Robustness and coherence of a three-protein circadian oscillator: landscape and flux perspectives

Biophys J. 2009 Dec 2;97(11):3038-46. doi: 10.1016/j.bpj.2009.09.021.


Three-protein circadian oscillations in cyanobacteria sustain for weeks. To understand how cellular oscillations function robustly in stochastic fluctuating environments, we used a stochastic model to uncover two natures of circadian oscillation: the potential landscape related to steady-state probability distribution of protein concentrations; and the corresponding flux related to speed of concentration changes which drive the oscillations. The barrier height of escaping from the oscillation attractor on the landscape provides a quantitative measure of the robustness and coherence for oscillations against intrinsic and external fluctuations. The difference between the locations of the zero total driving force and the extremal of the potential provides a possible experimental probe and quantification of the force from curl flux. These results, correlated with experiments, can help in the design of robust oscillatory networks.

Publication types

  • Research Support, Non-U.S. Gov't
  • Research Support, U.S. Gov't, Non-P.H.S.

MeSH terms

  • Bacterial Proteins / metabolism*
  • Circadian Rhythm / physiology*
  • Circadian Rhythm Signaling Peptides and Proteins / metabolism
  • Cyanobacteria / cytology
  • Cyanobacteria / metabolism
  • Kinetics
  • Models, Biological*
  • Probability
  • Stochastic Processes


  • Bacterial Proteins
  • Circadian Rhythm Signaling Peptides and Proteins
  • KaiA protein, cyanobacteria
  • KaiB protein, cyanobacteria
  • KaiC protein, cyanobacteria