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

Fabian J. Theis, Sebastian Bohl, Ursula Klingmüller

    Research output: Contribution to journalArticle

    4 Scopus citations


    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 A → B 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.

    Original languageEnglish (US)
    Pages (from-to)978-1003
    Number of pages26
    JournalBulletin of Mathematical Biology
    Issue number5
    StatePublished - May 1 2011


    • Quantitative modeling
    • Receptor ligand modeling
    • Regulatory networks
    • Systems biology

    ASJC Scopus subject areas

    • Neuroscience(all)
    • Computational Theory and Mathematics
    • Mathematics(all)
    • Pharmacology
    • Immunology
    • Biochemistry, Genetics and Molecular Biology(all)
    • Agricultural and Biological Sciences(all)
    • Environmental Science(all)

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