title: The role of mRNA and protein stability in the function of coupled positive and negative feedback systems in eukaryotic cells.
abstract: Oscillators and switches are important elements of regulation in biological systems. These are composed of coupling negative feedback loops, which cause oscillations when delayed, and positive feedback loops, which lead to memory formation. Here, we examine the behavior of a coupled feedback system, the Negative Autoregulated Frustrated bistability motif (NAF). This motif is a combination of two previously explored motifs, the frustrated bistability motif (FBM) and the negative auto regulation motif (NAR), which both can produce oscillations. The NAF motif was previously suggested to govern long term memory formation in animals, and was used as a synthetic oscillator in bacteria. We build a mathematical model to analyze the dynamics of the NAF motif. We show analytically that the NAF motif requires an asymmetry in the strengths of activation and repression links in order to produce oscillations. We show that the effect of time delays in eukaryotic cells, originating from mRNA export and protein import, are negligible in this system. Based on the reported protein and mRNA half-lives in eukaryotic cells, we find that even though the NAF motif possesses the ability for oscillations, it mostly promotes constant protein expression at the biologically relevant parameter regimes.
authors.affiliation: University of Copenhagen, Niels Bohr Institute, Blegdamsvej 17, DK-2100 Copenhagen, Denmark.
authors.forename: Kristian
authors.initials: K
authors.lastname: Moss Bendtsen
authors.affiliation: University of Copenhagen, Niels Bohr Institute, Blegdamsvej 17, DK-2100 Copenhagen, Denmark.
authors.forename: Mogens H
authors.initials: MH
authors.lastname: Jensen
authors.affiliation: University of Copenhagen, Niels Bohr Institute, Blegdamsvej 17, DK-2100 Copenhagen, Denmark.|Simons Centre for the Study of Living Machines, National Center for Biological Sciences, GKVK Campus, Bellary Road, Bangalore 560065, India.
authors.forename: Sandeep
authors.initials: S
authors.lastname: Krishna
authors.affiliation: University of Copenhagen, Niels Bohr Institute, Blegdamsvej 17, DK-2100 Copenhagen, Denmark.
authors.forename: Szabolcs
authors.initials: S
authors.lastname: Semsey
mesh_terms: D005057:Eukaryotic Cells / Q000378:metabolism; D006207:Half-Life; D008954:Models, Biological; D055550:Protein Stability; D011506:Proteins / Q000737:chemistry* / Q000378:metabolism; D020871:RNA Stability; D012333:RNA, Messenger / Q000378:metabolism*
chemical_list: D011506:Proteins; D012333:RNA, Messenger