Bulletin of Mathematical Biology

, Volume 74, Issue 1, pp 45–72 | Cite as

An Algebraic Approach to Signaling Cascades with n Layers

  • Elisenda Feliu
  • Michael Knudsen
  • Lars N. Andersen
  • Carsten Wiuf
Original Article


Posttranslational modification of proteins is key in transmission of signals in cells. Many signaling pathways contain several layers of modification cycles that mediate and change the signal through the pathway. Here, we study a simple signaling cascade consisting of n layers of modification cycles such that the modified protein of one layer acts as modifier in the next layer. Assuming mass-action kinetics and taking the formation of intermediate complexes into account, we show that the steady states are solutions to a polynomial in one variable and in fact that there is exactly one steady state for any given total amounts of substrates and enzymes.

We demonstrate that many steady-state concentrations are related through rational functions that can be found recursively. For example, stimulus-response curves arise as inverse functions to explicit rational functions. We show that the stimulus-response curves of the modified substrates are shifted to the left as we move down the cascade. Further, our approach allows us to study enzyme competition, sequestration, and how the steady state changes in response to changes in the total amount of substrates.

Our approach is essentially algebraic and follows recent trends in the study of posttranslational modification systems.


Mass action kinetics Sequestration Futile cycle Posttranslational modification Stimulus-response Rational function 


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Copyright information

© Society for Mathematical Biology 2011

Authors and Affiliations

  • Elisenda Feliu
    • 1
    • 2
  • Michael Knudsen
    • 2
  • Lars N. Andersen
    • 2
  • Carsten Wiuf
    • 2
  1. 1.Facultat de MatemàtiquesUniversitat de BarcelonaBarcelonaSpain
  2. 2.Bioinformatics Research CentreAarhus UniversityAarhus CDenmark

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