Bulletin of Mathematical Biology

, Volume 74, Issue 9, pp 2183–2203 | Cite as

A Model of Oscillatory Protein Dynamics in Bacteria

  • Peter Rashkov
  • Bernhard A. Schmitt
  • Lotte Søgaard-Andersen
  • Peter Lenz
  • Stephan Dahlke
Original Article


Spatial oscillations of proteins in bacteria have recently attracted much attention. The cellular mechanism underlying these oscillations can be studied at molecular as well as at more macroscopic levels. We construct a minimal mathematical model with two proteins that is able to produce self-sustained regular pole-to-pole oscillations without having to take into account molecular details of the proteins and their interactions. The dynamics of the model is based solely on diffusion across the cell body and protein reactions at the poles, and is independent of stimuli coming from the environment. We solve the associated system of reaction–diffusion equations and perform a parameter scan to demonstrate robustness of the model for two possible sets of the reaction functions.


Biological modeling Protein dynamics Dynamical systems Oscillatory behavior 



We would like to thank Thorsten Raasch for work done at the early stages of the project, Steffen Beck for advice on the MATLAB code, and Bruno Eckhardt for helpful discussions. This work has been supported by the Center for Synthetic Microbiology (SYNMIKRO) in Marburg, promoted by the LOEWE Excellence Program of the state of Hessen, Germany.


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Copyright information

© Society for Mathematical Biology 2012

Authors and Affiliations

  • Peter Rashkov
    • 1
  • Bernhard A. Schmitt
    • 1
  • Lotte Søgaard-Andersen
    • 2
  • Peter Lenz
    • 3
  • Stephan Dahlke
    • 1
  1. 1.Department of Mathematics and InformaticsPhilipps-Universität MarburgMarburgGermany
  2. 2.Max Planck Institute for Terrestrial MicrobiologyMarburgGermany
  3. 3.Department of PhysicsPhilipps-Universität MarburgMarburgGermany

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