Entrainment Maps: A New Tool for Understanding Properties of Circadian Oscillator Models

Document Type

Article

Publication Date

12-1-2016

Abstract

Circadian oscillators found across a variety of species are subject to periodic external light-dark forcing. Entrainment to light-dark cycles enables the circadian system to align biological functions with appropriate times of day or night. Phase response curves (PRCs) have been used for decades to gain valuable insights into entrainment; however, PRCs may not accurately describe entrainment to photoperiods with substantial amounts of both light and dark due to their reliance on a single limit cycle attractor. We have developed a new tool, called an entrainment map, that overcomes this limitation of PRCs and can assess whether, and at what phase, a circadian oscillator entrains to external forcing with any photoperiod. This is a 1-dimensional map that we construct for 3 different mathematical models of circadian clocks. Using the map, we are able to determine conditions for existence and stability of phase-locked solutions. In addition, we consider the dependence on various parameters such as the photoperiod and intensity of the external light as well as the mismatch in intrinsic oscillator frequency with the light-dark cycle. We show that the entrainment map yields more accurate predictions for phase locking than methods based on the PRC. The map is also ideally suited to calculate the amount of time required to achieve entrainment as a function of initial conditions and the bifurcations of stable and unstable periodic solutions that lead to loss of entrainment.

Identifier

84994761617 (Scopus)

Publication Title

Journal of Biological Rhythms

External Full Text Location

https://doi.org/10.1177/0748730416662965

e-ISSN

15524531

ISSN

07487304

PubMed ID

27754956

First Page

598

Last Page

616

Issue

6

Volume

31

Grant

1412877

Fund Ref

National Science Foundation

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