Interaction-Based Simulations for Integrative Spatial Systems Biology

  • Antoine SpicherEmail author
  • Olivier Michel
  • Jean-Louis Giavitto


Systems biology aims at integrating processes at various time and spatial scales into a single and coherent formal description to allow analysis and computer simulation. In this context, we focus on rule-based modeling and its integration in the domain-specific language MGS. Through the notions of topological collections and transformations, MGS allows the modeling of biological processes at various levels of description. We validate our approach through the description of various models of a synthetic bacteria designed in the context of the International Genetically Engineered Machine Competition, from a very simple biochemical description of the process to an individual-based model on a Delaunay graph topology. This approach is a first step into providing the requirements for the emerging field of spatial systems biology which integrates spatial properties into systems biology.


Cellular Automaton Synthetic Biology Cellular Automaton Ordinary Differential Equation Germinal Cell 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The authors would like to thank the reviewers for their valuable comments on a first version of this chapter.

We gratefully acknowledge all the people who contributed to make the first French participation in iGEM in 2007 a success: the students, D. Bikard, F. Caffin, N. Chiaruttini, T. Clozel, D. Guegan, T. Landrain, D. Puyraimond, A. Rizk, E. Shotar, G. Vieira, the instructors, F. Delaplace, S. Bottani, A. Jaramillo, A. Lindner, V. Schächter; the advisors, F. Le Fevre, M. Suarez, S. Smidtas, A. Spicher, and P. Tortosa.

Further acknowledgments are also due to J. Cohen, B. Calvez, F. Thonnerieux, C. Kodrnja, and F. Letierce who have contributed in various ways to the MGSproject.

This research is supported in part by the the University of Évry, the University of Paris-Est, the CNRS, GENOPOLE-Évry, the Institute for Complex Systems in Paris-Ile de France, the ANR white project AutoChem and the French working group GDR GPL/LTP.


  1. .
    F. Aurenhammer. Voronoi diagrams–A survey of a fundamental geometric data structure. ACM Comput Surv, 23 (3): 345–405, 1991CrossRefGoogle Scholar
  2. .
    F. Bailly and G. Longo. Mathmatiques et sciences de la nature. Hermann, Paris, 2006Google Scholar
  3. .
    J.-P. Banâtre and D. LeMetayer. Programming by multiset transformation. Comm ACM, 36 (1): 98, 1993Google Scholar
  4. .
    J.-P. Banâtre, P. Fradet, and Y. Radenac. Generalised multisets for chemical programming. Math Struct Comput Sci, 16 (4): 557–580, 2006CrossRefGoogle Scholar
  5. .
    P. Barbier de Reuille, I. Bohn-Courseau, K. Ljung, H. Morin, N. Carraro, C. Godin, and J. Traas. Computer simulations reveal novel properties of the cell-cell signaling network at the shoot apex in Arabidopsis. Proc Natl Acad Sc USA, 103 (5): 1627–1632, 2006aCrossRefGoogle Scholar
  6. .
    K. De Cock, X. Zhang, M. F. Bugallo, and P. M. Djuric. Stochastic simulation and parameter estimation of first order chemical reactions. In 12th European Signal Processing Conference (EUSIPCO’04), 2003Google Scholar
  7. .
    R. Durrett and S. Levin. The importance of being discrete (and spatial). Theor Popul Biol, 46 (3): 363–394, 1994CrossRefGoogle Scholar
  8. .
    M. Eden. A two-dimensional growth process. In Proceedings of Fourth Berkeley Symposium on Mathematics, Statistics, and Probability, Vol. 4, pages 223–239, 1961Google Scholar
  9. .
    M. Eigen and P. Schuster. The hypercycle: A principle of natural self-organization. Springer, Berlin, 1979Google Scholar
  10. .
    D. Endy. Foundations for engineering biology. Nature, 438: 449–453, 2005PubMedCrossRefGoogle Scholar
  11. .
    E. Fermi, J. Pasta, and S. Ulam. Studies of nonlinear problems, LASL Report LA-1940 (5). Technical report, 1965. Reprinted in the collected work of E. Fermi, Vol. 2, pp. 977–988, 1965Google Scholar
  12. .
    M. Fisher, G. Malcolm, and R. Paton. Spatio-logical processes in intracellular signalling. BioSystems, 55: 83–92, 2000PubMedCrossRefGoogle Scholar
  13. .
    W. Fontana. Algorithmic chemistry. In C. G. Langton, C. Taylor, J. D. Farmer, and S. Rasmussen, editors, Proceedings of the Workshop on Artificial Life (ALIFE’90), Vol. 5, pages 159–210, 1992Google Scholar
  14. .
    W. Fontana and L. W. Buss. “The arrival of the fittest”: Toward a theory of biological organization. Bull Math Biol, 1994Google Scholar
  15. .
    J.-L. Giavitto. Topological collections, transformations and their application to the modeling and the simulation of dynamical systems. In Rewriting Techniques and Applications (RTA’03), LNCS 2706, pages 208–233, 2003Google Scholar
  16. .
    J.-L. Giavitto and O. Michel. Declarative definition of group indexed data structures and approximation of their domains. In Proceedings of the 3rd ACM SIGPLAN International Conference on Principles and Practice of Declarative Programming (PPDP’01), pages 150–161, 2001Google Scholar
  17. .
    J.-L. Giavitto and O. Michel. Data structure as topological spaces. In Proceedings of the 3nd International Conference on Unconventional Models of Computation UMC’02, Vol. LNCS 2509, pages 137–150, 2002aGoogle Scholar
  18. .
    J.-L. Giavitto and O. Michel. Pattern-matching and rewriting rules for group indexed data structures. ACM SIGPLAN Not, 37 (12): 76–87, 2002bCrossRefGoogle Scholar
  19. .
    J.-L. Giavitto and O. Michel. The topological structures of membrane computing. Fundam Inform, 49: 107–129, 2002cGoogle Scholar
  20. .
    J.-L. Giavitto and O. Michel. Modeling the topological organization of cellular processes. BioSystems, 70 (2): 149–163, 2003PubMedCrossRefGoogle Scholar
  21. .
    J.-L. Giavitto and A. Spicher. Simulation of self-assembly processes using abstract reduction systems. In Systems self-assembly: Sultidisciplinary snapshots, pages 199–223. Elsevier, 2008aGoogle Scholar
  22. .
    J.-L. Giavitto and A. Spicher. Topological rewriting and the geometrization of programming. Physica D, 237: 1302–1314, 2008bCrossRefGoogle Scholar
  23. .
    J.-L. Giavitto, C. Godin, O. Michel, and P. Prusinkiewicz. Modelling and simulation of biological processes in the context of genomics. In Computational Models for Integrative and Developmental Biology, 2002aGoogle Scholar
  24. .
    J.-L. Giavitto, O. Michel, and J. Cohen. Pattern-matching and rewriting rules for group indexed data structures. In ACM Sigplan Workshop (RULE’02), pages 55–66, 2002bGoogle Scholar
  25. .
    J.-L. Giavitto, G. Malcolm, and O. Michel. Rewriting systems and the modelling of biological systems. Comp Funct Genomics, 5: 95–99, 2004PubMedCrossRefGoogle Scholar
  26. .
    M. C. Gibson, A. B. Patel, R. Nagpal, and N. Perrimon. The emergence of geometric order in proliferating metazoan epithelia. Nature, 442: 1038–1041, 2006PubMedCrossRefGoogle Scholar
  27. .
    D. T. Gillespie. Exact stochastic simulation of coupled chemical reactions. J Phys Chem, 81 (25): 2340–2361, 1977CrossRefGoogle Scholar
  28. .
    J. Greenberg and S. Hastings. Spatial patterns for discrete models of diffusion in excitable media. SIAM J Appl Math, pages 515–523, 1978Google Scholar
  29. .
    Y. Itkis. Control systems of variable structure. Wiley, New York, 1976Google Scholar
  30. .
    P. Jansson and J. Jeuring. PolyP – A polytypic programming language extension. In Principles of programming languages, pages 470–482. ACM, 1997Google Scholar
  31. .
    T. Knight. Idempotent vector design for standard assembly of biobricks, 2006. MIT Synthetic Biology Working GroupGoogle Scholar
  32. .
    A. Lindenmayer. Mathematical models for cellular interaction in development, Parts I and II. J Theor Biol, 18: 280–315, 1968aPubMedCrossRefGoogle Scholar
  33. .
    P. L. Luisi. Autopoiesis: A review and a reappraisal. Naturwissenschaften, 90: 49–59, 2003PubMedGoogle Scholar
  34. .
    J. Lynch. Logical characterization of individual-based models. In 23rd Annual IEEE Symposium on Logic in Computer Science (LICS’08), volume n, pages 379–390, 2008Google Scholar
  35. .
    H. McAdams and L. Shapiro. Circuit simulation of genetic networks. Science, 269 (5224): 650, 1995Google Scholar
  36. .
    O. Michel, A. Spicher, and J.-L Giavitto. Rule-based programming for integrative biological modeling – Application to the modeling of the λ phage genetic switch. Nat Comput, 8 (4): 865–889, 2009Google Scholar
  37. .
    J. Munkres. Elements of algebraic topology. Addison-Wesley, Reading, MA, 1984Google Scholar
  38. .
    G. Păun. From cells to computers: Computing with membranes (P systems). Biosystems, 59 (3): 139–158, 2001PubMedCrossRefGoogle Scholar
  39. .
    N.M. Shnerb, Y. Louzoun, E. Bettelheim, and S. Solomon. The importance of being discrete: Life always wins on the surface. PNAS, 97 (19): 10322–10324, 2000PubMedCrossRefGoogle Scholar
  40. .
    J. Smith. Shaping life: Genes, embryos and evolution. Yale University Press, New Haven, 1999Google Scholar
  41. .
    A. Spicher and O. Michel. Using rewriting techniques in the simulation of dynamical systems: Application to the modeling of sperm crawling. In Fifth International Conference on Computational Science (ICCS’05), Part I’, Vol. 3514 of LNCS, pages 820–827, 2005Google Scholar
  42. .
    A. Spicher and O. Michel. Declarative modeling of a neurulation-like process. BioSystems, 87 (2–3): 281–288, 2007.PubMedCrossRefGoogle Scholar
  43. .
    A. Spicher, N. Fats, and O. Simonin. From reactive multi-agents models to cellular automata. In International Conference on Agents and Artificial Intelligence, pages 422–429, 2009Google Scholar
  44. .
    A.M. Turing. The chemical basis of morphogenesis, Series B: Biological Sciences. Phil Trans R Soc Lond, 237: 37–72, 1952CrossRefGoogle Scholar
  45. .
    G. Turk. Generating textures for arbitrary surfaces using reaction-diffusion. In T.W. Sederberg, editor, Computer Graphics (SIGGRAPH ’91 Proceedings), pages 289–298, 1991Google Scholar
  46. .
    F.J. Varela, H.R. Maturana, and R. Uribe. Autopoiesis: The organization of living systems, its characterization and a model. BioSystems, 5: 187–196, 1974CrossRefGoogle Scholar
  47. .
    G. Von Dassow, E. Meir, E. M. Munro, and G. Odell. The segment polarity network is a robust developmental module. Nature, 406 (6792): 188–192, 2000CrossRefGoogle Scholar
  48. .
    J. Von Neumann. Theory of self-reproducing automata. University of Illinois Press, Urbana, 1966Google Scholar
  49. .
    S. Wolfram. Theory and applications of cellular automata. World Scientific Publication, Singapore, 1986Google Scholar
  50. .
    M. Woolridge and M. Wooldridge. Introduction to multiagent systems. Wiley, New York, 2001Google Scholar
  51. .
    X. Zhang, K. De Cock, M.F. Bugallo, and P.M. Djuric. Stochastic simulation and parameter estimation of enzyme reaction models. In IEEE Workshop on Statistical Signal Processing, 2003Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Antoine Spicher
    • 1
    Email author
  • Olivier Michel
  • Jean-Louis Giavitto
  1. 1.LACL – EA 4219 – Université de Paris 12Créteil CedexFrance

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