A P System Description of the Sodium-Potassium Pump

  • Daniela Besozzi
  • Gabriel Ciobanu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3365)


The sodium-potassium pump is a fundamental transmembrane protein present in all animal cells. The functioning of the pump is described and analyzed in the formal framework of P systems, considered here as tools for modelling a bio-cellular process. New features such as variable membrane labelling, activation conditions for rules, membrane bilayer and specific communication rules are defined, to the aim of providing a more appropriate description of the pump. A Sevilla carpet of the sodium-potassium pump is given, as a starting point to identify the pumps as the processors able to execute the rules of a high-level P system in a maximal parallel and nondeterministic manner, activated and controlled by steady-state concentrations. Some related topics for further research are proposed.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Alberts, B., Johnson, A., Lewis, J., Raff, M., Roberts, K., Walter, P.: Molecular Biology of the Cell, 4th edn. Garland Science, New York (2002)Google Scholar
  2. 2.
    Bernardini, F., Manca, V.: P systems with boundary rules. In: Păun, G., Rozenberg, G., Salomaa, A., Zandron, C. (eds.) WMC 2002. LNCS, vol. 2597, pp. 107–118. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  3. 3.
    Besozzi, D., Ardelean, I.I., Mauri, G.: The potential of P systems for modelling the activity of mechanosensitive channels in E. coli. In: Pre-Proc. Workshop on Membrane Computing, Rovira i Virgili University TR 28, pp. 84–102 (2003)Google Scholar
  4. 4.
    Besozzi, D.: Computational and Modelling Power of P Systems, PhD Thesis, University of Milano (2003)Google Scholar
  5. 5.
    Ciobanu, G.: Pumps systems of membranes. In: Proc. 2nd Brainstorming Week on Membrane Computing, University of Seville, pp. 130–134 (2004)Google Scholar
  6. 6.
    Ciobanu, G.: Software verification of the biomolecular systems. In: Modelling in Molecular Biology. Natural Computing Series, pp. 40–59. Springer, Heidelberg (2004)Google Scholar
  7. 7.
    Ciobanu, G., Ciubotariu, V., Tanasă, B.: A pi-calculus model of the Na pump. Genome Informatics, pp. 469–472. Universal Academy Press, Tokyo (2002)Google Scholar
  8. 8.
    Ciobanu, G., Păun, G., Ştefănescu, G.: Sevilla Carpets Associated with P Systems, Tech. Report 26, Rovira i Virgili University, 2003, 135–140. To appear in New Generation Computing, Springer (2004)Google Scholar
  9. 9.
    Csuhaj-Varjú, E., Vaszil, G.: P automata or purely communicating accepting P systems. In: Păun, G., Rozenberg, G., Salomaa, A., Zandron, C. (eds.) WMC 2002. LNCS, vol. 2597, pp. 219–233. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  10. 10.
    Franco, G., Manca, V.: A membrane system for the leukocyte selective recruitment. In: Martín-Vide, C., Mauri, G., Păun, G., Rozenberg, G., Salomaa, A. (eds.) WMC 2003. LNCS, vol. 2933, pp. 181–190. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  11. 11.
    Glitsch, H.G.: Electrophysiology of the sodium-potassium-ATPase in cardiac cells. Physiological Reviews 81(4), 1791–1826 (2001)Google Scholar
  12. 12.
    Glynn, I.M.: A hundred years of sodium pumping. Annu. Rev. Physiol. 64, 1–18 (2002)CrossRefGoogle Scholar
  13. 13.
    Holmgren, M., Wagg, J., Bezanilla, F., Rakowski, R.F., de Weer, P., Gadsby, D.C.: Three distinct and sequential steps in the release of sodium ions by the Na/K-ATPase. Nature 403, 898–901 (2000)CrossRefGoogle Scholar
  14. 14.
    Kaplan, J.H.: Biochemistry of Na,K-ATPase. Annu. Rev. Biochem. 71, 511–535 (2002)CrossRefGoogle Scholar
  15. 15.
    Lingrel, J.B., Kuntzweiler, T.: Na + ,K + -ATPase. Journal of Biological Chemistry 269(31), 19659–19662 (1994)Google Scholar
  16. 16.
    Lodish, H., Berk, A., Zipursky, S.L., Matsudaira, P., Baltimore, D., Darnell, J.: Molecular Cell Biology, 4th edn. W.H. Freeman and Co., New York (2000)Google Scholar
  17. 17.
    Păun, G.: Computing with membranes. Journal of Computer and System Sciences 61(1), 108–143 (2000)MATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Păun, G.: Membrane Computing. An Introduction. Springer, Berlin (2002)MATHGoogle Scholar
  19. 19.
    Therien, A.G., Blostein, R.: Mechanisms of sodium pump regulation. Am. J. Physiol. Cell Physiol. 279, C541–C566 (2000)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Daniela Besozzi
    • 1
  • Gabriel Ciobanu
    • 2
  1. 1.Dipartimento di Informatica e ComunicazionemUniversità degli Studi di MilanoMilanoItaly
  2. 2.Institute of Computer ScienceRomanian AcademyIaşiRomania

Personalised recommendations