Dynamics of phase tumbling and the reentrainment of circadian oscillators

Circadian clocks are comprised of networks of cellular oscillators that synchronize to produce endogenous daily rhythms in gene expression and protein abundance. These clocks have evolved to align the physiology and behavior of organisms to the 24-h environmental cycles arising from Earth's rotation. Rapid travel across time zones causes misalignment between an organism's circadian rhythms and its environment, leading to sleep problems and other jet lag symptoms until the circadian system entrains to the external cycles of the new time zone. Experimental and modeling work has shown that phase tumbling, defined as desynchronizing networks of circadian oscillators prior to an abrupt phase shift of the light-dark cycle, can speed up the process of reentrainment. Here, we use a mathematical model of circadian oscillators and 2-D entrainment maps to analyze the conditions under which phase tumbling has a positive, neutral, or negative effect on reentrainment time. We find that whether or not phase tumbling is beneficial depends on the size of the external phase shift and the location of the perturbed oscillator with respect to the fixed points and invariant manifolds of the entrainment map.