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Lattice-Gas Cellular Automaton Modeling of Emergent Behavior in Interacting Cell Populations

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Book cover Simulating Complex Systems by Cellular Automata

Part of the book series: Understanding Complex Systems ((UCS))

Abstract

Biological organisms are complex systems characterized by collective behavior emerging out of the interaction of a large number of components (molecules and cells). In complex systems, even if the basic and local interactions are perfectly known, it is possible that the global (collective) behavior obeys new laws that are not obviously extrapolated from the individual properties. Only an understanding of the dynamics of collective effects at the molecular, and cellular scale allows answers to biological key questions such as: what enables ensembles of molecules to organize themselves into cells? How do ensembles of cells create tissues and whole organisms? Key to solving these problems is the design and analysis of appropriate mathematical models for spatio-temporal pattern formation.

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References

  1. F.J. Alexander, I.Edrei, P.L. Garrido, J.L. Lebowitz, Phase transitions in a probabilistic cellular automaton: growth kinetics and critical properties. J. Statist. Phys. 68(3/4), 497–514, (1992)

    Article  MATH  Google Scholar 

  2. A.R. Anderson, A.M. Weaver, P.T. Cummings, V. Quaranta, Tumor morphology and phenotypic evolution driven by selective pressure from the microenvironment. Cell 127(5), 905–915, (2006)

    Article  Google Scholar 

  3. D. Basanta, H. Hatzikirou, A. Deutsch, The emergence of invasiveness in tumours: A game theoretic approach. Eur. Phys. J. B 63, 393–397, (2008)

    Article  MATH  MathSciNet  Google Scholar 

  4. D. Basanta, M. Simon, H. Hatzikirou, A. Deutsch, An evolutionary game theory perspective elucidates the role of glycolysis in tumour invasion. Cell Prolif. 41, 980–987, (2008)

    Article  Google Scholar 

  5. R.D. Benguria, M.C. Depassier, V. Mendez, Propagation of fronts of a reaction-convection-diffusion equation. Phys. Rev. E 69, 031106, (2004)

    Article  MathSciNet  Google Scholar 

  6. D. Bray, Cell Movements (Garland Publishing, New York, 1992)

    Google Scholar 

  7. H.P. Breuer, W. Huber, F. Petruccione, Fluctuation effects on wave propagation in a reaction-diffusion process. Phys. D 73, 259, (1994)

    Article  MATH  Google Scholar 

  8. A. Bru, S. Albertos, J.L. Subiza, J. Lopez Garcia-Asenjo, I. Bru, The universal dynamics of tumor growth. Bioph. J. 85, 2948–2961, (2003)

    Article  Google Scholar 

  9. I. Brunet, B. Derrida Shift in the velocity of a front due to a cutoff. Phys. Rev. E 56(3), 2597–2604, (1997)

    Article  MathSciNet  Google Scholar 

  10. I. Brunet, B. Derrida Effect of microscopic noise in front propagation. J. Stat. Phys. 103(1/2), 269–282, (2001)

    Article  MATH  MathSciNet  Google Scholar 

  11. H. Bussemaker, Analysis of a pattern forming lattice gas automaton: Mean field theory and beyond. Phys. Rev. E 53(4), 1644–1661, (1996)

    Google Scholar 

  12. S.B. Carter, Principles of cell motility: the direction of cell movement and cancer invasion. Nature 208(5016), 1183–1187, (1965)

    Article  Google Scholar 

  13. B. Chopard, M. Droz, Cellular Automata Modeling of Physical Systems (Cambridge University Press, Cambridge, 1998)

    Book  MATH  Google Scholar 

  14. E. Cohen, D. Kessler, H. Levine, Fluctuation-regularized front propagation dynamics in reaction-diffusion systems. Phys. Rev. Lett. 94, 158302, (2005)

    Article  Google Scholar 

  15. A. Deutsch, S. Dormann, Cellular Automaton Modeling of Biological Pattern Formation (Birkhäuser, Basel 2005)

    MATH  Google Scholar 

  16. R.B. Dickinson, R.T. Tranquillo, A stochastic model for cell random motility and haptotaxis based on adhesion receptor fuctuations. J. Math. Biol. 31, 563–600, (1993).

    Article  MATH  Google Scholar 

  17. G.D. Doolen, Lattice Gas Methods for Partial Differential Equations (Addison-Wesley, New York, 1990)

    MATH  Google Scholar 

  18. D. Drasdo, S. Höhme, Individual-based approaches to birth and death in avascular tumors. Math. Comp. Model. 37, 1163–1175, (2003)

    Article  MATH  Google Scholar 

  19. P. Friedl, Prespecification and plasticity: shifting mechanisms of cell migration. Curr. Opin. Cell. Biol. 16(1), 14–23, (2004)

    Article  Google Scholar 

  20. U. Frisch, D. d’Humieres, B. Hasslacher, P. Lallemand, Y. Pomeau, J.P. Rivet, Lattice gas hydrodynamics in two and three dimensions. Compl. Syst. 1, 649–707, (1987)

    MATH  MathSciNet  Google Scholar 

  21. H. Hatzikirou, L. Brusch, C. Schaller, M. Simon, A. Deutsch, Prediction of traveling front behavior in a lattice-gas cellular automaton model for tumor invasion. Comput. Math. Appl. 59, 2326–2339, (2010)

    Article  MATH  MathSciNet  Google Scholar 

  22. H. Hatzikirou, A. Deutsch, Cellular automata as microscopic models of cell migration in heterogeneous environments. Curr. Top. Dev. Biol. 81, 401–434, (2008)

    Article  Google Scholar 

  23. A. Lesne, Discrete vs continuous controversy in physics. Math. Struct. Comp. Sc. 17(2), 185–223, (2007)

    Article  MATH  MathSciNet  Google Scholar 

  24. J.B. McCarthy, L.T. Furcht, Laminin and fibronectin promote the haptotactic migration of b16 mouse melanoma cells. J. Cell Biol. 98(4), 1474–1480, (1984)

    Article  Google Scholar 

  25. H. Meinhardt, Models of Biological Pattern Formation (Academic New York, 1982)

    Google Scholar 

  26. J. Murray, Mathematical Biology I: An Introduction (Springer, Heidelberg 2001)

    Google Scholar 

  27. S.P. Palecek, J.C. Loftus, M.H. Ginsberg, D.A. Lauffenburger, A. F. Horwitz, Integrin-ligand binding governs cell-substratum adhesiveness. Nature 388(6638), 210, (1997)

    Article  Google Scholar 

  28. D.H. Rothman, S. Zaleski, Lattice-gas models of phase separation: interfaces, phase transitions, and multiphase flow. Rev. Mod. Phys. 66(4), 1417–1479, (1994)

    Article  Google Scholar 

  29. M. Saxton, Anomalous diffusion due to obstacles: a Monte Carlo study. Biophys. J. 66, 394–401, (1994)

    Article  Google Scholar 

  30. M.V. Velikanov, R. Kapral, Fluctuation effects on quadratic autocatalysis fronts. J. Chem. Phys. 110, 109–115, (1999)

    Article  Google Scholar 

  31. J. von Neumann, Theory of Self-Reproducing Automata (University of Illinois Press, Urbana, IL, 1966)

    Google Scholar 

  32. D.A. Wolf-Gladrow, Lattice-gas Cellular Automata and Lattice Boltzmann Models: An Introduction (Springer, Heidelberg 2005)

    Google Scholar 

  33. S. Wolfram, A New Kind of Science (Wolfram Media, Inc., Champaign, IL 2002)

    MATH  Google Scholar 

  34. M.H. Zaman, P. Matsudaira, D.A. Lauffenburger, Understanding effects of matrix protease and matrix organization on directional persistence and translational speed in three-dimensional cell migration. Ann. Biomed. Eng. 35(1), 91–100, (2006)

    Article  Google Scholar 

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Authors and Affiliations

  1. Center for Information Services and High Performance Computing, Technische Universität Dresden, Nöthnitzerstr. 46, 01069, Dresden, Germany

    Haralambos Hatzikirou & Andreas Deutsch

Authors
  1. Haralambos Hatzikirou
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  2. Andreas Deutsch
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Corresponding author

Correspondence to Haralambos Hatzikirou .

Editor information

Editors and Affiliations

  1. Havlickova 482, Stahlavy, CZ 33203, Czech Republic

    Jiri Kroc

  2. Fac. Science, Informatics Institute, Universiteit Amsterdam, Kruislaan 403, Amsterdam, 1098 SJ, Netherlands

    Peter M.A. Sloot

  3. , Computational Science Faculty, University of Amsterdam, Science Park 107, Amsterdam, 1098 XG, Netherlands

    Alfons G. Hoekstra

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Hatzikirou, H., Deutsch, A. (2010). Lattice-Gas Cellular Automaton Modeling of Emergent Behavior in Interacting Cell Populations. In: Kroc, J., Sloot, P., Hoekstra, A. (eds) Simulating Complex Systems by Cellular Automata. Understanding Complex Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12203-3_13

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  • DOI: https://doi.org/10.1007/978-3-642-12203-3_13

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-12202-6

  • Online ISBN: 978-3-642-12203-3

  • eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)

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