Accelerating recovery from jet lag: prediction from a multi-oscillator model and its experimental confirmation in model animals

Abstract

The endogenous circadian clock drives oscillations that are completely synchronized with the environmental day-night rhythms with a period of approximately 24 hours. Temporal misalignment between one's internal circadian clock and the external solar time often occurs in shift workers and long-distance travelers; such misalignments are accompanied by sleep disturbances and gastrointestinal distress. Repeated exposure to jet lag and rotating shift work increases the risk of lifestyle-related diseases, such as cardiovascular complaints and metabolic insufficiencies. However, the mechanism behind the disruption of one's internal clock is not well understood. In this paper, we therefore present a new theoretical concept called "jet lag separatrix" to understand circadian clock disruption and slow recovery from jet lag based on the mathematical model describing the hierarchical structure of the circadian clock. To demonstrate the utility of our theoretical study, we applied it to predict that re-entrainment via a two-step jet lag in which a four-hour shift of the light-dark cycle is given in the span of two successive days requires fewer days than when given as a single eight-hour shift. We experimentally verified the feasibility of our theory in C57BL/6 strain mice, with results indicating that this pre-exposure of jet lag is indeed beneficial.

Figure 1. Based on the anatomical structure of the SCN, a schematic of our model consisting of three oscillators (numbered 0, 1, and 2).

Oscillator 0 represents a group of neurons receiving input from the retina, whereas oscillators 1 and 2 represent groups of neurons receiving input from neurons of oscillator 0.

Figure 2

Illustrating the flow direction of relative phase ψ(t), depicted on a unit circle using red and blue curves and open arrows (a) before jet lag and after jet lag (b) smaller and (c) larger than the jet lag separatrix δ^*. The flow direction around ψ_s (which is a stable fixed point before jet lag) is counterclockwise and clockwise in (b,c), respectively. Thus, ψ(t), which converges to ψ_s in (a), will increase or decrease to approach in (b,c) after jet lag, respectively. The green curve illustrates the trajectory of ψ. Finally, we present (d) the actual time series of ψ(t) for different values of jet lag δ. The clock system re-entrains by advancing its phase for δ < δ^* but by delaying it for , where jet lag separatrix δ^* is c.a. 10.5/24.

Figure 3. Adaptation time (PS₅₀) vs various values of jet lag δ.

PS₅₀ is defined by the 50% phase-shift value of ψ( = ψ_1,2) for K₂ = 0.0 and Ψ for K₂ = 1.2.

Figure 4

Adaptation process in the presence of (a–d) weak and (e–h) strong AVP interactions. Relative phases, defined by ψ_i = ϕ_i − Ωt and Ψ = Φ − Ωt, are plotted for (a,e) δ = 4/24, (b,f) δ = 8/24, and (c,g) δ = −8/24. In (d,h), SCN output G(t) is plotted for δ = ±8/24.

Figure 5

Schematic presentation of the adaptation process in the presence of (a–c) weak and (d–f) strong AVP interactions, where (b,c,e,f) correspond to (b,c,f,g) in Fig. 4, respectively. The flow direction depicted on each circle, shown as red and blue curves and open arrows, is based only on the action of the VIP coupling, i.e., the same as that of Fig. 2(d). The pink and green curves illustrate the trajectories of ψ₁ and ψ₂, respectively.

Figure 6

The adaptation process for two-step jet lag, showing (a) relative phase, (b) SCN output, and (c) onset time.

Figure 7. Experimental confirmation: Faster behavioral re-entrainment in the mice subjected to two-step 4-hr jet lags compared with one-step 8-hr jet lag.

(a) Representative double-plotted actogram of mice subjected to 4-hr jet lag in LD cycle twice in the consecutive days. After 3 weeks, they were subjected to one-step 8-hr jet lag. (b) Representative double-plotted actogram of mice subjected to one-step 8-hr jet lag in LD cycle. After 3 weeks, they were subjected to 4-hr jet lag in LD cycle twice in the consecutive days. (c) Average onset of locomotor activity under one- and two-step jet lag (mean ± s.e.m.; n = 15 each). (d) Pairwise comparison in PS₅₀ values (^**P = 0.0014, paired t-test, n = 15).