Inducing phase-locking and chaos in cellular oscillators by modulating the driving stimuli

FEBS Lett. 2012 Jun 4;586(11):1664-8. doi: 10.1016/j.febslet.2012.04.044. Epub 2012 May 3.


Inflammatory responses in eucaryotic cells are often associated with oscillations in the nuclear-cytoplasmic translocation of the transcription factor NF-kB. In most laboratory realizations, the oscillations are triggered by a cytokine stimulus. We use a mathematical model to show that an oscillatory external stimulus can synchronize the NF-kB oscillations into states where the ratios of the internal to external frequency are close to rational numbers. We predict a response diagram of the TNF-driven NF-kB system which exhibits bands of synchronization known as "Arnold tongues". We suggest that when the amplitude of the external stimulus exceeds a certain threshold, chaotic dynamics of the nuclear NF-kB concentration may occur. This behavior seems independent of the shape of the external oscillation and the non-linearities transducing this signal.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Active Transport, Cell Nucleus
  • Cell Nucleus / metabolism
  • DNA Damage
  • Feedback, Physiological
  • Inflammation / metabolism
  • Inflammation / pathology
  • Models, Biological*
  • NF-kappa B / metabolism
  • Nonlinear Dynamics*
  • Stress, Physiological
  • Tumor Necrosis Factor-alpha / metabolism
  • Tumor Suppressor Protein p53 / metabolism


  • NF-kappa B
  • Tumor Necrosis Factor-alpha
  • Tumor Suppressor Protein p53