Reaction of the endogenous regulatory mechanisms to early weekday wakeups: a review of its popular explanations in light of model-based simulations

Abstract

Introduction: Several widely held explanations of the mechanisms underlying the responses of endogenous sleep-wake-regulating processes to early weekday wakeups have been proposed. Here, they were briefly reviewed and validated against simulations based on the rhythmostatic version of a two-process model of sleep-wake regulation. Methods: Simulated sleep times on weekdays and weekends were compared with the times averaged over 1,048 samples with either earlier or later weekday risetimes. In total, 74 paired samples were collected before and during lockdown, and 93 paired samples were collected during early and later school start times. Results: The counterintuitive predictions of the simulations included the following: 1) only one night of ad lib sleep is sufficient to restore the endogenously determined sleep times after 1 day/5 days of larger/smaller reduction/extension of the sleep/wake phase of the circadian sleep-wake cycle; 2) sleep loss on weekdays is irrecoverable; 3) irrespective of the amount of such deadweight loss, sleep on weekends is not prolonged; and 4) the control of the circadian clocks over the sleep-wake cyclicity is not disrupted throughout the week. Discussion: The following popular explanations of the gaps between weekends and weekdays in sleep timing and duration were not supported by these simulations: 1) early weekday wakeups cause "social jetlag," viewed as the weekend and weekday (back and forth) shifts of the sleep phase relative to the unchanged phase of the circadian clocks, and 2) early weekday wakeups cause an accumulation of "sleep debt paid back" on weekends, or, in other terms, people can "catch-up" or "compensate" sleep on weekends.

Keywords: circadian clocks; model; simulation; sleep deficiency; sleep–wake regulation.

FIGURE 1

Sleep–wake cycles challenged by 1 or 5 days with the prolongation of wakefulness. Two phases of the process of sleep–wake regulation S(t) can be simply described as daily alternations of an inverse exponential buildup during the wake phase (11a) and an exponential decay during the sleep phase (11b), but only in the absence of the circadian clocks. During their presence in the body, the parameters of S(t) are proposed to be additionally modulated by these clocks. A sine-form function with a 24-h period, C(t) (12), accounts for this modulation. S _d (t) and S _b (t): The highest allowed buildup and the lowest allowed decay of S(t), respectively, i.e., sleep onset and offset, respectively, determined by this endogenous sleep–wake-regulating process (1, 2) (Putilov, 1995). PoW: Forced or voluntary prolongation of wakefulness beyond the highest allowed buildup, i.e., further increase in S(t) after crossing S _d (t). Two sleep–wake cycles (R0 and R1) illustrate that the durations of reestablishment of normal (endogenously determined) sleep times after only 1 day (A) and 5 (week)days of PoW = +1.00 h B). The rate of this reestablishment is practically identical due to the permanent circadian modulation, C(t), of the parameters of S(t). Namely, it takes only 1 day with ad lib sleep to restore the baseline times of sleep onset, offset, and duration (23:00, 7:00, and 8.00 h, respectively), i.e., the alternations of two phases—sleep and wake—of this process between S _d (t) and S _b (t). It should be noted that PoW for either 1 or 5 days (A or B) leads to further buildup of S(t) that can be interpreted as accumulation of “sleep debt” that is “paid off” during the following (recovery ad lib) sleep. This sleep is predicted to be longer than the sleep started at the same time point at S _d (t). In these computations, any sleep episode is terminated at S _b (t) (C). The processes of recovery of normal (endogenously determined) sleep duration and timing are also practically identical after 5 (week)days of combination of PoW = +1.00 h with earlier wakeups (EWU = −1.00 h). Again, due to the circadian modulation C(t) of the parameters of S(t), it takes only 1 day with ad lib sleep to restore the baseline times of sleep onset, offset, and duration (23:00, 7:00, and 8.00 h, respectively) determined by the endogenous sleep–wake regulator (Putilov, 1995). However, the preceding ad lib sleep reflects the extent of shortening of the sleep phase. It is terminated either at 7:30 in (A,B) or later, at 8:45, in (C). See also the initial model parameters for these calculations in Table 1.

FIGURE 2

Sleep–wake cycles challenged by 1 or 5 days with earlier weekday wakeups. The reestablishment of normal (endogenously determined) sleep timing and duration after earlier wakeup (EWU = –1 h) either for only 1 day (A) or for 5 (week)days in a row (B). Two sleep–wake cycles (R0 and R1) illustrate that due to the circadian modulation C(t) of the parameters of S(t), it takes only 1 day with ad lib sleep to restore the baseline times of sleep onset, offset, and duration (23:00, 7:00, and 8.00 h, respectively), i.e., the alternations of two phases—sleep and wake—of the sleep–wake cycle between S _d (t) and S _b (t) determined by the endogenous sleep–wake regulator (Putilov, 1995). Sleep is always started at S _d (t) to be terminated either by EWU or by this endogenous sleep–wake-regulator at S _b (t) in the case of ad lib sleep. Such a sleep is started at 22:45 on any of the days with EWU at 6:00. It should be noted that since PoW = 0 h before and after EWU (i.e., sleep onset is set at 23:00 at baseline and remains to be terminated even earlier, at S _d (t), after EMU), no such EWU can lead to the accumulation of “sleep debt.” Therefore, there is nothing to be “paid off” during the following ad lib sleep. Such a sleep can be named “relaxatory” rather than “recovery” sleep. See also the legend of Figure 1 and the initial model parameters used for these calculations in Table 1.

FIGURE 3

Sleep–wake cycles challenged by different earlier weekday risetimes. R0 and R1: Two sleep–wake cycles after challenging the cycle by 5 days with earlier weekday risetimes (ERT). S(t): Two-phase process of sleep–wake regulation, i.e., an inverse exponential buildup (11a) and exponential decay (11b), i.e., the wake and sleep phases of the sleep–wake cycle, respectively. The parameters of this process are modulated by a sine-form function with a 24-h period, C(t) (12). S _d (t) and S _b (t): The highest allowed buildup and the lowest allowed decay of S(t), respectively, i.e., bedtime and risetime, BT and RT, respectively, determined by the endogenous sleep–wake regulator (Putilov, 1995). In three calculations (A–C), ERTs are suggested to be either large or usual or small; i.e., RT is advanced by 3 h or 2 h or 1 h, respectively, relative to RT on vacation days with ad lib BT and RT. Due to the influence of the sleep–wake-regulating mechanism, sleep is initiated at S _d (t) on any of the 5 days of the week, but it is terminated either by EWU or at S _b (t) after ad lib sleep. Therefore, this sleep is started approximately at 22:45, 23:20, and 23:45 on the last day with EWU at 6:00, 7:00, and 8:00, respectively. Due to the circadian modulation C(t) of the parameters of S(t), it takes only 1 day with ad lib sleep to restore the baseline bedtimes and risetimes and time in bed (24:00, 9:00, and 9.00 h, respectively), i.e., the alternation of two phases—sleep and wake—of the sleep–wake cycle between S _d (t) and S _b (t) determined by the endogenous sleep–wake regulator (Putilov, 1995). It should be noted that no EWU can lead to the accumulation of “sleep debt” because PoW = 0 h on any of the days before and after EWU; i.e., sleep onset is set at 23:00 at the baseline and remains to be terminated at S _d (t) after EWU. Therefore, since there is nothing to be “paid off” during ad lib sleep after days with EWU without PoW, such a sleep can be named “relaxatory” rather than “recovery” sleep. See also the legends to Figures 1, 2 for other notes, Table 1 for the model parameters, and Table 2 for sleep times for 10 days.

FIGURE 4

Seven simulated sleep–wake cycles on two subintervals (around bedtimes and risetimes). Simulations from Figure 3 are shown for 7 days of the week on two short time intervals, from 22:00 to 24:00 (around bedtime) and from 6:00 to 9:30 (around risetime the following day). (A–C) Simulations for weekday risetimes (wRT) at 8:00, 7:00, and 6:00 respectively. See also Figure 4 and Table 2.

FIGURE 5

Two simulated sleep–wake cycles on two subintervals (around bedtimes and risetimes). Simulations from Figures 3, 4 are shown for 2 days of the week on two short time intervals, from 22:00 to 24:00 (around bedtime) and from 6:00 to 9:30 (around risetime at the following day). (A–C) Two weekdays, two transitions between weekdays and weekends, and one weekday and one weekend, respectively, in the simulations of three different wRTs, 8:00, 7:00, and 6:00.

FIGURE 6

Simulations of the sleep–wake cycles in comparison of sleep times from the whole dataset. (A) Simulations of the sequence of 10 sleep–wake cycles consisting of 2 last days of vacation (Sa and Su), 5 weekdays (Mo–Fr), two weekend days (Sa–Su), and the first weekday of the next week (Mo). (B, C) Two subintervals of this 10-day interval, for a weekday (B) and the last 3 days (C). S(t): Two-phase process of sleep–wake regulation, i.e., an inverse exponential buildup (11a) and exponential decay (11b) in which parameters are modulated by a sine-form function with 24-h period (12). S _d (t) and S _b (t): The highest expected buildup and decay of S(t) (i.e., bedtime and risetime, BT and RT, respectively, determined by the sleep–wake regulator). PoW: An example of buildup caused by the prolongation of wakefulness beyond the highest expected buildup, i.e., further buildup of S(t) at an approximately 1-day interval; wBT and fBT and wRT and fRT: Weekday and weekend bedtimes and risetimes, respectively, in the whole dataset (n = 1,048). For the model parameters, sleep times for each of 10 simulated cycles, and this whole dataset, see also Tables 1–3.

FIGURE 7

Simulation of the sleep–wake cycles observed before and during lockdown. See Table 4 for the comparison of sleep times before and during lockdown (74 paired samples). (A) Simulations of the sequence of 10 sleep–wake cycles consisting of 2 last days of vacation (Sa and Su), 5 weekdays (Mo–Fr), two weekend days (Sa–Su), and the first weekday of the next week (Mo). (B, C) Two subintervals of this 10-day interval, for a weekday (B) and the last 3 days (C).

FIGURE 8

Simulation of the sleep–wake cycles during early and later school start times. See Table 5 for the comparison of data on early and later school start times (93 paired samples). (A) Simulations of the sequence of 10 sleep–wake cycles consisting of 2 last days of vacation (Sa and Su), 5 weekdays (Mo–Fr), two weekend days (Sa–Su), and the first weekday of the next week (Mo). (B, C) Two subintervals of this 10-day interval, for a weekday (B) and the last 3 days (C).