On Using Divide and Conquer in Modeling Natural Systems

  • Yaki SettyEmail author
  • Irun R. Cohen
  • Avi E. Mayo
  • David Harel
Part of the Natural Computing Series book series (NCS)


In recent years, we have been studying approaches to the realistic modeling of natural systems, especially biological systems. We have tested several of these in a project devoted to modeling pancreatic organogenesis, a complex system that dynamically promotes structural and molecular development. Here, we describe one of these approaches—a kind of ‘divide and conquer’ technique, in which the system is disassembled into modules to specify behaviors on the scale of the organ (i.e., morphogenesis) and the cell (i.e., molecular interactions). At run-time, these modules are re-assembled to direct development in individual cells. This approach employs multi-scaling and dynamics, two important characteristics of natural systems, but avoids cross-scaling. It thus appears to be useful for systems in which the importance of cross-scaling seems to be less significant, such as the development of phyllotaxis in plants. In pancreatic organogenesis, cross-scaling was found to be a significant characteristic, and thus by using ‘divide and conquer’ we could cover only its preliminary stages. We discuss the approach and our use of it, as well as he various methods to analyze the achievements and limitations of the end result.


Endodermal Cell Hybrid Automaton Curr Opin Plant Biol Modeling Natural System Pancreatic Organogenesis 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    3D Game Studio.
  2. 2.
    Axelrod JD (2006) Cell shape in proliferating epithelia: a multifaceted problem. Cell 126:643–645 CrossRefGoogle Scholar
  3. 3.
    Cardelli L (2005) Abstract machines of systems biology. Trans Comput Syst Biol 3:145–168 Google Scholar
  4. 4.
    Chakrabarti SK, Mirmira RG (2003) Transcription factors direct the development and function of pancreatic beta cells. Trends Endocrinol Metab 14:78–84 CrossRefGoogle Scholar
  5. 5.
    Chu K, Nemoz-Gaillard E, Tsai MJ (2001) BETA2 and pancreatic islet development. Recent Prog Horm Res 56:23–46 CrossRefGoogle Scholar
  6. 6.
    Ciliberto A, Novak B, Tyson JJ (2003) Mathematical model of the morphogenesis checkpoint in budding yeast. J Cell Biol 163:1243–1254 CrossRefGoogle Scholar
  7. 7.
    Cohen IR, Harel D (2007) Explaining a complex living system: dynamics, multi-scaling and emergence. J R Soc Interface 4:175–182 CrossRefGoogle Scholar
  8. 8.
    Edelstein-Keshet L (2005) Mathematical models in biology. Society for Industrial and Applied Mathematics, Philadelphia zbMATHGoogle Scholar
  9. 9.
    Edlund H (2002) Pancreatic organogenesis—developmental mechanisms and implications for therapy. Nat Rev Genet 3:524–532 CrossRefGoogle Scholar
  10. 10.
    Efroni S, Harel D, Cohen IR (2005) Reactive animation: realistic modeling of complex dynamic systems. IEEE Comput 38:38–47 Google Scholar
  11. 11.
    Finkelstein A, Hetherington J, Li L, Margoninski O, Saffrey P, Seymour R, Warner A (2004) Computational challenges of systems biology. IEEE Comput 37(5):26–33 Google Scholar
  12. 12.
    Fisher J, Henzinger TA (2007) Executable cell biology. Nat Biotechnol 25:1239–1249 CrossRefGoogle Scholar
  13. 13.
    Ghosh R, Tomlin C (2004) Symbolic reachable set computation of piecewise affine hybrid automata and its application to biological modelling: delta–notch protein signalling. Syst Biol (Stevenage) 1:170–183 CrossRefGoogle Scholar
  14. 14.
    Gibson MC, Patel AB, Nagpal R, Perrimon N (2006) The emergence of geometric order in proliferating metazoan epithelia. Nature 442:1038–1041 CrossRefGoogle Scholar
  15. 15.
    Gorgevik D, Loskovska S, Mihajlov D (1994) Lindenmayer system application on the human kidney arterial system. In: Proceedings of the 12th international congress of the European federation for medical informatics, pp 127–131 Google Scholar
  16. 16.
    Harel D (1987) Statecharts: a visual formalism for complex systems. Sci Comput Program 8:231–274 zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Harel D, Gery E (1997) Executable object modeling with statecharts. IEEE Comput 30:31–42 Google Scholar
  18. 18.
    Harel D, Setty Y (2007) Generic reactive animation: realistic modeling of natural complex systems (submitted) Google Scholar
  19. 19.
    Heath J, Kwiatkowska M, Norman G, Parker D, Tymchyshyn O (2006) Probabilistic model checking of complex biological pathways. In: Priami C (ed) Proceedings of the computational methods in systems biology (CMSB’06). Lecture notes in bioinformatics, vol 4210. Springer, Berlin, pp 32–47 CrossRefGoogle Scholar
  20. 20.
    Jensen J (2004) Gene regulatory factors in pancreatic development. Dev Dyn 229:176–200 CrossRefGoogle Scholar
  21. 21.
    Kim SK, MacDonald RJ (2002) Signaling and transcriptional control of pancreatic organogenesis. Curr Opin Genet Dev 12:540–547 CrossRefGoogle Scholar
  22. 22.
    Lindenmayer A (1968) Mathematical models for cellular interaction in development. J Theor Biol 18:280–315 CrossRefGoogle Scholar
  23. 23.
    The MathWorks.
  24. 24.
    Mundermann L, Erasmus Y, Lane B, Coen E, Prusinkiewicz P (2005) Quantitative modeling of arabidopsis development. Plant Physiol 139:960–968 CrossRefGoogle Scholar
  25. 25.
    Mundermann L, MacMurchy P, Pivovarov J, Prusinkiewicz P (2003) Modeling lobed leaves. In: Proceedings of computer graphics international Google Scholar
  26. 26.
    Murtaugh LC, Melton DA (2003) Genes, signals, and lineages in pancreas development. Annu Rev Cell Dev Biol 19:71–89 CrossRefGoogle Scholar
  27. 27.
    Nelson CM, Vanduijn MM, Inman JL, Fletcher DA, Bissell MJ (2006) Tissue geometry determines sites of mammary branching morphogenesis in organotypic cultures. Science 314:298–300 CrossRefGoogle Scholar
  28. 28.
    Noble D (2005) The heart is already working. Biochem Soc Trans 33:539–542 CrossRefGoogle Scholar
  29. 29.
    Pictet RL, Clark WR, Williams RH, Rutter WJ (1972) An ultrastructural analysis of the developing embryonic pancreas. Dev Biol 29:436–467 CrossRefGoogle Scholar
  30. 30.
    Priami C, Quaglia P (2004) Modelling the dynamics of biosystems. Brief Bioinform 5:259–269 CrossRefGoogle Scholar
  31. 31.
    Prusinkiewicz P (2004) Modeling plant growth and development. Curr Opin Plant Biol 7:79–83 CrossRefGoogle Scholar
  32. 32.
    Prusinkiewicz P, Hanan J (1989) Lindenmayer systems, fractals and plants. Springer, New York zbMATHGoogle Scholar
  33. 33.
    Prusinkiewicz P, Rolland-Lagan AG (2006) Modeling plant morphogenesis. Curr Opin Plant Biol 9:83–88 CrossRefGoogle Scholar
  34. 34.
    Regev A, Shapiro E (2002) Cellular abstractions: cells as computation. Nature 419:343 CrossRefGoogle Scholar
  35. 35.
    Regev A, Silverman W, Shapiro E (2001) Representation and simulation of biochemical processes using the pi-calculus process algebra. In: Pacific symposium on biocomputing, pp 459–470 Google Scholar
  36. 36.
    Roux-Rouquié M, daRosa DS (2006) Ten top reasons for systems biology to get into model-driven engineering. In: GaMMa’06: proceedings of the 2006 international workshop on global integrated model management. New York, ACM, pp 55–58 CrossRefGoogle Scholar
  37. 37.
    Schonhoff SE, Giel-Moloney M, Leiter AB (2004) Minireview: development and differentiation of gut endocrine cells. Endocrinology 145:2639–2644 CrossRefGoogle Scholar
  38. 38.
    Segel LA (1984) Modeling dynamic phenomena in molecular and cellular biology. Cambridge University Press, New York zbMATHGoogle Scholar
  39. 39.
    Segel LA (1991) Biological kinetics. Cambridge University Press, New York zbMATHGoogle Scholar
  40. 40.
    Setty Y, Cohen IR, Dor Y, Harel D (2008) Four-dimensional realistic modeling of pancreatic organogenesis. Proc Natl Acad Sci USA 105(51):20374–20379 CrossRefGoogle Scholar
  41. 41.
    Slack JM (1995) Developmental biology of the pancreas. Development 121:1569–1580 Google Scholar
  42. 42.
    Smith RS, Guyomarc’h S, Mandel T, Reinhardt D, Kuhlemeier C, Prusinkiewicz P (2006) A plausible model of phyllotaxis. Proc Natl Acad Sci USA 103:1301–1306 CrossRefGoogle Scholar
  43. 43.
    Taubner C, Merker T (2005) Discrete modelling of the ethylene-pathway. In: ICDEW’05: proceedings of the 21st international conference on data engineering workshops. Washington, IEEE Computer Society, p 1152 CrossRefGoogle Scholar
  44. 44.
  45. 45.
    Webb K, White T (2006) Cell modeling with reusable agent-based formalisms. Appl Intell 24(2):169–181 CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Yaki Setty
    • 1
    Email author
  • Irun R. Cohen
    • 2
  • Avi E. Mayo
    • 2
  • David Harel
    • 3
  1. 1.Computational Biology GroupMicrosoft ResearchCambridgeUK
  2. 2.Weizmann Institute of ScienceRehovotIsrael
  3. 3.Department of Computer Science and Applied MathematicsWeizmann Institute of ScienceRehovotIsrael

Personalised recommendations