Enzyme-sharing as a cause of multi-stationarity in signalling systems

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  • E. Feliu, Aarhus University
  • ,
  • Carsten Henrik Wiuf
Multi-stationarity in biological systems is a mechanism of cellular decision-making. In particular, signalling pathways regulated by protein phosphorylation display features that facilitate a variety of responses to different biological inputs. The features that lead to multi-stationarity are of particular interest to determine, as well as the stability, properties of the steady states. In this paper, we determine conditions for the emergence of multi-stationarity in small motifs without feedback that repeatedly occur in signalling pathways. We derive an explicit mathematical relationship w between the concentration of a chemical species at steady state and a conserved quantity of the system such as the total amount of substrate available. We show that w determines the number of steady states and provides a necessary condition for a steady state to be stable-that is, to be biologically attainable. Further, we identify characteristics of the motifs that lead tomulti-stationarity, and extend the view that multi-stationarity in signalling pathways arises from multi-site phosphorylation. Our approach relies on massaction kinetics, and the conclusions are drawn in full generality without resorting to simulations or random generation of parameters. The approach is extensible to other systems.
Original languageEnglish
JournalJournal of the Royal Society. Interface
Pages (from-to)1224-1232
Number of pages9
Publication statusPublished - 7 Jun 2012

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