title: Core signalling motif displaying multistability through multi-state enzymes.
abstract: Bistability, and more generally multistability, is a key system dynamics feature enabling decision-making and memory in cells. Deciphering the molecular determinants of multistability is thus crucial for a better understanding of cellular pathways and their (re)engineering in synthetic biology. Here, we show that a key motif found predominantly in eukaryotic signalling systems, namely a futile signalling cycle, can display bistability when featuring a two-state kinase. We provide necessary and sufficient mathematical conditions on the kinetic parameters of this motif that guarantee the existence of multiple steady states. These conditions foster the intuition that bistability arises as a consequence of competition between the two states of the kinase. Extending from this result, we find that increasing the number of kinase states linearly translates into an increase in the number of steady states in the system. These findings reveal, to our knowledge, a new mechanism for the generation of bistability and multistability in cellular signalling systems. Further the futile cycle featuring a two-state kinase is among the smallest bistable signalling motifs. We show that multi-state kinases and the described competition-based motif are part of several natural signalling systems and thereby could enable them to implement complex information processing through multistability. These results indicate that multi-state kinases in signalling systems are readily exploited by natural evolution and could equally be used by synthetic approaches for the generation of multistable information processing systems at the cellular level.
authors.affiliation: School of Life Sciences, University of Warwick, Coventry, UK.
authors.forename: Song
authors.initials: S
authors.lastname: Feng
authors.affiliation: Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark.
authors.forename: Meritxell
authors.initials: M
authors.lastname: Sáez
authors.affiliation: Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark.
authors.forename: Carsten
authors.initials: C
authors.lastname: Wiuf
authors.affiliation: Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark efeliu@math.ku.dk.
authors.forename: Elisenda
authors.initials: E
authors.lastname: Feliu
authors.affiliation: School of Life Sciences, University of Warwick, Coventry, UK o.soyer@warwick.ac.uk.
authors.forename: Orkun S
authors.identifier: 0000-0002-9504-3796
authors.initials: OS
authors.lastname: Soyer
mesh_terms: D000818:Animals; D006801:Humans; D008954:Models, Biological; D011494:Protein Kinases / Q000378:metabolism*; D015398:Signal Transduction / Q000502:physiology*
chemical_list: D011494:Protein Kinases
keywords: bistability; competition; futile cycles; signalling networks; synthetic biology