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A Multi-volume Approach to Stochastic Modeling with Membrane Systems

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Algorithmic Bioprocesses

Part of the book series: Natural Computing 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.

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References

  1. Arkin A, Ross J, McAdams HH (1998) Genetics 149:1633–1648

    Google Scholar 

  2. Besozzi D, Cazzaniga P, Pescini D, Mauri G (2007) Prog Nat Sci 17(4):392–400

    Article  MATH  MathSciNet  Google Scholar 

  3. Besozzi D, Cazzaniga P, Pescini D, Mauri G (2008) Biosystems 91(3):499–514

    Article  Google Scholar 

  4. Blake WJ, Kærn M, Cantor CR, Collins JJ (2003) Nature 422:633–637

    Article  Google Scholar 

  5. Cao Y, Gillespie DT, Petzold LR (2005) J Chem Phys 123:054104

    Article  Google Scholar 

  6. Cao Y, Gillespie DT, Petzold LR (2006) J Chem Phys 124:044109

    Article  Google Scholar 

  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. Chatterjee A, Vlachos DG, Katsoulakis MA (2005) J Chem Phys 122:024112

    Article  Google Scholar 

  9. Ciobanu G, Păun G, Pérez-Jiménez MJ (eds) (2005) Applications of membrane computing. Springer, Berlin

    Google Scholar 

  10. Elf J, Ehrenberg M (2004) Syst Biol 1(2):230–236

    Article  Google Scholar 

  11. Elowitz MB, Leibler S (2000) Nature 403:335–338

    Article  Google Scholar 

  12. Elowitz MB, Levine AJ, Siggia ED, Swain PS (2002) Science 297:1183–1186

    Article  Google Scholar 

  13. Fedoroff N, Fontana W (2002) Science 297:1129–1131

    Article  Google Scholar 

  14. Garcia-Ojalvo J, Elowitz MB, Strogatz SH (2004) Proc Natl Acad Sci 101(30):10955–10960

    Article  MATH  MathSciNet  Google Scholar 

  15. Gibson M, Bruck J (2000) J Phys Chem 104:1876–1889

    Google Scholar 

  16. Gillespie DT (1977) J Phys Chem 81:2340–2361

    Article  Google Scholar 

  17. Gillespie DT, Petzold LR (2001) J Chem Phys 115:1716–1733

    Article  Google Scholar 

  18. Gillespie DT, Petzold LR (2003) J Chem Phys 119:8229–8234

    Article  Google Scholar 

  19. Marquez-Lago TT, Burrage K (2007) J Chem Phys 127:104101

    Article  Google Scholar 

  20. McAdams HH, Arkin A (1997) Proc Natl Acad Sci 94:814–819

    Article  Google Scholar 

  21. Meng TC, Somani S, Dhar P (2004) Silico Biol 4:0024

    Google Scholar 

  22. Miller MB, Bassler BL (2001) Annu Rev Microbiol 55:165–199

    Article  Google Scholar 

  23. Nelson DL, Cox MM (2004) Lehninger principles of biochemistry, 4th edn. Freeman, New York

    Google Scholar 

  24. Parsek MR, Val DL, Hanzelka BL, Cronan JE, Greenberg EP (1999) Proc Natl Acad Sci 96:4360–4365

    Article  Google Scholar 

  25. Păun G (2000) J Comput Syst Sci 61(1):108–143

    Article  MATH  Google Scholar 

  26. Păun G (2002) Membrane computing. An introduction. Springer, Berlin

    MATH  Google Scholar 

  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. Pescini D, Besozzi D, Mauri G, Zandron C (2006) Int J Found Comput Sci 17(1):183–204

    Article  MATH  MathSciNet  Google Scholar 

  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. Rosenfeld N, Young JW, Alon U, Swain PS, Elowitz MB (2005) Science 307:1962–1965

    Article  Google Scholar 

  31. Swain PS, Elowitz MB, Siggia ED (2002) Proc Natl Acad Sci 99(20):12795–12800

    Article  Google Scholar 

  32. Tian T, Burrage K (2004) J Chem Phys 121:10356–10364

    Article  Google Scholar 

  33. Turner TE, Schnell S, Burrage K (2004) Comput Biol Chem 28:165–178

    Article  MATH  Google Scholar 

  34. Waters CM, Bassler BL (2005) Annu Rev Cell Dev Biol 21:319–346

    Article  Google Scholar 

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Correspondence to Daniela Besozzi .

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Besozzi, D., Cazzaniga, P., Pescini, D., Mauri, G. (2009). A Multi-volume Approach to Stochastic Modeling with Membrane Systems. In: Condon, A., Harel, D., Kok, J., Salomaa, A., Winfree, E. (eds) Algorithmic Bioprocesses. Natural Computing Series. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88869-7_26

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  • DOI: https://doi.org/10.1007/978-3-540-88869-7_26

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  • Print ISBN: 978-3-540-88868-0

  • Online ISBN: 978-3-540-88869-7

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