Quantitative Biology Seminar | Understanding Entrainment Properties of Circadian Oscillator Models Using a One-dimensional Map
Amit Bose (NJIT)
A central feature of many oscillatory networks is their ability to display phase-locked solutions where the constituent elements fall into a well-defined pattern in which the phase difference between pairs of oscillators can be determined. Often the networks contain an identifiable pacemaker or external forcing. In these cases, the network is said to be entrained, because the pacemaker determines the overall network period and phasing. In this talk, we consider entrainment that arises in circadian systems. Such networks are subject to an external, pacemaking 24 hour light-dark drive in which the intensity and total hours of light within the 24 hour cycle are important parameters. We will introduce a new computational tool, a 1-dimensional entrainment map, to assess whether and at what phase a circadian oscillator entrains to periodic light-dark (LD) forcing. We have applied the map to a variety of circadian oscillators ranging from the Novak-Tyson model for protein-mRNA interactions to the Kronauer model of the human circadian rhythm. Using the entrainment map, we systematically investigate how various intrinsic properties of the circadian oscillator interact with properties of the LD forcing to produce stable circadian rhythms. We will focus on how to use the map to study the reentrainment process due long-distance travel to address the so-called east-west asymmetry of jet lag. Further, we show that individuals can experience jet lag after purely north-south travel. The mathematical and computational methods used to study these problems should be of wide interest to members of the mathematics community.
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