A nested bistable module within a negative feedback loop ensures different types of oscillations in signaling systems

Area of Science:

• Systems biology
• Biochemical signaling networks
• Nonlinear dynamics

Background:

• Double phosphorylation cycles are common signaling modules exhibiting bistability due to positive feedback.
• Protein-protein interactions in signaling networks can introduce negative feedback, creating combined positive and negative feedback systems.
• Such combined feedback systems have been linked to relaxation-type oscillations.

Purpose of the Study:

• To investigate the oscillatory dynamics arising from the interplay of positive and negative feedback in bistable signaling modules.
• To characterize the different types of oscillations generated by these combined feedback mechanisms.
• To establish a framework for understanding oscillatory behavior in complex biological systems.

Main Methods:

• Bifurcation analysis to identify different dynamical regimes.
• Amplitude vs. frequency curves to classify oscillation types.
• Modeling of a double phosphorylation cycle and a generalized system with a bistable module and negative feedback.

Main Results:

• The combination of positive and negative feedbacks generates two distinct oscillation types: relaxation-type and a smoother type.
• Both feedback types are essential for oscillation emergence, with their hierarchy dictating the oscillation type.
• A narrow frequency range exists for the smoother oscillations; amplitudes are compromised outside this range.
• The study demonstrates transitions between oscillation types and other behaviors like excitability.

Conclusions:

• The interplay between bistability and negative feedback creates rich oscillatory dynamics.
• The hierarchy of positive and negative feedbacks is a key determinant of oscillatory behavior in signaling systems.
• This work provides a generalizable framework for studying oscillations in diverse biological contexts, from simple models to complex cascades like MAPK and cell cycle oscillators.