Abstract
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.
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Notes
- 1.
The SMB: Synthetic Multicellular Bacterium (iGEM’07) Paris Team Web site: http://parts.mit.edu/igem07/index.php/Paris.
- 2.
Relying on a mean-field approach where the idea is to replace all interactions to any entity with an average interaction, reducing any multiple entities problem into an effective one-entity problem.
- 3.
Bailly and Longo (2006) recognize the importance of this class of dynamical systems and call it “dynamicité auto-constituante” (which could be translated to “self-producing dynamicity”), a distinctive feature of living organisms.
- 4.
The Website of the project is http://mgs.spatial-computing.org.
- 5.
The BioBricks are available in the Registry of Standard Biological Parts at the following Web site http://partsregistry.org/Main_Page.
- 6.
- 7.
The third dimension is not considered as the SMBis supposed to grow in the plane of a Petri dish, for example.
- 8.
The whole MGSprogram of the simulation is available at http://mgs.spatial-computing.org/integrative_biology.tgz.
References
F. Aurenhammer. Voronoi diagrams–A survey of a fundamental geometric data structure. ACM Comput Surv, 23 (3): 345–405, 1991
F. Bailly and G. Longo. Mathmatiques et sciences de la nature. Hermann, Paris, 2006
J.-P. Banâtre and D. LeMetayer. Programming by multiset transformation. Comm ACM, 36 (1): 98, 1993
J.-P. Banâtre, P. Fradet, and Y. Radenac. Generalised multisets for chemical programming. Math Struct Comput Sci, 16 (4): 557–580, 2006
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, 2006a
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), 2003
R. Durrett and S. Levin. The importance of being discrete (and spatial). Theor Popul Biol, 46 (3): 363–394, 1994
M. Eden. A two-dimensional growth process. In Proceedings of Fourth Berkeley Symposium on Mathematics, Statistics, and Probability, Vol. 4, pages 223–239, 1961
M. Eigen and P. Schuster. The hypercycle: A principle of natural self-organization. Springer, Berlin, 1979
D. Endy. Foundations for engineering biology. Nature, 438: 449–453, 2005
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, 1965
M. Fisher, G. Malcolm, and R. Paton. Spatio-logical processes in intracellular signalling. BioSystems, 55: 83–92, 2000
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, 1992
W. Fontana and L. W. Buss. “The arrival of the fittest”: Toward a theory of biological organization. Bull Math Biol, 1994
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, 2003
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, 2001
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, 2002a
J.-L. Giavitto and O. Michel. Pattern-matching and rewriting rules for group indexed data structures. ACM SIGPLAN Not, 37 (12): 76–87, 2002b
J.-L. Giavitto and O. Michel. The topological structures of membrane computing. Fundam Inform, 49: 107–129, 2002c
J.-L. Giavitto and O. Michel. Modeling the topological organization of cellular processes. BioSystems, 70 (2): 149–163, 2003
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, 2008a
J.-L. Giavitto and A. Spicher. Topological rewriting and the geometrization of programming. Physica D, 237: 1302–1314, 2008b
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, 2002a
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, 2002b
J.-L. Giavitto, G. Malcolm, and O. Michel. Rewriting systems and the modelling of biological systems. Comp Funct Genomics, 5: 95–99, 2004
M. C. Gibson, A. B. Patel, R. Nagpal, and N. Perrimon. The emergence of geometric order in proliferating metazoan epithelia. Nature, 442: 1038–1041, 2006
D. T. Gillespie. Exact stochastic simulation of coupled chemical reactions. J Phys Chem, 81 (25): 2340–2361, 1977
J. Greenberg and S. Hastings. Spatial patterns for discrete models of diffusion in excitable media. SIAM J Appl Math, pages 515–523, 1978
Y. Itkis. Control systems of variable structure. Wiley, New York, 1976
P. Jansson and J. Jeuring. PolyP – A polytypic programming language extension. In Principles of programming languages, pages 470–482. ACM, 1997
T. Knight. Idempotent vector design for standard assembly of biobricks, 2006. MIT Synthetic Biology Working Group
A. Lindenmayer. Mathematical models for cellular interaction in development, Parts I and II. J Theor Biol, 18: 280–315, 1968a
P. L. Luisi. Autopoiesis: A review and a reappraisal. Naturwissenschaften, 90: 49–59, 2003
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, 2008
H. McAdams and L. Shapiro. Circuit simulation of genetic networks. Science, 269 (5224): 650, 1995
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, 2009
J. Munkres. Elements of algebraic topology. Addison-Wesley, Reading, MA, 1984
G. Păun. From cells to computers: Computing with membranes (P systems). Biosystems, 59 (3): 139–158, 2001
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, 2000
J. Smith. Shaping life: Genes, embryos and evolution. Yale University Press, New Haven, 1999
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, 2005
A. Spicher and O. Michel. Declarative modeling of a neurulation-like process. BioSystems, 87 (2–3): 281–288, 2007.
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, 2009
A.M. Turing. The chemical basis of morphogenesis, Series B: Biological Sciences. Phil Trans R Soc Lond, 237: 37–72, 1952
G. Turk. Generating textures for arbitrary surfaces using reaction-diffusion. In T.W. Sederberg, editor, Computer Graphics (SIGGRAPH ’91 Proceedings), pages 289–298, 1991
F.J. Varela, H.R. Maturana, and R. Uribe. Autopoiesis: The organization of living systems, its characterization and a model. BioSystems, 5: 187–196, 1974
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, 2000
J. Von Neumann. Theory of self-reproducing automata. University of Illinois Press, Urbana, 1966
S. Wolfram. Theory and applications of cellular automata. World Scientific Publication, Singapore, 1986
M. Woolridge and M. Wooldridge. Introduction to multiagent systems. Wiley, New York, 2001
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, 2003
Acknowledgements
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.
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Spicher, A., Michel, O., Giavitto, JL. (2011). Interaction-Based Simulations for Integrative Spatial Systems Biology. In: Dubitzky, W., Southgate, J., Fuß, H. (eds) Understanding the Dynamics of Biological Systems. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-7964-3_10
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