Entrainment dynamics of forced hierarchical circadian systems revealed by 2-dimensional maps

TL;DR

This paper extends the entrainment map to hierarchical circadian systems, providing a new analytical framework to understand how central and peripheral oscillators synchronize with light-dark cycles.

Contribution

It introduces a generalized 2-D entrainment map for hierarchical circadian systems, enabling analysis of entrainment stability and dynamics in coupled oscillators.

Findings

Conditions for stable periodic entrainment are derived.

Hierarchical structure affects phase advance and delay assessments.

The map predicts how parameters influence entrainment timing and stability.

Abstract

The ability of a circadian system to entrain to the 24-hour light-dark cycle is one of its most important properties. A new tool, called the entrainment map, was recently introduced to study this process for a single oscillator. Here we generalize the map to study the effects of light-dark forcing in a hierarchical system consisting of a central circadian oscillator that drives a peripheral circadian oscillator. We develop techniques to reduced the higher dimensional phase space of the coupled system to derive a generalized 2-D entrainment map. Determining the nature of various fixed points, together with an understanding of their stable and unstable manifolds, leads to conditions for existence and stability of periodic orbits of the circadian system. We use the map to investigate how various properties of solutions depend on parameters and initial conditions including the time to and direction of entrainment. We show that the concepts of phase advance and phase delay need to be carefully assessed when considering hierarchical systems.