In distributive phosphorylation catalytic constants enable non-trivial dynamics

Area of Science:

• Biochemistry
• Systems Biology
• Biophysics

Background:

• Ordered distributive double phosphorylation is a key mechanism in intracellular signaling.
• Sequential and cyclic phosphorylation are two distinct modes of this process.
• Previous work established conditions for multistationarity in sequential phosphorylation.

Purpose of the Study:

• To investigate the dynamic behaviors, specifically sustained oscillations, in cyclic distributive double phosphorylation.
• To determine if catalytic constants can enable non-trivial dynamics in cyclic phosphorylation.
• To provide a method for generating rate constant values that lead to oscillations.

Main Methods:

• Analysis of cyclic distributive double phosphorylation networks.
• Derivation of inequalities for catalytic constants.
• Reduction of cyclic networks to a 'single extreme ray' model.
• Investigation of Hopf bifurcations for sustained oscillations.

Main Results:

• An inequality involving catalytic constants is identified for cyclic distributive double phosphorylation, enabling Hopf bifurcations and sustained oscillations.
• This inequality is analogous to the one known for multistationarity in sequential phosphorylation.
• A procedure is presented to generate rate constant values that induce oscillations in cyclic systems.
• Cyclic networks can be simplified to a 'single extreme ray' model for analysis.

Conclusions:

• Catalytic constants are shown to enable non-trivial dynamics (sustained oscillations) in cyclic distributive double phosphorylation.
• The findings extend the understanding of how phosphorylation motifs contribute to complex biological signaling.
• The study provides a framework for exploring oscillatory dynamics in biological networks.