Dynamics of ERK regulation in the processive limit

Abstract

We consider a model of extracellular signal-regulated kinase (ERK) regulation by dual-site phosphorylation and dephosphorylation, which exhibits bistability and oscillations, but loses these properties in the limit in which the mechanisms underlying phosphorylation and dephosphorylation become processive. Our results suggest that anywhere along the way to becoming processive, the model remains bistable and oscillatory. More precisely, in simplified versions of the model, precursors to bistability and oscillations (specifically, multistationarity and Hopf bifurcations, respectively) exist at all "processivity levels". Finally, we investigate whether bistability and oscillations can exist together.

Algebra, Geometry and Topology of ERK Kinetics

“…Algebraic analyses and invariants of multi-site phosphorylation have revealed geometric information of steady-state varieties, informed experimental design, and enabled model the comparison using steady-state data [49,84,35,31,48]. However, such systems have also been shown to exhibit nontrivial transient dynamics and oscillations [14,66]. In recent years, the fields of systems biology and CRNT have extended the repertoire of techniques to assert other dynamics [6,14,20,55,42,22,2], reduce models systematically [64,29,24,80,11,40], and assess identifiability [46,59,52,38,9].…”

“…However, such systems have also been shown to exhibit nontrivial transient dynamics and oscillations [14,66]. In recent years, the fields of systems biology and CRNT have extended the repertoire of techniques to assert other dynamics [6,14,20,55,42,22,2], reduce models systematically [64,29,24,80,11,40], and assess identifiability [46,59,52,38,9]. Furthermore, combinatorial structures, such as simplicial complexes, and techniques from computational algebraic topology have enabled comparison of chemical reaction network models and their parameters [89,57].…”