In the absence of artificial light, we wake at dawn

The mathematical model takes light as an input and produces time courses for the circadian wake propensity, the sleep homeostat and sleep-wake timing. Full details of the model are given in the Methods section and in the Supplementary material, but typical outputs are shown in Fig. 1.

Hunter-gatherers living near the equator, with no access to electric light, receive very bright day-time light (averaging approximately 4000 lux) and very low light levels before dawn and after dusk (less than 5 lux), when the only available light is from small fires. Objective assessment of sleep timing in three groups of hunter-gatherers has demonstrated that bed-times occur approximately two to four hours after sunset and wake-time follows on average 7.7 h later, approximately one hour before sunrise. Using the average measured light profiles22 as inputs to the model, with no constraints on the model’s sleep timing, the model closely replicates sleep duration and timing for the three groups (see Fig. 2). Thus, the model predicts that in the absence of access to artificial light our circadian system is entrained such that we wake at dawn. The simulations suggest that this is two to three hours after the minimum of circadian wake propensity (the maximum of circadian sleep propensity), as shown by the position of the orange circles in Fig. 1d,e.

Figure 2: Timing of sleep and circadian rhythmicity when exposed to natural light/dark cycles. (a–c) Average light profiles (yellow) and sleep and wake timing (blue) (±standard deviation in red) for the Hadza and the San people who live a traditional hunter-gather lifestyle with no access to electrical light22. Sleep-timing as determined by the mathematical model using these same light profiles (grey) compare well with those determined in the field. (d–f) Computed sleep timing in relation to sunset and sunrise. Timing of the computed minimum of the circadian wake propensity is indicated by the orange circles. No fitting has been carried out for any of the model predictions: intrinsic circadian period is set to the human population average of 24.2 h; parameters for homeostatic rise during sleep and circadian amplitude have been set to be consistent with the age of the participants (see the Supplementary Material for further details on the relationship between parameters and age and the values of all other parameters). Full size image

Access to self-selected evening light delays spontaneous sleep-wake timing in a dose-dependent manner that is greater when exposure to day light is reduced

The model predicts that increasing the brightness of artificial evening light delays the spontaneous timing of sleep (Fig. 3a,b). Here, sunset and sunrise have been set at 6:00 h and 18:00 h, respectively, and maximum day light levels have been set at values typically observed in industrialized societies20. Even at less than 40 lux of evening light, for those with an intrinsic period of 24.2 h, spontaneous wake-time is predicted to occur up to three hours after sunrise (Fig. 3b). Although sleep timing is delayed, the phase-relationship between wake-time and the minimum of circadian wake propensity is not markedly affected. Spontaneous wake-times consistently occur two to three hours after the circadian wake propensity minimum, as shown by the position of the orange circles.

Figure 3: Sleep timing and timing of minimum circadian wake propensity during free days: dependence on levels of day and evening light. (a) Sleep timing for evening light of 5 lux (light grey) and 40 lux (dark grey) (day light 700 lux) with a photoperiod of 12 h centered on noon. The values of 700 lux and 40 lux were motivated by typical light levels reported for an industrialized society in the summer months20. The clock time of the minimum of the circadian wake propensity rhythm is shown by the orange circles. (b) Sleep timing as a function of different levels of evening light (day light 700 lux). At high levels of evening light, the model no longer synchronizes to a 24 h pattern. The orange curve marks the time of the minimum of the circadian wake propensity rhythm. (c) Timing of the minimum of circadian wake propensity as a function of evening light for different intrinsic periods. The average intrinsic period of 24.2 h has been picked out in orange. (d) Timing of the minimum of circadian wake propensity as a function of day light for different levels of evening light. While increasing evening light shifts timing later, increasing day light shifts timing earlier. Intrinsic period 24.2 h. Parameters for the homeostatic rise during wake and circadian set appropriate for age 30y in all panels. Full size image

The impact of evening light on spontaneous sleep timing is predicted to strongly depend on intrinsic circadian period (Fig. 3c). In approximately 80% of humans the intrinsic period is longer than 24 h and our simulated range of 23.5 h to 24.7 h covers approximately 99% of the intrinsic periods observed in healthy adults3. Hence our results imply that the impact of evening light will vary greatly between individuals, with those with longer intrinsic periods predicted to be very susceptible to the effects of evening light.

The effect of evening light on spontaneous sleep timing can, to some extent, be offset by increasing day-time light exposure (Fig. 3d). However, the relationship is highly nonlinear, with large increases in day-time light intensity needed to offset small increases in evening light intensity. This can be seen from the vertical distance between the lines for different evening lux values. For example, for a circadian wake propensity minimum time of 5:00 h, a factor of two increase in day-time light is required to compensate for each increase in evening light of ten lux. We note that both in Fig. 3b–d and in subsequent figures, we have computed data points at sufficiently fine intervals that using only linear interpolation the curves appear smooth, even in regions of high curvature.

Socially imposed wake-times lead to accumulation of sleep debt during work days and later sleep timing during free days

Work schedules may override spontaneous wake timing. The model predicts that the effect of work schedules on the alignment of sleep-wake cycles with circadian rhythmicity strongly depends on artificial evening light. This is illustrated in Fig. 4a, where the social constraint of rising at (or before) 7:00 h on week days is imposed for two different light conditions: one with evening light and one without. For the example shown, in the absence of evening light, the model naturally wakes a few minutes before the 7:00 h alarm time, and sleep-wake timing is uniform across the week (light grey bars). Once access to evening light is introduced, the circadian wake propensity rhythm shifts later; bed-times are later and spontaneous wake-time occurs after 7:00 h. Because of the forced awakening during work days, differences between work days and weekends emerge, replicating the basic features of social jetlag, namely sleeping longer at the weekend to make up for accrued sleep debt during the week (dark grey bars) and sleep occurring in and out of phase with the circadian rhythmicity. The phase changes can be seen by the position of the orange circles that mark the minimum of the circadian wake propensity. When sleep is unconstrained, the minimum of the circadian wake propensity rhythm occurs two to three hours before wake (Fig. 4a). With the inclusion of social constraints, the position of the circadian minimum still occurs two to three hours before wake time at the weekend, but during the week, occurs much closer to wake time. With the social constraint, sleep on Sunday night is particularly short, because the circadian clock has been delayed as a result of sleeping in over the weekend, yet there is the requirement to wake at 7:00 h on Monday morning. Figure 4a simulates one particular set of parameters, but social jet-lag, quantified here as the difference between wake-time on Saturday and wake-time on week days, is dependent on both light exposure and physiological factors. Those with less light exposure during the day, more light exposure in the evening, longer intrinsic circadian periods, or other age-related physiological factors that result in later unconstrained wake-times, are predicted to experience more social jet-lag (see Fig. 4b,c). Note that insufficient light during the day can result in those with longer intrinsic periods having spontaneous wake times after the alarm time of 7:00 h and can result in social jetlag even in the absence of evening light. This can be seen both in Fig. 4b and c, and is consistent with the dependence of spontaneous sleep timing on day-time light, as shown for an intrinsic period of 24.2 h in Fig. 3d.

Figure 4: Effects of social constraints on sleep timing, social jet-lag and wake effort. (a) Sleep timing over a two-week period with a social constraint (forced wake time at 7:00 h) for five days of the week. The light/dark grey bars show sleep timing in the absence/presence of evening light. In this example, in the absence of evening light the model wakes spontaneously before the forced wake time. No social constraint is applied to bedtime, so sleep onset is spontaneous in both cases. The time of the minimum of the circadian wake propensity rhythm is indicated by orange circles. (b,c) Social jet-lag, as measured by the difference between wake time on Saturday and wake time during the week, for different values of evening light and different intrinsic periods. b day-time light 300 lux; c day-time light 700 lux. The values of 300/700 lux were motivated by typical values reported in the winter/summer months for an industrialized society20. (d) Daily time course of homeostatic sleep pressure across the two-week period in the absence/presence of evening light (light/dark grey). Red regions indicate times of wake effort. e Detail of sleep pressure on Wednesday morning, showing the region of wake effort. Parameters: day-time light level 300 lux typical for observed values during the winter months20. Evening light either 0 or 60 lux. Intrinsic period 24.3 h in (a,d and e), which is chosen to indicate a simulation with clear wake effort. Parameters for the homeostatic rise during wake and circadian amplitude set for age 17y. Full size image

For the example shown in Fig. 4a, the alarm time occurs close to the minimum of the circadian wake propensity and the model predicts it will initially require effort to stay awake. This notion of ‘wake effort’30 corresponds to times when the model would naturally fall asleep if not kept awake by other wake-promoting factors. In the model, this is represented by an increased ‘drive’ to wake-promoting neurons, which could include the effect of caffeine or conscious effort devoted to remaining awake. The wake effort, which is different from the transient process of ‘waking up’ referred to as sleep inertia, is not required all day. As the day progresses, the wake promoting effect of the circadian wake propensity rhythm increases. Once it is sufficiently large to counterbalance the sleep-inducing effects of the homeostatic sleep pressure, wake effort is not needed. For the example shown, the wake effort lasts for approximately 1.2 h (regions in red in Fig. 4d, magnified in Fig. 4e). As for social jet-lag, the length of the wake effort period is dependent on physiological factors and day/evening light exposure: this is discussed further in the next section. Thus, during a week the model suggests many of us experience considerable wake effort during work days and this is associated with a cycle of accumulation and dissipation of slept debt across the week. Note that only at the weekend are levels of homeostatic sleep pressure comparable with the unconstrained case, see Fig. 4d, where the light grey line indicates the unconstrained case and the dark grey line shows the constrained case.

In the presence of artificial light, delaying social cues such as work or school start-times leads to an initial reduction in social jet-lag which, in some cases, is only transitory

One suggested remedy for social jet-lag is to delay work/school start-times. However, changes to social constraints will also modify patterns of light exposure31. For example, delaying school start-time could delay both sleep-times and wake-times, leading to delayed circadian rhythms. This is shown in Fig. 5, where we model the impact of changing the week day alarm time from 7:00 h to 8:00 h, with sunrise occurring at 6:00 h. Sleep duration is significantly increased on the first day the alarm is changed and wake effort is no longer required (Fig. 5b,c). However, in the example shown, the increase in sleep duration and reduction in wake effort is largely transitory: after five weeks, the maximum increase in sleep duration on any one day is four minutes and mean week day wake effort is eight minutes. This is because the self-selection of evening light leads to a delay in the circadian wake-propensity rhythm (Fig. 5d).

Figure 5: Short term effect of a change in alarm time. (a) Sleep timing over a three-week period where the alarm is set to 7:00 h for the first week and is changed to 8:00 h at the beginning of the second week. (b,c,d and e) show homeostatic sleep pressure, sleep duration, the minimum of the circadian wake propensity rhythm, and the number of hours per day of wake effort, respectively, over the same three-week period. Parameters are the same as for Fig. 4 a and d. Full size image

The effects of changing the social schedule depend on intrinsic circadian period and evening light. This is shown in Fig. 6a–c, where social jet-lag, sleep duration, and wake effort are all compared before and ten weeks after the alarm change, as a function of evening light and intrinsic period. The width of the grey band at a given light level indicates the change in social jet-lag/sleep duration/wake effort. The height of the grey band gives the reduction in evening light that would be needed to produce an equivalent effect. For example, with an intrinsic period of 24.2 h and 60 lux of evening light, the one hour delay in alarm time reduces social jet-lag from 1.76 h to 1.62 h, a reduction of eight minutes. An equivalent reduction could be achieved by decreasing evening light by 6 lux to 54 lux. Typically, the one hour delay in alarm time results in decreases in social jet-lag, increases in sleep duration, and a reduction in wake effort of substantially less than 1 h (Fig. 6d–f). Our results suggest that those with the longest intrinsic period have the most extreme social jet-lag, shortest sleep duration, and longest period of wake effort, yet they are also the ones who will be helped the least by a change in alarm time. For this group, reduction of evening light consumption is relatively much more effective.

Figure 6: Long term effects of a change in alarm time. (a–c) Social jet-lag, mean week day sleep duration, and mean week day wake effort, respectively, before and 10 weeks after an alarm change from 7:00 h to 8:00 h for different intrinsic periods. The shaded regions highlight the magnitude of the change with the right-hand/left-hand edge of each shaded region representing the values before/after the change respectively. (d–f) The change in social jet-lag, sleep duration and wake effort, respectively, for different intrinsic circadian periods. (g–l) Show the analogous figures for an alarm change from 5:00 h to 6:00 h. Full size image

The choice of changing the alarm time from 7:00 h to 8:00 h was motivated by proposed changes in the UK: typical school start-times for adolescents are currently 8:30 h to 9:00 h and a shift to 9:30 to 10:00 h has been mooted32. This follows an extensive and on-going debate in the USA. A recent review33, highlights the fact that, although as many as 80 school districts may have already shifted school timing for adolescents and some positive benefits have been reported, there is a need for further systematic research to quantify the effectiveness of this intervention. A key difference between the USA and the UK is that school start-times are substantially earlier in the USA, with some schools starting as early as 7:00 h. With the light profile used here, a shift in alarm time from 5:00 h to 6:00 h delays alarm time from an hour before sunrise to sunrise. Qualitatively, the results are similar to those for the change from 7:00 h to 8:00 h, but the social jet-lag is larger, sleep durations are shorter, wake effort lasts longer, and the change in alarm has a more beneficial effect. It is therefore possible that, for these very early start times, enough people would benefit to make a delay in start times worthwhile.

Adolescents are particularly sensitive to the effects of evening light

It is well-documented that preferred sleep timing changes across the lifespan, being latest at the end of adolescence34. Physiological changes across the lifespan that contribute to changes in preferred sleep timing may include a reduction in the rate of homeostatic rise during wake35,36 and a reduction in the circadian amplitude37,38. It has previously been shown that monotonically reducing the rate of homeostatic rise during wake and circadian amplitude reproduces age-related changes in sleep timing29. In Fig. 7 we show that monotonically reducing the rate of homeostatic rise during wake and circadian amplitude using our modified model using a realistic light profile also replicates age-related changes in sleep timing. The reported biological data34 considers times of the midpoint of sleep on ‘free’ days where there are no constraints on wake times. The comparison shown is therefore with simulations with no social constraints. Interestingly, however, this trend only matches the data that were collected from the general population when self-selected evening light is included. Keeping the same maximum day light level of 700 lux, but removing evening light, the predicted differences in sleep timing with age are modest. Using mean light data from the Hadza22, shown in Fig. 2a, yields a similar prediction, although the higher intensity of day light systematically shifts the sleep of all age groups to earlier times. The simulations also show that the interval between wake time and the minimum of the circadian wake propensity becomes smaller with increasing light exposure and with age. The latter observation is in accordance with empirical observations18. Overall the simulations imply that the profound delay in sleep observed in adolescents in modern industrialized societies is largely a result of our ability to self-select patterns of light exposure.

Figure 7: Sleep timing across the lifespan. (a) Sleep timing as measured by mid-sleep on days with no social constraints, (b) sleep duration, and (c) difference between wake-time and the minimum of the circadian wake propensity across the lifespan. Data for sleep timing and duration34,70 are shown as black circles. Results are shown for: day/evening light levels of 700/40 lux (purple); day/evening light levels of 700/20 and 700/10 lux (green); the light profile in Fig. 2a for the Hadza (blue)22. Further details on the age dependence of the circadian amplitude and the rise of the sleep homeostat during wake are given in Supplementary Material. The intrinsic circadian period is set to 24.2 h. Full size image

Theoretical underpinning and model robustness

One might argue that the effects of artificial light presented here are model-dependent, and that varying the model will vary the results. However, any model that describes circadian rhythmicity as an oscillator entrained by light will show similar phenomena. This is because an entrainable oscillator necessarily has a resonant ‘tongue’. The tongue describes how the combination of parameters (intensity of light and intrinsic period) affects entrainment. The rainbow-colored balloon shaped areas in Fig. 8a represent combinations of parameters for which the circadian oscillator is phase-locked (entrained) to the 24-h light-dark cycle. In the center of the tongue, small changes in the light profile have little impact on the circadian phase of entrainment. Whereas near the edges of the tongue the circadian phase of entrainment is highly sensitive to changes in the light profile. The sensitivity to changes in light at the tongue margins is a consequence of approaching a bifurcation (specifically, the transition from entrained to non-entrained states occurs via a saddle-node bifurcation and local to the saddle-node point any phase marker has a square-root behavior). The presence of the saddle-node bifurcation means that, near the tongue margins, entrainment takes a long time (so-called critical slowing-down).

Figure 8: Resonance tongues with and without self-selected evening light. (a and b) The colored balloon-shaped regions show the regions of entrainment by light, with contours indicating different phases of the minimum of the circadian wake propensity rhythm for evening light 0/40 lux respectively. In the light grey region, light alone is insufficient to entrain the model but the model can be entrained to an average of 24 h by social constraints applied for five days per week. In the black regions the model does not entrain even with social constraints. In the dark grey region, the model entrains to sleeping during the day. The thin black line splits this dark grey in two, to the right of this line, in the presence of social constraints the model is entrained to a schedule of sleeping at night. Age parameters set to 30y. The white dashed lines are to help guide the eye and mark the average intrinsic period of 24.2 (vertical line) and the levels of 700 and 300 lux (horizontal lines) that are used in many of the other simulations in the paper. (c,d) Circadian phase as a function of the parameters modelling the rate of homeostatic rise during wake and circadian amplitude. Circles indicate the position of the age-dependent parameters chosen to match reported data34,70 with 700 lux during the day. c Evening lux 0. d Evening lux 40. Full size image

Self-selection of light results in a reduced entrainment region, as shown in Fig. 8b for 40 lux of self-selected evening light in addition to the day-time light used in Fig. 8a. The minimum of the tongue is now at 40 lux: if the day light and the evening light are identical then there is no daily rhythm of light to entrain the model. It is this tongue structure that underpins the results shown in Figs 3, 4, 5, 6. The position of the white dashed lines in Fig. 8a,b are to guide the eye and mark the position of the average intrinsic period of 24.2 h and the levels of 300 and 700 lux used in many of the simulations. The position of these lines in Fig. 8b highlights the importance of social constraints to maintain entrainment in the absence of sufficient differentiation between day light and evening light. In the light grey region, light alone is insufficient to entrain the model to 24 h, but the model can be entrained to a weekly schedule by social constraints. In other words, the simulations suggest that in the presence of self-selection of artificial light, synchronization to the 24 h day is compromised in a large section of the population, particularly when daylight light exposure is low. Specifically, using the measured distribution of intrinsic periods in humans3, for 300 lux of day light and 40 lux of evening light, our simulations suggest that more than 60% of the population require social constraints to remain entrained. When social constraints are needed for entrainment, delaying alarm times does not greatly reduce social jet-lag.

The position of the tongue-shaped region is dependent on other model parameters. As discussed above, variation in sleep timing with age can be explained by decreasing homeostatic rise during wake and decreasing circadian amplitude. Variations in these two parameters result in a shift, first towards the edge of the tongue and then away from it. This is illustrated in Fig. 8d for the light profile that was used to match the sleep timing data in34, and shows the delay of approximately two hours in sleep timing from ages 11y to 20y and subsequent shift back to earlier sleep at later ages. The fact that this variation in sleep timing is largely eliminated if evening light is removed, as shown in Fig. 7, is a consequence of the increase in size of the entrainment region for decreasing evening light: Fig. 8c shows the change in phase that results from the same variation of homeostatic rise during wake and circadian amplitude with no evening light.