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Lattice-gas Cellular Automaton Modeling of Developing Cell Systems

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Book cover Single-Cell-Based Models in Biology and Medicine

Part of the book series: Mathematics and Biosciences in Interaction ((MBI))

Abstract

Cellular automata can be viewed as spatially extended decentralized systems made up of a number of individual components and may serve as simple models of complex systems. Here, we show that a particular cellular automaton class, lattice-gas cellular automata (LGCA), is well suited for the modeling of developing cell systems characterized by motion and interaction of biological cells. As examples, we present LGCA models of adhesion and chemotaxis. We conclude with a detailed discussion on the relevance of LGCA models.

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References

  1. T. Alarcon, H. Byrne, and P. K. Maini. A cellular automaton for tumour growth in inhomogeneous environment. J. Theor. Biol., 225:257–274, 2003.

    Article  Google Scholar 

  2. F. J. Alexander, I. Edrei, P. L. Garrido, and 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 

  3. W. Alt and G. Hoffmann, editors. Biological motion. Springer-Verlag, Berlin, Heidelberg, New York, 1990.

    MATH  Google Scholar 

  4. P. B. Armstrong. The control of cell motility during embryogenesis. Cancer Metast. Rev., 4:59–80, 1985.

    Article  Google Scholar 

  5. F. Bagnoli. Cellular automata. In F. Bagnoli, P. Lio, and S. Ruffo, editors, Dynamical modelling in biotechnologies. World Scientific, Singapore, 1998.

    Google Scholar 

  6. U. Börner, A. Deutsch, H. Reichenbach, and M. Bär. Rippling patterns in aggregates of myxobacteria arise from cell-cell collisions. Phys. Rev. Lett., 89:078101, 2002.

    Article  Google Scholar 

  7. H. Bussemaker. Analysis of a pattern forming lattice gas automaton: mean field theory and beyond. Phys. Rev. E, 53(2):1644–1661, 1996.

    Article  Google Scholar 

  8. J. L. Casti. Alternate realities. John Wiley, New York, 1989.

    MATH  Google Scholar 

  9. J. L. Casti. Science is a computer program. Nature, 417:381–382, 2002. book review.

    Article  Google Scholar 

  10. Y. Y. Chang. Cyclic 3′,5′-adenosine monophosphate phosphodiesterase produced by the slime mold Dictyostelium discoideum. Science, 161:57–59, 1968.

    Article  Google Scholar 

  11. P. P. Chaudhuri, D. R. Chowdhury, S. Nandi, and S. Chatterjee. Additive cellular automata — Theory and Applications, vol. 1. IEEE Computer Society Press, CA, USA, 1997.

    MATH  Google Scholar 

  12. M. Y. Chen, R. H. Insall, and P. N. Devreotes. Signaling through chemoattractant receptors in Dictyostelium. Trends Genet., 12:52–57, 1996.

    Article  Google Scholar 

  13. B. Chopard and M. Droz. Cellular automata modeling of physical systems. Cambridge University Press, Cambridge, 1998.

    MATH  Google Scholar 

  14. B. Chopard, A. Dupuis, A. Masselot, and P. Luthi. Cellular automata and lattice Boltzmann techniques: an approach to model and simulate complex systems. Adv. Compl. Syst., 5(2), 2002.

    Google Scholar 

  15. A. Czirók, A. Deutsch, and M. Wurzel. Individual-based models of cohort migration in cell cultures. In W. Alt, M. Chaplain, M. Griebel, and J. Lenz, editors, Models of polymer and cell dynamics, Basel, 2003. Birkhäuser.

    Google Scholar 

  16. J. C. Dallon, H. G. Othmer, C. v. Oss, A. Panfilov, P. Hogeweg, T. Höfer, and P. K. Maini. Models of Dictyostelium discoideum aggregation. In W. Alt, A. Deutsch, and G. Dunn, editors, Dynamics of cell and tissue motion, pages 193–202. Birkhäuser, Basel, 1997.

    Google Scholar 

  17. A. Deutsch and S. Dormann. Cellular automaton modeling of biological pattern formation. Birkhauser, Boston, 2005.

    MATH  Google Scholar 

  18. S. Dormann and A. Deutsch. Modeling of self-organized avascular tumor growth with a hybrid cellular automaton. In Silico Biol., 2:0035, 2002.

    Google Scholar 

  19. D. Drasdo. On selected individual-based approaches to the dynamics in multicellular systems. In W. Alt, M. Chaplain, M. Griebel, and J. Lenz, editors, Models of polymer and cell dynamics. Birkhäuser, Basel, 2003.

    Google Scholar 

  20. R. Durrett and S. Levin. The importance of being discrete (and spatial). Theor. Popul. Biol., 46:363–394, 1994.

    Article  MATH  Google Scholar 

  21. U. Frisch, B. Hasslacher, and Y. Pomeau. Lattice-gas automata for the Navier-Stokes equation. Phys. Rev. Lett., 56(14):1505–1508, 1986.

    Article  Google Scholar 

  22. R. Gatenby and P. K. Maini. Cancer summed up. Nature, 421:321, 2003.

    Article  Google Scholar 

  23. J. A. Glazier and F. Graner. Simulation of the differential adhesion driven rearrangement of biological cells. Phys. Rev. E, 47(3):2128–2154, 1993.

    Article  Google Scholar 

  24. D. Godt and U. Tepass. Drosophila oocyte localization is mediated by differential cadherin-based adhesion. Nature, 395:387–391, 1998.

    Article  Google Scholar 

  25. A. Goldbeter. Oscillations and waves of cyclic AMP in Dictyostelium discoideum: a prototype for spatio-temporal organizaation and pulsatile intercellular communication. Bull. Math. Biol., 68:1095–1109, 2006.

    Article  Google Scholar 

  26. J. Hardy, Y. Pomeau, and O. de Pazzis. Time evolution of a two-dimensional model system. i. invariant states and time correlation functions. J. Math. Phys., 14:1746, 1973.

    Article  Google Scholar 

  27. L. P. Kadanoff. On two levels. Phys. Today, Sept.:7–9, 1986.

    Google Scholar 

  28. E. F. Keller and L. A. Segel. Initiation of slime mold aggregation viewed as an instability. J. Theor. Biol., 26:399–415, 1970.

    Article  Google Scholar 

  29. E. F. Keller and L. A. Segel. A model for chemotaxis. J. Theor. Biol., 30:225–234, 1971.

    Article  Google Scholar 

  30. E. F. Keller and L. A. Segel. Travelling bands of chemotactic bacteria: A theoretical analysis. J. Theor. Biol., 30:235–248, 1971.

    Article  Google Scholar 

  31. P. K. Maini. Mathematical models in morphogenesis. In V. Capasso and O. Dieckmann, editors, Mathematics Inspired by Biology, pages 151–189. Springer, Berlin, 1999.

    Chapter  Google Scholar 

  32. P. K. Maini, K. J. Painter, and H. N. P. Chau. Spatial pattern formation in chemical and biological systems. J. Chem. Soc., Faraday Trans., 93(20):3601–3610, 1997.

    Article  Google Scholar 

  33. A. F. M. Marée and P. Hogeweg. How amoeboids self-organize into a fruiting body: Multicellular coordination in Dictyostelium discoideum. Proc. Natl. Acad. Sci. USA, 98:3879–3883, 2001.

    Article  Google Scholar 

  34. M. Mitchell. Is the universe a universal computer? Science, 298:65–68, 2002. book review.

    Article  Google Scholar 

  35. J. Moreira and A. Deutsch. Cellular automaton models of tumour development — a critical review. Adv. Compl Syst. (ACS), 5(2):1–21, 2002.

    Google Scholar 

  36. J. D. Murray. Mathematical Biology. Springer, New York, 3 edition, 2002.

    MATH  Google Scholar 

  37. H. G. Othmer, P. K. Maini, and J. D. Murray, editors. Experimental and theoretical advances in biological pattern formation, New York, 1993. Plenum Press.

    Google Scholar 

  38. M. Pfeifer. Developmental biology: birds of a feather flock together. Nature, 395:324–325, 1998.

    Article  Google Scholar 

  39. N. J. Savill and P. Hogeweg. Modeling morphogenesis: from single cells to crawling slugs. J. Theor. Biol., 184:229–235, 1997.

    Article  Google Scholar 

  40. B. Schönfisch. Anisotropy in cellular automata. BioSystems, 41:29–41, 1997.

    Article  Google Scholar 

  41. B. Schönfisch and A. de Roos. Synchronous and asynchronous updating in cellular automata. BioSystems, 51:123–143, 1999.

    Article  Google Scholar 

  42. K. Sigmund. Games of life — explorations in ecology, evolution, and behaviour. Oxford University Press, Oxford, 1993.

    Google Scholar 

  43. J. Starruss, T. Bley, L. Soegaard-Andersen, and A. Deutsch. A new mechanism for collective migration of Myxococcus xanthus. J. Statist. Phys., 2007.

    Google Scholar 

  44. A. M. Turing. The chemical basis of morphogenesis. Phil. Trans. R. Soc. London, 237:37–72, 1952.

    Article  Google Scholar 

  45. A. Voss-Böhme and A. Deutsch. An interacting particle approach to models of differential adhesion, 2007. in preparation.

    Google Scholar 

  46. J. R. Weimar. Coupling microscopic and macroscopic cellular automata. Parall. Comput., 27:601–611, 2001.

    Article  MATH  Google Scholar 

  47. J. R. Weimar, D. Dab, J.-P. Boon, and S. Succi. Fluctuation correlations in reactiondiffusion systems: Reactive lattice gas automata approach. Europhys. Lett., 20(7):627–632, 1992.

    Article  Google Scholar 

  48. S. Wolfram, editor. Theory and applications of cellular automata, Singapore, 1986. World Publishing Co.

    Google Scholar 

  49. S. Wolfram. A new kind of science. Wolfram Media, Inc, 2002.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Center for Information Services and High Performance Computing, Dresden University of Technology, Zellescher Weg 12, D-01062, Dresden, Germany

    Andreas Deutsch

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  1. Andreas Deutsch
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Editor information

Editors and Affiliations

  1. Division of Mathematics, University of Dundee, 23 Perth Road, Dundee, DD1 4HN, UK

    Alexander R. A. Anderson , Mark A. J. Chaplain  & Katarzyna A. Rejniak ,  & 

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© 2007 Birkhäuser Verlag Basel/Switzerland

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Deutsch, A. (2007). Lattice-gas Cellular Automaton Modeling of Developing Cell Systems. In: Anderson, A.R.A., Chaplain, M.A.J., Rejniak, K.A. (eds) Single-Cell-Based Models in Biology and Medicine. Mathematics and Biosciences in Interaction. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8123-3_2

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