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. 2023 Oct;38(5):492-509.
doi: 10.1177/07487304231180953. Epub 2023 Jul 10.

Modeling the Effects of Napping and Non-napping Patterns of Light Exposure on the Human Circadian Oscillator

Shelby R Stowe  1 , Monique K LeBourgeois  2 , Cecilia Diniz Behn  1   3
Affiliations

Modeling the Effects of Napping and Non-napping Patterns of Light Exposure on the Human Circadian Oscillator

Shelby R Stowe et al. J Biol Rhythms. 2023 Oct.

Abstract

In early childhood, consolidation of sleep from a biphasic to a monophasic sleep-wake pattern, that is, the transition from sleeping during an afternoon nap and at night to sleeping only during the night, represents a major developmental milestone. Reduced napping behavior is associated with an advance in the timing of the circadian system; however, it is unknown if this advance represents a standard response of the circadian clock to altered patterns of light exposure or if it additionally reflects features of the developing circadian system. Using a mathematical model of the human circadian pacemaker, we investigated the impact of napping and non-napping patterns of light exposure on entrained circadian phases. Simulated light schedules were based on published data from 20 children (34.2 ± 2.0 months) with habitual napping or non-napping sleep patterns (15 nappers). We found the model predicted different circadian phases for napping and non-napping light patterns: both the decrease in afternoon light during the nap and the increase in evening light associated with napping toddlers' later bedtimes contributed to the observed circadian phase difference produced between napping and non-napping light schedules. We systematically quantified the effects on phase shifting of nap duration, timing, and light intensity, finding larger phase delays occurred for longer and earlier naps. In addition, we simulated phase response curves to a 1-h light pulse and 1-h dark pulse to predict phase and intensity dependence of these changes in light exposure. We found the light pulse produced larger shifts compared with the dark pulse, and we analyzed the model dynamics to identify the features contributing to this asymmetry. These findings suggest that napping status affects circadian timing due to altered patterns of light exposure, with the dynamics of the circadian clock and light processing mediating the effects of the dark pulse associated with a daytime nap.

Keywords: circadian oscillator; early childhood; light; mathematical model; napping; phase response curve.

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Conflict of interest statement

The author(s) declared the following potential conflicts of interest with respect to the research, authorship, and/or publication of this article: SRS has no financial or personal conflicts to declare. MKL reports receiving travel funds from the Australian Research Council and research support from the National Institutes of Health, beyond the submitted work. CDB reports receiving research support from the National Institutes of Health, the National Science Foundation, LumosTech, and the Juvenile Diabetes Research Foundation, outside the submitted work.

Figures

Figure 1.
Figure 1.
Napping and non-napping light schedules produce distinct solution trajectories and circadian phase predictions. (a) 24-h napping and non-napping light schedules describe light timing and intensities during nighttime sleep, waking, and napping. Waking light intensity is 2241 lux and sleeping light intensity is 0 lux for both schedules. In the napping schedule, the light was set to 2 lux from 1354 to 1536 h to simulate a 102-min nap centered around 1445 h. Wake time is 0700 h in both schedules, and bedtime differed between the two schedules by 43 min (bedtime is 2020 h in the napping schedule, and 1933 h in the non-napping schedule). (b) Simulation time traces of the circadian variable, x, under the napping and non-napping light schedules show that the circadian phase is delayed in the napping schedule compared with the non-napping schedule. The predicted timing of the minimums of x, representing minimum core body temperature, occur at 0159 h for the non-napping schedule and 0240 h for the napping schedule. Thus, the non-napping schedule produces an advance in circadian phase of approximately 41 min compared with the napping schedule. (c) Phase space solution trajectories, including constant light and constant dark limit cycles.
Figure 2.
Figure 2.
Contributions of nap and bedtime on phase shifts and the effects of varying nap properties. Light intensities for wake, sleep, and nap and the napping and non-napping light schedules are as in Figure 1. (a) Four regular light schedules are simulated: napping (timing and durations as in the napping schedule in Figure 1); nap only (102-min nap occurrence from 1354 to 1536 h and bedtime at 1933 h); late bedtime only (no nap and bedtime set to 2020 h); and non-napping (timing and durations as in the non-napping schedule in Figure 1). The four light schedules are associated with four distinct circadian phases between 0159 and 0240 h. (b) The non-napping schedule produces the earliest entrained circadian phase. The nap only, late bedtime only, and napping schedules produce circadian phases that are delayed with respect to the non-napping schedule by 0.15, 0.53, and 0.69 h respectively. (c) The heat map reports the calculated phase difference between the non-napping schedule and variations of the napping schedule (negative values are phase delays). The largest phase differences occur for long naps that occur early in the day, and the smallest phase differences occur for long naps that occur late in the day. The white marker indicates the nap start time and nap duration associated with the default napping light schedule.
Figure 3.
Figure 3.
Simulated phase response curves (PRCs) to a 1-h exposure of light or dark. Each PRC protocol was simulated with early childhood initial conditions generated from the non-napping schedule. For the light pulse PRCs, a 1-h light exposure of 150 (open) or 5000 (closed) lux is administered between constant dim periods of 2 lux and produces PRCs with troughs slightly after DLMO = 0 h. For the dark pulse PRCs, a 1-h dark exposure of 2 lux is administered between constant light periods with two background light intensities of 150 (open) or 5000 (closed) lux and produces PRCs with peaks slightly after DLMO = 0 h. (a) PRCs show both intensity dependence and phase dependence for both light and dark stimuli. The light pulses produce larger magnitude phase shifts compared with the dark pulses at most circadian phases. 5000-lux light pulses or background conditions produce larger phase shifts in the light and dark pulse PRCs, respectively. (b) Adjusting the PRCs to account for phase shifting due to constant background light conditions and the system’s intrinsic period preserves phase dependence in both the light and dark pulse PRCs but reduces the intensity dependence in the dark pulse PRCs. Abbreviation: DLMO = dim light melatonin onset.
Figure 4.
Figure 4.
In constant light conditions, the solution trajectories form a cone of asymmetric limit cycles on planes corresponding to the steady state of n. (a) The steady state value of n, n∞, depends on (constant) light intensity and increases asymptotically toward 1 as the light level increases. (b) Limit cycle solutions for constant light inputs ranging from 0 to 5000 lux in the x−xc−n phase space. The amplitude of oscillations and the vertical distance between solutions both decrease as constant light intensity increases. (c) Limit cycle solutions projected into the x−xc plane. The magnitude of the [dx/dt,dxc/dt] vectors, denoted by the color bar, represents velocities around the limit cycles in the x−xc plane. As indicated by the colors, the velocity of the solution varies with phase around each limit cycle. (d) Velocity of limit cycle solutions for constant light inputs ranging from 0 to 5000 lux in the x−xc−n phase space varies inversely with n∞ such that velocities are slower on the limit cycles associated with high light levels compared with the velocities on limit cycles associated with low light levels.
Figure 5.
Figure 5.
Transient solution dynamics depend on both the starting light level and the magnitude of the change in light intensity. (a) 24-h light schedules for transient solution simulations. Two schedules involve a dark pulse of 2 lux at the time of the minimum of x, with background light set to 150 or 5000 lux. In addition, two schedules involve a light pulse of 150 or 5000 lux at the time of the minimum of x, with background light set to 2 lux. (b) The heat map shows how the velocity of n, dn/dt, varies with light level and n value. The fastest changes in n occur when n is low and light intensity is high. The white circles indicate the steady state value of n for each light level. Arrows indicate the transitions in light intensities when light level is decreased from 5000 or 150 to 2 lux or increased from 2 to 150 or 5000 lux as occurs in the PRC simulations. (c) Four solution trajectories in the x−xc−n phase space approach limit cycles associated with constant light conditions and show transient excursions away from these limit cycles due to increases or decreases in light intensity. (d) Magnitude of velocity vector (dx/dt,dxc/dt,dn/dt) along four solution trajectories in the x−xc−n phase space that approach limit cycles associated with constant light conditions and show transient excursions away from these limit cycles due to increases or decreases in light intensity. Abbreviation: PRC = phase response curve.
Figure 6.
Figure 6.
Eliminating n dynamics alters the phase shifting properties of the model. In the 2D model, n dynamics are eliminated by setting n=n∞. The light and dark pulse PRC protocols described in Figure 3 were simulated for the 2D model with early childhood initial conditions generated from the non-napping schedule. (a) PRCs for the 2D model show both intensity dependence and phase dependence for both light and dark stimuli. In contrast with the 3D model, the dark pulses produce larger magnitude shifts compared with the light pulses at most circadian phases. (b) Adjusting the PRCs for the 2D model to account for phase shifting due to constant background light conditions and the model system’s intrinsic period preserves phase dependence in both the light and dark pulse PRCs but reduces the intensity dependence in the dark pulse PRCs. (c) Four solution trajectories for the 2D model plotted in the x−xc−n phase space show instantaneous changes in n with changes in light intensity. When changes in n are instantaneous, n dynamics do not contribute to the observed phase shifts due to changes in light intensity. Abbreviations: PRC = phase response curve; 2D = two-dimensional; 3D = three-dimensional.
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