Bulletin of Mathematical Biology

, Volume 73, Issue 5, pp 978–1003 | Cite as

Theoretical Analysis of Time-to-Peak Responses in Biological Reaction Networks

  • Fabian J. TheisEmail author
  • Sebastian Bohl
  • Ursula Klingmüller
Original Article


Processing of information by signaling networks is characterized by properties of the induced kinetics of the activated pathway components. The maximal extent of pathway activation (maximum amplitude) and the time-to-peak-response (position) are key determinants of biological responses that have been linked to specific outcomes. We investigate how the maximum amplitude of pathway activation and its position depend on the input and wiring of a signaling network. For this purpose, we consider a simple reaction AB that is regulated by a transient input and extended this to include back-reaction and additional partners. In particular, we show that a unique maximum of B(t) exists. Moreover, we prove that the position of the maximum is independent of the applied input but regulated by degradation reactions of B. Indeed, the time-to-peak-response decreases with increasing degradation rate, which we prove for small models and show in simulations for more complex ones. The identified dependencies provide insights into design principles that facilitate the realization dynamical characteristics like constant position of maximal pathway activation and thereby guide the characterization of unknown kinetics within larger protein networks.


Receptor ligand modeling Regulatory networks Quantitative modeling Systems biology 


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Supplementary material

11538_2010_9548_MOESM1_ESM.pdf (472 kb)
Supplement to ‘Theoretical analysis of time-to-peak responses in biological reaction networks’ (PDF 402 KB)


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Copyright information

© Society for Mathematical Biology 2010

Authors and Affiliations

  • Fabian J. Theis
    • 1
    • 2
    Email author
  • Sebastian Bohl
    • 3
  • Ursula Klingmüller
    • 3
  1. 1.Institute of Bioinformatics and Systems BiologyHelmholtz Zentrum MünchenNeuherbergGermany
  2. 2.Department of Mathematical ScienceTechnische Universität MünchenMünchenGermany
  3. 3.DKFZHeidelbergGermany

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