Oscillations in delayed positive feedback systems

• Published in: Physical chemistry chemical physics : PCCP 2024-10, Vol.26 (38), p.24861-24869
• Main Authors: Ryzowicz, Christopher J, Bertram, Richard, Karamched, Bhargav R
• Format: Article
• Language: English
• Subjects: Biological effects; CDC2 Protein Kinase - metabolism; Cyclin B - metabolism; Delay; Feedback loops; Feedback, Physiological; Gene Regulatory Networks; Initial conditions; Models, Biological; Negative feedback; Positive feedback; Transient oscillations
• ISSN: 1463-9076; 1463-9084; 1463-9084
• DOI: 10.1039/d4cp01867b

Positive feedback loops exist in many biological circuits important for organismal function. In this work, we investigate how temporal delay affects the dynamics of two canonical positive feedback models. We consider models of a genetic toggle switch and a one-way switch with delay added to the feedback terms. We show that long-lasting transient oscillations exist in both models under general conditions and that the duration depends strongly on the magnitude of the delay and initial conditions. We then show the existence of long-lasting oscillations in specific biological examples: the Cdc2-Cyclin B/Wee1 system and a genetic regulatory network. Our results challenge fundamental assumptions underlying oscillatory behavior in biological systems. While generally delayed negative feedback systems are canonical in generating oscillations, we show that delayed positive feedback systems are a mechanism for generating oscillations as well. Delayed positive feedback can generate oscillations in biochemical systems that may outlast the lifespan of the species in which they occur. This finding challenges the current norm of attributing oscillatory behavior to delayed negative feedback.