Advertisement

A Multi-volume Approach to Stochastic Modeling with Membrane Systems

  • Daniela BesozziEmail author
  • Paolo Cazzaniga
  • Dario Pescini
  • Giancarlo Mauri
Chapter
Part of the Natural Computing Series book series (NCS)

Abstract

In the last decades, experimental investigations have evidenced the role of biological noise in cellular processes, and several stochastic approaches have been proposed to modeling and simulation of biochemical networks. Here, we review the main stochastic procedures defined for single-volume biochemical systems (SSA, tau-leaping), and discuss their practical utility and limitations. Then, within the framework of membrane systems, we propose a multi-volume generalization of the tau-leaping algorithm, called τ-DPP, feasible for the stochastic analysis of complex biochemical systems. Finally, we present a case-study application of τ-DPP to an intracellular genetic oscillator, coupled with an intercellular communication mechanism.

Keywords

Membrane System Time Increment Evolution Rule Stochastic Simulation Algorithm Chemical Master Equation 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Arkin A, Ross J, McAdams HH (1998) Genetics 149:1633–1648 Google Scholar
  2. 2.
    Besozzi D, Cazzaniga P, Pescini D, Mauri G (2007) Prog Nat Sci 17(4):392–400 zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Besozzi D, Cazzaniga P, Pescini D, Mauri G (2008) Biosystems 91(3):499–514 CrossRefGoogle Scholar
  4. 4.
    Blake WJ, Kærn M, Cantor CR, Collins JJ (2003) Nature 422:633–637 CrossRefGoogle Scholar
  5. 5.
    Cao Y, Gillespie DT, Petzold LR (2005) J Chem Phys 123:054104 CrossRefGoogle Scholar
  6. 6.
    Cao Y, Gillespie DT, Petzold LR (2006) J Chem Phys 124:044109 CrossRefGoogle Scholar
  7. 7.
    Cazzaniga P, Pescini D, Besozzi D, Mauri G (2006) In: Hoogeboom HJ, Păun G, Rozenberg G, Salomaa A (eds) Lecture notes in computer science, vol 4361. Springer, Berlin, pp 298–313 Google Scholar
  8. 8.
    Chatterjee A, Vlachos DG, Katsoulakis MA (2005) J Chem Phys 122:024112 CrossRefGoogle Scholar
  9. 9.
    Ciobanu G, Păun G, Pérez-Jiménez MJ (eds) (2005) Applications of membrane computing. Springer, Berlin Google Scholar
  10. 10.
    Elf J, Ehrenberg M (2004) Syst Biol 1(2):230–236 CrossRefGoogle Scholar
  11. 11.
    Elowitz MB, Leibler S (2000) Nature 403:335–338 CrossRefGoogle Scholar
  12. 12.
    Elowitz MB, Levine AJ, Siggia ED, Swain PS (2002) Science 297:1183–1186 CrossRefGoogle Scholar
  13. 13.
    Fedoroff N, Fontana W (2002) Science 297:1129–1131 CrossRefGoogle Scholar
  14. 14.
    Garcia-Ojalvo J, Elowitz MB, Strogatz SH (2004) Proc Natl Acad Sci 101(30):10955–10960 zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Gibson M, Bruck J (2000) J Phys Chem 104:1876–1889 Google Scholar
  16. 16.
    Gillespie DT (1977) J Phys Chem 81:2340–2361 CrossRefGoogle Scholar
  17. 17.
    Gillespie DT, Petzold LR (2001) J Chem Phys 115:1716–1733 CrossRefGoogle Scholar
  18. 18.
    Gillespie DT, Petzold LR (2003) J Chem Phys 119:8229–8234 CrossRefGoogle Scholar
  19. 19.
    Marquez-Lago TT, Burrage K (2007) J Chem Phys 127:104101 CrossRefGoogle Scholar
  20. 20.
    McAdams HH, Arkin A (1997) Proc Natl Acad Sci 94:814–819 CrossRefGoogle Scholar
  21. 21.
    Meng TC, Somani S, Dhar P (2004) Silico Biol 4:0024 Google Scholar
  22. 22.
    Miller MB, Bassler BL (2001) Annu Rev Microbiol 55:165–199 CrossRefGoogle Scholar
  23. 23.
    Nelson DL, Cox MM (2004) Lehninger principles of biochemistry, 4th edn. Freeman, New York Google Scholar
  24. 24.
    Parsek MR, Val DL, Hanzelka BL, Cronan JE, Greenberg EP (1999) Proc Natl Acad Sci 96:4360–4365 CrossRefGoogle Scholar
  25. 25.
    Păun G (2000) J Comput Syst Sci 61(1):108–143 zbMATHCrossRefGoogle Scholar
  26. 26.
    Păun G (2002) Membrane computing. An introduction. Springer, Berlin zbMATHGoogle Scholar
  27. 27.
    Pescini D, Besozzi D, Mauri G (2005) In: Proceedings of 7th international symposium on symbolic and numeric algorithms for scientific computing (SYNASC’05). IEEE Computer Press, Los Alamitos, pp 440–447 Google Scholar
  28. 28.
    Pescini D, Besozzi D, Mauri G, Zandron C (2006) Int J Found Comput Sci 17(1):183–204 zbMATHCrossRefMathSciNetGoogle Scholar
  29. 29.
    Pescini D, Besozzi D, Zandron C, Mauri G (2006) In: Pierce N, Carbone A (eds) Lecture notes in computer science, vol 3892. Springer, Berlin, pp 236–247 Google Scholar
  30. 30.
    Rosenfeld N, Young JW, Alon U, Swain PS, Elowitz MB (2005) Science 307:1962–1965 CrossRefGoogle Scholar
  31. 31.
    Swain PS, Elowitz MB, Siggia ED (2002) Proc Natl Acad Sci 99(20):12795–12800 CrossRefGoogle Scholar
  32. 32.
    Tian T, Burrage K (2004) J Chem Phys 121:10356–10364 CrossRefGoogle Scholar
  33. 33.
    Turner TE, Schnell S, Burrage K (2004) Comput Biol Chem 28:165–178 zbMATHCrossRefGoogle Scholar
  34. 34.
    Waters CM, Bassler BL (2005) Annu Rev Cell Dev Biol 21:319–346 CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Daniela Besozzi
    • 1
    Email author
  • Paolo Cazzaniga
    • 2
  • Dario Pescini
    • 2
  • Giancarlo Mauri
    • 2
  1. 1.Dipartimento di Informatica e ComunicazioneUniversità degli Studi di MilanoMilanoItaly
  2. 2.Dipartimento di Informatica, Sistemistica e ComunicazioneUniversità degli Studi di Milano—BicoccaMilanoItaly

Personalised recommendations