiscale Computational Model of the Human Epidermis. PLoS ONE 5, e8511 (2010)

    Article  Google Scholar 

  2. Aegerter-Wilmsen, T., Smith, A.C., Christen, A.J., Aegerter, C.M., Hafen, E., Basler, K.: Exploring the effects of mechanical feedback on epithelial topology. Development 137, 499506 (2010)

    Article  Google Scholar 

  3. Aguirre-Ghiso, J.A.: Models, mechanisms and clinical evidence for cancer dormancy. Nat Rev Cancer 7, 834–846 (2007)

    Article  Google Scholar 

  4. Alarcon, T., Byrne, H.M., Maini, P.K.: A cellular automaton model for tumour growth in inho- mogeneous environment. J Theor Biol 225, 257–274 (2003)

    Article  Google Scholar 

  5. Alarcon, T., Byrne, H.M., Maini, P.K.: A Multiple Scale Model for Tumor Growth. Mult Mod Sim 3, 440–475 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  6. Anderson, A.R.A., Chaplain, M.A.J., Rejniak, K.A.: Single-Cell-Based Models in Biology and Medicine. Birkhauser, Basel, Switzerland (2007)

    Book  MATH  Google Scholar 

  7. Anderson, A.R.A., Hassanein, M., Branch, K.M., Lu, J., Lobdell, N.A., Maier, J., Basanta, D., Weidow, B., Narasanna, A., Arteaga, C.L., Reynolds, A.B., Quaranta, V., Estrada, L., Weaver, A.M.: Microenvironmental Independence Associated with Tumor Progression. Cancer Res 69, 8797-8806(2009)

    Article  Google Scholar 

  8. Anderson, A.R.A., Rejniak, K., Gerlee, P., Quaranta, V.: Microenvironment driven invasion: a multiscale multimodel investigation. J Math Biol 58, 579–624 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  9. Anderson, A.R.A., Weaver, A.M., Cummings, P.T., Quaranta, V.: Tumor morphology and phenotypic evolution driven by selective pressure from the microenvironment. Cell 127, 905915 (2006)

    Article  Google Scholar 

  10. Anderson, A.R.A., Quaranta, V.: Integrative mathematical oncology. Nat Rev Cancer 8, 227234 (2008)

    Article  Google Scholar 

  11. Araujo, R., McElwain, D.: A history of the study of solid tumour growth: The contribution of mathematical modelling. Bull Math Biol 66, 1039–1091 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  12. Attolini, C.S.O., Michor, F.: Evolutionary Theory of Cancer. Ann NY Acad Sci 1168, 23–51 (2009)

    Article  Google Scholar 

  13. Axelrod, R., Axelrod, D.E., Pienta, K.J.: Evolution of cooperation among tumor cells. PNAS 103, 13474–13479 (2006) 10.1073/pnas.0606053103

    Article  Google Scholar 

  14. Baker, N.E., Li, W.: Cell Competition and Its Possible Relation to Cancer. Cancer Res 68, 5505–5507 (2008)

    Article  Google Scholar 

  15. Barabasi, A.L., Albert, R.: Emergence of Scaling in Random Networks. Science 286, 509–512 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  16. Beerenwinkel, N., Antal, T., Dingli, D., Traulsen, A., Kinzler, K.W., Velculescu, V.E., Vogelstein, B., Nowak, M.A.: Genetic Progression and the Waiting Time to Cancer. PLoS Comput Biol 3, e225 (2007)

    Article  MathSciNet  Google Scholar 

  17. Bellomo, N., Li, N.K., Maini, P.K.: On the foundations of cancer modelling: Selected topics, speculations, and perspectives. Math Model Meth Appl Sci 18, 593–646 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  18. Bidard, F.C., Pierga, J.Y., Vincent-Salomon, A., Poupon, M.-F.: A “class action” against the microenvironment: do cancer cells cooperate in metastasis? Cancer and Metastasis Rev 27, 5-10(2008)

    Article  Google Scholar 

  19. Bock, M., Tyagi, A., Kreft, J.U., Alt, W.: Generalized Voronoi Tessellation as a Model of Two-dimensional Cell Tissue Dynamics. Bull Math Biol 72, 1696–1731 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  20. Byrne, H.M.: Dissecting cancer through mathematics: from the cell to the animal model. Nat Rev Cancer 10, 221–230 (2010)

    Article  Google Scholar 

  21. Cairns, J.: Mutation selection and the natural history of cancer. Nature 255, 197–200 (1975)

    Article  Google Scholar 

  22. Cavaliere, M., Sedwards, S., Tarnita, C.E., Nowak, M.A., Csikasz-Nagy, A.: Prosperity is associated with instability in dynamical networks. J Theor Biol 299, 126–38 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  23. Chaplain, M.A.J.: Multiscale mathematical modelling in biology and medicine. IMA J Appl Math 76, 371-388(2011)

    Article  MATH  MathSciNet  Google Scholar 

  24. Craig Maclean, R., Brandon, C.: Stable public goods cooperation and dynamic social interactions in yeast. J Evol Biol 21, 1836–1843 (2008)

    Article  Google Scholar 

  25. Csikasz-Nagy, A.: Computational systems biology of the cell cycle. Brief Bioinform 10, 424434 (2009)

    Article  Google Scholar 

  26. d’Onofrio, A.: A general framework for modeling tumor-immune system competition and immunotherapy: Mathematical analysis and biomedical inferences. Physica D 208, 220–235 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  27. d’Onofrio, A., Gandolfi, A.: A family of models of angiogenesis and anti-angiogenesis anticancer therapy. Math Med Biol 26, 63–95 (2009)

    Article  MATH  Google Scholar 

  28. d’Onofrio, A., Gatti, F., Cerrai, P., Freschi, L.: Delay-induced oscillatory dynamics of tumour-immune system interaction. Math Comp Modell 51, 572–591 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  29. d’Onofrio, A., Tomlinson, I.P.M.: A nonlinear mathematical model of cell turnover, differentiation and tumorigenesis in the intestinal crypt. J Theor Biol 244, 367–374 (2007)

    Article  MathSciNet  Google Scholar 

  30. Deisboeck, T.S., Stamatakos, G.S.: Multiscale cancer modeling. CRC Press, Boca-Raton (2010)

    Book  MATH  Google Scholar 

  31. Deutsch, A., Dormann, S.: Cellular automaton modeling of biological pattern formation: characterization, applications, and analysis. Birkhauser, Basel (2005)

    MATH  Google Scholar 

  32. Dingli, D., Chalub, F.A.C.C., Santos, F.C., Van Segbroeck, S., Pacheco, J.M.: Cancer pheno- type as the outcome of an evolutionary game between normal and malignant cells. Br J Cancer 101, 1130–1136 (2009)

    Article  Google Scholar 

  33. Drasdo, D., Hoehme, S.: A single-cell-based model of tumor growth in vitro : monolayers and spheroids. Phys Biol 2, 133 (2005)

    Article  Google Scholar 

  34. Drasdo, D., Hoehme, S., Block, M.: On the Role of Physics in the Growth and Pattern Formation of Multi-Cellular Systems: What can we Learn from Individual-Cell Based Models? J Stat Phys 128, 287–345 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  35. Dubertret, B., Aste, T., Ohlenbusch, H.M., Rivier, N.: Two-dimensional froths and the dynamics of biological tissues. Phys Rev E 58, 6368 (1998)

    Article  Google Scholar 

  36. Duvdevani-Bar, S., Segel, L.: On Topological Simulations in Developmental Biology. J Theor Biol 166, 33-50(1994)

    Article  Google Scholar 

  37. Edelman, L.B., Eddy, J.A., Price, N.D.: In silico models of cancer. WIRE Syst Biol Med 2, 438-459(2010)

    Article  Google Scholar 

  38. Enderling, H., Anderson, A.R.A., Chaplain, M.A.J., Beheshti H., Hlatky, L., Hahnfeldt, P.: Paradoxical Dependencies of Tumor Dormancy and Progression on Basic Cell Kinetics. Cancer Res 69, 8814–8821 (2009)

    Article  Google Scholar 

  39. Enderling, H., Hahnfeldt, P.: Cancer stem cells in solid tumors: Is ‘evading apoptosis’ a hallmark of cancer? Prog Biophys Mol Biol 106, 391–399 (2011)

    Article  Google Scholar 

  40. Escudero, L.M., da F. Costa, L., Kicheva, A., Briscoe, J., Freeman, M., Babu, M.M.: Epithelial organisation revealed by a network of cellular contacts. Nat Commun 2, 526 (2011)

    Article  Google Scholar 

  41. Farhadifar, R., Röper, J.C., Aigouy, B., Eaton, S., Jülicher, F.: The influence of cell mechanics, cell-cell interactions, and proliferation on epithelial packing. Curr Biol 17, 2095–2104 (2007)

    Article  Google Scholar 

  42. Fozard, J., Kirkham, G., Buttery, L., King, J., Jensen, O., Byrne, H.: Techniques for analysing pattern formation in populations of stem cells and their progeny. BMC Bioinf 12, 396 (2011)

    Article  Google Scholar 

  43. Galle, J., Aust, G., Schaller, G., Beyer, T., Drasdo, D.: Individual cell-based models of the spatial-temporal organization of multicellular systems—Achievements and limitations. Cytometry A 69, 704–710 (2006)

    Article  Google Scholar 

  44. Galle, J., Loeffler, M., Drasdo, D.: Modeling the Effect ofDeregulated Proliferation and Apoptosis on the Growth Dynamics of Epithelial Cell Populations In Vitro. Biophys J 88, 62–75 (2005)

    Article  Google Scholar 

  45. Gatenby, R.A., Gillies, R.J.: A microenvironmental model of carcinogenesis. Nat Rev Cancer 8, 56–61 (2008)

    Article  Google Scholar 

  46. Gatenby, R.A., Gillies, R.J., Brown, J.S.: The evolutionary dynamics of cancer prevention. Nat Rev Cancer 10, 526–527 (2010)

    Article  Google Scholar 

  47. Gatenby, R.A., Vincent, T.L.: An Evolutionary Model Of Carcinogenesis. Cancer Res 63, 6212–6220 (2003)

    Google Scholar 

  48. Gibson, M.C., Patel, A.B., Nagpal, R., Perrimon, N.: The emergence of geometric order in proliferating metazoan epithelia. Nature 442, 1038–1041 (2006)

    Article  Google Scholar 

  49. Gibson, W.T., Veldhuis, J.H., Rubinstein, B., Cartwright, H.N., Perrimon, N., Brodland, G.W., Nagpal, R., Gibson, M.C.: Control of the Mitotic Cleavage Plane by Local Epithelial Topology. Cell 144, 427–438 (2011)

    Article  Google Scholar 

  50. Grant, M.R., Mostov, K.E., Tlsty, T.D., Hunt, C.A.: Simulating Properties of In Vitro Epithelial Cell Morphogenesis. PLoS Comput Biol 2, e129 (2006)

    Article  Google Scholar 

  51. Greaves, M., Maley, C.C.: Clonal evolution in cancer. Nature 481, 306–313 (2012)

    Article  Google Scholar 

  52. Gross, T., Blasius, B.: Adaptive coevolutionary networks: a review. J R Soc Interface 5, 259271 (2008)

    Google Scholar 

  53. Guillaud, M., Clem, C., MacAulay, C.: An in silico platform for the study of epithelial preinvasive neoplastic development. Biosystems 102, 22–31 (2010)

    Article  Google Scholar 

  54. Hanahan, D., Weinberg, R.A.: The hallmarks of cancer. Cell 100, 57–70 (2000)

    Article  Google Scholar 

  55. Hanahan, D., Weinberg, R.A.: Hallmarks of Cancer: The Next Generation. Cell 144, 646–674 (2011)

    Article  Google Scholar 

  56. Hofbauer, J., Sigmund, K.: Evolutionary games and population dynamics. London Mathematical Society Student Texts. Cambridge University Press, Cambridge (1988)

    MATH  Google Scholar 

  57. Hofbauer, J., Sigmund, K.: Evolutionary game dynamics. Bull Am Math Soc 40, 479 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  58. Honda, H., Tanemura, M., Nagai, T.: A three-dimensional vertex dynamics cell model of space-filling polyhedra simulating cell behavior in a cell aggregate. J Theor Biol 226, 439453 (2004)

    Article  MathSciNet  Google Scholar 

  59. Hsu, Y.C., Fuchs, E.: A family business: stem cell progeny join the niche to regulate homeostasis. Nat Rev Mol Cell Biol 13, 103–114 (2012)

    Article  Google Scholar 

  60. Hu, M., Polyak, K.: Microenvironmental regulation of cancer development. Curr Opin Gen Dev 18, 27–34 (2008)

    Article  Google Scholar 

  61. Hunter, T.: Signaling—2000 and Beyond. Cell 100, 113–127 (2000)

    Article  Google Scholar 

  62. Izaguirre, J.A., Chaturvedi, R., Huang, C., Cickovski, T., Coffland, J., Thomas, G., Forgacs, G., Alber, M., Hentschel, G., Newman, S.A., Glazier, J.A.: CompuCell, a multi-model framework for simulation of morphogenesis. Bioinformatics 20, 1129–1137 (2004)

    Article  Google Scholar 

  63. Jackson, M.O.: Social and Economic Networks. Princeton University Press, Princeton (2008)

    MATH  Google Scholar 

  64. Johnston, L.A.: Competitive Interactions Between Cells: Death, Growth, and Geography. Science 324, 1679–1682 (2009)

    Article  Google Scholar 

  65. Johnston, M.D., Maini, P.K., Jonathan Chapman, S., Edwards, C.M., Bodmer, W.F.: On the proportion of cancer stem cells in a tumour. J Theor Biol 266, 708–711 (2010)

    Article  MathSciNet  Google Scholar 

  66. Kholodenko, B.N.: Cell-signalling dynamics in time and space. Nat Rev Mol Cell Biol 7, 165176 (2006)

    Article  Google Scholar 

  67. Kim, S., Debnath, J., Mostov, K., Park, S., Hunt, C.A.: A computational approach to resolve cell level contributions to early glandular epithelial cancer progression. BMC Syst Biol 3, 122 (2009)

    Article  Google Scholar 

  68. Lecuit, T., Lenne, P.-F.: Cell surface mechanics and the control of cell shape, tissue patterns and morphogenesis. Nat Rev Mol Cell Biol 8, 633–644 (2007)

    Article  Google Scholar 

  69. Lewis, F.T.: The correlation between cell division and the shapes and sizes of prismatic cells in the epidermis of cucumis. Anat Rec 38, 341–376 (1928)

    Article  Google Scholar 

  70. Lewis, J.: From Signals to Patterns: Space, Time, and Mathematics in Developmental Biology. Science 322, 399–403 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  71. Lieberman, E., Hauert, C., Nowak, M.A.: Evolutionary dynamics on graphs. Nature 433, 312- 316(2005)

    Article  Google Scholar 

  72. Liotta, L.A., Kohn, E.C.: The microenvironment of the tumour-host interface. Nature 411, 375-379(2001)

    Article  Google Scholar 

  73. Mansury, Y., Diggory, M., Deisboeck, T.S.: Evolutionary game theory in an agent-based brain tumor model: Exploring the ‘Genotype-Phenotype’ link. J Theor Biol 238, 146–156 (2006)

    Article  MathSciNet  Google Scholar 

  74. Martin, F.A., Herrera, S.C., Morata, G.S.: Cell competition, growth and size control in the Drosophila wing imaginal disc. Development 136, 3747–3756 (2009)

    Article  Google Scholar 

  75. Marusyk, A., Polyak, K.: Tumor heterogeneity: Causes and consequences. BBA-Rev Cancer 1805, 105-117(2010)

    Google Scholar 

  76. Maynard Smith, J.: The theory of games and the evolution of animal conflicts. J Theor Biol 47, 209–221 (1974)

    Article  MathSciNet  Google Scholar 

  77. Meinhardt, H.: The algorithmic beauty of sea shells. Springer-Verlag New York, Inc., (1995)

    Book  MATH  Google Scholar 

  78. Merks, R.M.H., Glazier, J.A.: A cell-centered approach to developmental biology. Physica A 352, 113-130(2005)

    Article  Google Scholar 

  79. Merks, R.M.H., Guravage, M., Inze, D., Beemster, G.T.S.: VirtualLeaf: an open-source framework for cell-based modeling of plant tissue growth and development. Plant Physiol 155, 656- 666(2011)

    Article  Google Scholar 

  80. Merlo, L.M.F., Pepper, J.W., Reid, B.J., Maley, C.C.: Cancer as an evolutionary and ecological process. Nat Rev Cancer 6, 924–935 (2006)

    Article  Google Scholar 

  81. Meyer-Hermann, M.: Delaunay-Object-Dynamics: Cell Mechanics with a 3D Kinetic and Dynamic Weighted Delaunay-Triangulation. Curr Top in Dev Biol 81, 373–399 (2008)

    Article  Google Scholar 

  82. Michor, F., Iwasa, Y., Nowak, M.A.: Dynamics of cancer progression. Nat Rev Cancer 4, 197–205 (2004)

    Article  Google Scholar 

  83. Moreira, J., Deutsch, A.: Cellular Automation Models of Tumor Development: A Critical Review. Adv Compl Sys 5, 247–268 (2002)

    Article  MATH  Google Scholar 

  84. Moreno, E.: Is cell competition relevant to cancer? Nat Rev Cancer 8, 141–147 (2008)

    Article  Google Scholar 

  85. Morrison, S.J., Spradling, A.C.: Stem Cells and Niches: Mechanisms That Promote Stem Cell Maintenance throughout Life. Cell 132, 598–611 (2008)

    Article  Google Scholar 

  86. Murray, J.D.: Mathematical biology, vol. 2. Springer, (2002)

    MATH  Google Scholar 

  87. Nadell, C.D., Xavier, J.B., Foster, K.R.: The sociobiology of biofilms. FEMS Microbiol Rev 33, 206–224 (2009)

    Article  Google Scholar 

  88. Nagpal, R., Patel, A., Gibson, M.C.: Epithelial topology. Bioessays 30, 260–266 (2008)

    Google Scholar 

  89. Nowak, M.A.: Evolutionary Dynamics: Exploring the Equations of Life. Harvard University Press, Cambridge, MA (2006)

    MATH  Google Scholar 

  90. Nowak, M.A., Michor, F., Komarova, N.L., Iwasa, Y.: Evolutionary dynamics of tumor suppressor gene inactivation. PNAS 101, 10635–10638 (2004)

    Article  Google Scholar 

  91. Nowak, M.A., Sigmund, K.: Evolutionary Dynamics of Biological Games. Science 303, 793799 (2004)

    Google Scholar 

  92. Nowell, P.C.: The clonal evolution of tumor cell populations. Science 194, 23–28 (1976)

    Article  Google Scholar 

  93. Ohtsuki, H., Hauert, C., Lieberman, E., Nowak, M.A.: A simple rule for the evolution of cooperation on graphs and social networks. Nature 441, 502–505 (2006)

    Article  Google Scholar 

  94. Ohtsuki, H., Nowak, M.A.: Evolutionary stability on graphs. J Theor Biol 251, 698–707 (2008)

    Article  MathSciNet  Google Scholar 

  95. Orr, A.W., Helmke, B.P., Blackman, B.R., Schwartz, M.A.: Mechanisms of Mechanotrans- duction. Develop Cell 10, 11–20 (2006)

    Article  Google Scholar 

  96. Osborne, J.M., Walter, A., Kershaw, S.K., Mirams, G.R., Fletcher, A.G., Pathmanathan, P., Gavaghan, D., Jensen, O.E., Maini, P.K., Byrne, H.M.: A hybrid approach to multi-scale modelling of cancer. Phil Trans Roy Soc A 368, 5013–5028 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  97. Pacheco, J.M., Traulsen, A., Nowak, M.A.: Coevolution of Strategy and Structure in Complex Networks with Dynamical Linking. Phys Rev Lett 97, 258103–258104 (2006)

    Article  Google Scholar 

  98. Patel, A.B., Gibson, W.T., Gibson, M.C., Nagpal, R.: Modeling and Inferring Cleavage Patterns in Proliferating Epithelia. PLoS Comput Biol 5, e1000412 (2009)

    Article  Google Scholar 

  99. Perc, M., Szolnoki, A.: Coevolutionary games-A mini review. Biosystems 99, 109–125 (2010)

    Article  Google Scholar 

  100. Pienta, K.J., McGregor, N., Axelrod, R., Axelrod, D.E.: Ecological therapy for cancer: defining tumors using an ecosystem paradigm suggests new opportunities for novel cancer treatments. Transl Oncol 1, 158–164 (2008)

    Article  Google Scholar 

  101. Polyak, K., Haviv, I., Campbell, I.G.: Co-evolution of tumor cells and their microenvironment. Trends Genet 25, 30–38 (2009)

    Article  Google Scholar 

  102. Preziosi, L.: Cancer modelling and simulation, vol. 3. CRC Press, (2003)

    Book  MATH  Google Scholar 

  103. Preziosi, L., Tosin, A.: Multiphase modelling of tumour growth and extracellular matrix interaction: mathematical tools and applications. J Math Biol 58, 625–656 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  104. Prusinkiewicz, P., Lindenmayer, A., Hanan, J.: The algorithmic beauty of plants. Springer Verlag, (1990)

    Book  MATH  Google Scholar 

  105. Rainey, P.B., Kerr, B.: Cheats as first propagules: A new hypothesis for the evolution of individuality during the transition from single cells to multicellularity. BioEssays 32, 872- 880(2010)

    Article  Google Scholar 

  106. Rankin, D.J., Bargum, K., Kokko, H.: The tragedy of the commons in evolutionary biology. Trends Ecol Evol 22, 643–651 (2007)

    Article  Google Scholar 

  107. Rejniak, K.A.: An immersed boundary framework for modelling the growth of individual cells: An application to the early tumour development. J Theor Biol 247, 186–204 (2007)

    Article  MathSciNet  Google Scholar 

  108. Rejniak, K.A., Anderson, A.R.A.: Hybrid models of tumor growth. WIRE Syst Biol Med 3, 115-125(2011)

    Article  Google Scholar 

  109. Rosen, R.: The theory of graphs and its applications. Bull Math Biol 24, 441–443 (1962)

    Google Scholar 

  110. Rozenberg, G.: Handbook of graph grammars and computing by graph transformation: volume I: Foundations. World Scientific, River Edge, NJ, USA (1997)

    Book  MATH  Google Scholar 

  111. Santorelli, L.A., Thompson, C.R.L., Villegas, E., Svetz, J., Dinh, C., Parikh, A., Sucgang, R., Kuspa, A., Strassmann, J.E., Queller, D.C., Shaulsky, G.: Facultative cheater mutants reveal the genetic complexity of cooperation in social amoebae. Nature 451, 1107–1110 (2008)

    Article  Google Scholar 

  112. Santos, F.C., Pacheco, J.M.: Scale-Free Networks Provide a Unifying Framework for the Emergence of Cooperation. Phys Rev Letters 95, 098104 (2005)

    Article  Google Scholar 

  113. Schaller, G., Meyer-Hermann, M.: Kinetic and dynamic Delaunay tetrahedralizations in three dimensions. Comp Phys Comm 162, 9–23 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  114. Schrader, J., Deuster, O., Rinn, B., Schulz, M., Kautz, A., Dodel, R., Meyer, B., Al-Abed, Y., Balakrishnan, K., Reese, J., Bacher, M.: Restoration of contact inhibition in human glioblastoma cell lines after MIF knockdown. BMC Cancer 9, 464 (2009)

    Article  Google Scholar 

  115. Seluanov, A., Hine, C., Azpurua, J., Feigenson, M., Bozzella, M., Mao, Z., Catania, K.C., Gorbunova, V.: Hypersensitivity to contact inhibition provides a clue to cancer resistance of naked mole-rat. PNAS 106, 19352–19357 (2009)

    Article  Google Scholar 

  116. Shirinifard, A., Gens, J.S., Zaitlen, B.L., Poplawski, N.J., Swat, M., Glazier, J.A.: 3D Multi- Cell Simulation of Tumor Growth and Angiogenesis. PLoS ONE 4, e7190 (2009)

    Article  Google Scholar 

  117. Shraiman, B.I.: Mechanical feedback as a possible regulator of tissue growth. PNAS 102, 3318-3323(2005)

    Article  Google Scholar 

  118. Skyrms, B., Pemantle, R.: A dynamic model of social network formation. PNAS 97, 93409346 (2000)

    Article  MATH  Google Scholar 

  119. Smallwood, R.: Computational modeling of epithelial tissues. WIRE Syst Biol Med 1, 191- 201(2009)

    Article  Google Scholar 

  120. Smith, R.S., Guyomarc’h, S., Mandel, T., Reinhardt, D., Kuhlemeier, C., Prusinkiewicz, P.: A plausible model of phyllotaxis. PNAS 103, 1301–1306 (2006)

    Article  Google Scholar 

  121. Spencer, S.L., Gerety, R.A., Pienta, K.J., Forrest, S.: Modeling Somatic Evolution in Tumori- genesis. PLoS Comput Biol 2, e108 (2006)

    Article  Google Scholar 

  122. Szabo, G., Fath, G.: Evolutionary games on graphs. Phys Rep 446, 97–216 (2007)

    Article  MathSciNet  Google Scholar 

  123. Thorne, B.C., Bailey, A.M., Peirce, S.M.: Combining experiments with multi-cell agent- based modeling to study biological tissue patterning. Brief Bioinform 8, 245–257 (2007)

    Article  Google Scholar 

  124. Tomlinson, I.P.M.: Game-theory models of interactions between tumour cells. Eur J Cancer 33, 1495-1500(1997)

    Article  Google Scholar 

  125. Vogel, V., Sheetz, M.: Local force and geometry sensing regulate cell functions. Nat Rev Mol Cell Biol 7, 265–275 (2006)

    Article  Google Scholar 

  126. Walker, D., Georgopoulos, N., Southgate, J.: From pathway to population - a multiscale model of juxtacrine EGFR-MAPK signalling. BMC Sys Biol 2, 102 (2008)

    Article  Google Scholar 

  127. Wang, C.C., Jamal, L., Janes, K.A.: Normal morphogenesis of epithelial tissues and progression of epithelial tumors. WIRE Sys Biol Med 4, 51–78 (2011)

    Article  Google Scholar 

  128. Wang, L.D., Wagers, A.J.: Dynamic niches in the origination and differentiation of haematopoietic stem cells. Nat Rev Mol Cell Biol 12, 643–655 (2011)

    Article  Google Scholar 

  129. West, S.A., Griffin, A.S., Gardner, A.: Social semantics: altruism, cooperation, mutualism, strong reciprocity and group selection. J Evol Biol 20, 415–432 (2007)

    Article  Google Scholar 

  130. Xavier, J.B.: Social interaction in synthetic and natural microbial communities. Mol Syst Biol 7, 483 (2011)

    Article  Google Scholar 

  131. Zhang, L., Athale, C.A., Deisboeck, T.S.: Development of a three-dimensional multiscale agent-based tumor model: Simulating gene-protein interaction profiles, cell phenotypes and multicellular patterns in brain cancer. J Theor Biol 244, 96–107 (2007)

    Article  MathSciNet  Google Scholar 

  132. Zhang, L., Wang, Z., Sagotsky, J.A., Deisboeck, T.S.: Multiscale agent-based cancer modeling. J Math Biol 58, 545–559 (2009)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Acknowledgements

The authors are grateful to Peter Csermely for comments on the manuscript and acknowledge support from the Italian Research Fund FIRB (RBPR0523C3) and from program JAEDoc15 (“Programa junta para la ampliacion de estudios”).

Author information

Authors and Affiliations

  1. The Microsoft Research, University of Trento Centre for Computational and Systems Biology, 38123, Povo (Trento), Italy

    Attila Csikász-Nagy

  2. Logic of Genomic Systems Laboratory, Spanish National Biotechnology Centre (CNB-CSIC), Darwin 3, Campus de Cantoblanco, 28049, Madrid, Spain

    Matteo Cavaliere

  3. INRIA Rennes, Bretagne Atlantique, Campus universitaire de Beaulieu, 35042, Rennes Cedex, France

    Sean Sedwards

Authors
  1. Attila Csikász-Nagy
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Matteo Cavaliere
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sean Sedwards
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Attila Csikász-Nagy .

Editor information

Editors and Affiliations

  1. Department of Experimental Oncology, European Institute of Oncology, Milan, Italy

    Alberto d’Onofrio

  2. Department of Mathematics, University of Pisa, Italy

    Paola Cerrai

  3. Istituto di Analisi dei Sistemi ed Informatica “A. Ruberti“ — CNR, Rome, Italy

    Alberto Gandolfi

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Italia

About this chapter

Cite this chapter

Csikász-Nagy, A., Cavaliere, M., Sedwards, S. (2012). Combining Game Theory and Graph Theory to Model Interactions between Cells in the Tumor Microenvironment. In: d’Onofrio, A., Cerrai, P., Gandolfi, A. (eds) New Challenges for Cancer Systems Biomedicine. SIMAI Springer Series. Springer, Milano. https://doi.org/10.1007/978-88-470-2571-4_1

Download citation

Publish with us

Policies and ethics

Search

Navigation