Advertisement

Frequency Synchronization of a Set of Cells Coupled by Quorum Sensing

  • Jianbao Zhang
  • Zengrong Liu
  • Ying Li
  • Luonan Chen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4689)

Abstract

Collective behavior of a set of cells coupled by quorum sensing is a hot topic of biology. Noticing the potential applications of frequency synchronization, the paper studies frequency synchronization of a set of cells with different frequencies coupled by quorum sensing. By phase reduced method, the multicell system is transformed to a phase equation, which can be studied by master stability function method. The sufficient conditions for frequency synchronization of the multicell system is obtained under two general hypotheses. Numerical simulations confirm the validity of the results.

Keywords

Quorum Sensing Phase Synchronization Intercellular Signaling Complete Synchronization Collective Dynamic 
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.
    Wang, R., Jing, Z., Chen, L.: Modelling periodic oscillation in gene regulatory networks by cyclic feedback networks. Bull. Math. Biol. 67, 339–367 (2004)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Wang, R., Chen, L.: Synchronizing Genetic Oscillators by Signaling Molecules. Journal of biological Rhythms 20, 257–269 (2005)CrossRefGoogle Scholar
  3. 3.
    Li, Y., Zhang, J., Liu, Z.: Circadian Oscillators and Phase Synchronization under a Light-Dark Cycle. International Journal of Nonlinear Science 1, 131–138 (2006)MathSciNetGoogle Scholar
  4. 4.
    Taga, M.E., Bassler, B.L.: Chemical communication among bacteria. PNAS 100, 14549–14554 (2003)CrossRefGoogle Scholar
  5. 5.
    Weiss, R., Knight, T.F.: Engineering communications for microbial robotics. DNA 6, 13–17 (2000)Google Scholar
  6. 6.
    Chen, L., Wang, R., Zhou, T., Aihara, K.: Noise-induced cooperative behavior in a multi-cell system. Bioinformatics 21, 51–62 (2005)zbMATHCrossRefGoogle Scholar
  7. 7.
    Garcia-Ojalvo, J., Elowitz, M., Strogatz, S.H.: Modeling a synthetic multicellular clock: repressilators coupled by quorum sensing. PNAS 101, 10955–10960 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Guckenheimer, J.: Isochrons and phaseless sets. J. Math. Biol. 1, 259C273 (1975)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Kuramoto, Y.: Chemical Oscillations, Waves and Turbulence. Springer, New York (1984)zbMATHGoogle Scholar
  10. 10.
    Winfree, A.T.: Biological Rhythms and the Behavior of Populations of Coupled Oscillators. J. Theoret. Biol. 16, 15–42 (1967)CrossRefGoogle Scholar
  11. 11.
    Izhikevich, E.M.: Phase equations for relaxation oscillators. SIAM Journal on Applied Mathematics 60, 1789–1804 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Strogatz, S.H.: From Kuramoto to Crawford: Exploring the onset of synchronization in populations of coupled oscillators. Physica D 143, 1–20 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Li, X.: Phase synchronization in complex networks with decayed long-range interactions. Physica D 223, 242C247 (2006)zbMATHCrossRefGoogle Scholar
  14. 14.
    Teramae, J., Tanaka, D.: Robustness of the noise-induced phase synchronization in a general class of limit cycle oscillators. Physical Review Letters 93, 20 (2004)CrossRefGoogle Scholar
  15. 15.
    Nakao, H., Arai, K., Nagai, K., Tsubo, Y., Kuramoto, Y.: Synchrony of limit-cycle oscillators induced by random external impulses. Phys. Rev. E. 72, 026220 (2005)CrossRefMathSciNetGoogle Scholar
  16. 16.
    Zhang, J., Liu, Z., Li, Y.: An approach to analyze phase synchronization in oscillator networks with weak coupling. Chinese Physics Review Letters 24(6) (2007)Google Scholar
  17. 17.
    Pecora, L.M., Carroll, T.L.: Master Stability Functions for Synchronized Coupled Systems. Phycical Review Letters 80, 2109 (1998)CrossRefGoogle Scholar
  18. 18.
    Jordi, G.O., Elowitz, M.B., Steven, H.S.: Modeling a synthetic multicellular clock: Repressilators coupled by quorum sensing. PNAS 101, 10955–10960 (2004)zbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Jianbao Zhang
    • 2
  • Zengrong Liu
    • 1
  • Ying Li
    • 2
  • Luonan Chen
    • 1
  1. 1.Institute of Systems Biology, Shanghai University, Shanghai. 200444China
  2. 2.College of Sciences, Shanghai University, Shanghai, 200444China

Personalised recommendations