Circadian Clock Model with Sequestration Repression Motif: Existence of Periodic Orbits and Entrainment Properties

TL;DR

This paper analyzes a mathematical model of the mammalian circadian clock incorporating a sequestration motif, demonstrating the existence of periodic orbits, specific phase response characteristics, and robustness features compared to classic oscillators.

Contribution

It introduces a simplified model with sequestration motif, proving periodic orbits and unique entrainment properties, advancing understanding of circadian rhythm regulation.

Findings

Periodic orbit exists over a large parameter region.

Sequestration induces a narrow window phase response curve.

Model shows robustness similar to classic oscillators.

Abstract

Protein sequestration motifs appear in many biological regulatory networks and introduce special properties into the network dynamics. Sequestration can be described as a mode of inactivation of a given protein by its binding to a second protein to form a new complex. In this complexed form, the original protein is prevented from performing its specific functions and is thus rendered inactive. We study a mathematical model of the mammalian circadian clock with a protein sequestration motif, which generates one of the negative feedback loops that guarantees periodic behavior. First, the motif permits a time-scale separation, which can be used to simplify the model. We show that the simplified model admits a periodic orbit over a fairly large region of parameters. Second, we are able to show that the sequestration motif induces a phase response curve with a very specific form, implying that external perturbations can affect the system only in a narrow window of the periodic orbit. Finally, we compare our model with a classic Goodwin oscillator, to illustrate the dynamical and robustness properties induced by the protein sequestration motif.