Errata: Erratum Volume 18, Issue 4, 480, Article first published online: 17 November 2009
T. de Boer, PhD, Laboratory for Neurophysiology, Department of Molecular Cell Biology, LUMC S-05-P, PO Box 9600, 2300 RC Leiden, The Netherlands. Tel.: +31 71 526 9771; fax: +31 71 526 8270; e-mail: email@example.com
According to the two-process model of sleep regulation, a homeostatic Process S increases during waking and decreases during sleep. The time course of Process S can be derived on the basis of changes in vigilance states and changes in electroencephalogram slow-wave activity (SWA, activity below 4 Hz) during non-rapid eye movement (NREM) sleep. In most mouse strains, an optimal fit between S and SWA was achieved with one increasing (active during waking and REM sleep) and one decreasing time constant (active during NREM sleep) for Process S. However, in the rat, systematic deviations in the light and dark periods were observed, which were resolved by introducing different decreasing time constants between the light and dark periods. The present study shows that this difference between the rest (light) and active (dark) phases remains, and may even be larger, after animals are adapted to constant dark conditions for at least a week. In addition, the data show that the build-up rate of SWA at the onset of a NREM sleep episode is slow compared with the increase rate under light–dark conditions, and that this build-up rate changes with the circadian phase. The slow build-up rate introduces a systematic error between the simulation of Process S and SWA in NREM sleep. The circadian modulation of the build-up rate may, together with circadian changes in NREM sleep episode duration, be the source of the necessity of introducing a difference in the decreasing time constant between the rest and active phases.
In mammals slow waves (1–4 Hz) in the electroencephalogram (EEG) during non-rapid eye movement (NREM) sleep reflect synchronized burst-pause firing patterns of hyperpolarized thalamocortical neurons (Steriade et al., 1993). The activity of these slow waves (slow-wave activity, SWA) can be quantified by a spectral analysis of the EEG. SWA positively correlated with arousal thresholds (Neckelmann and Ursin, 1993) and negatively with NREM sleep fragmentation (Franken et al., 1991a) and is therefore seen as a measure of NREM sleep intensity.
In contrast to the mathematical model applied in humans, where Process S is estimated based on the actual SWA expressed by the subjects (Achermann et al., 1993), the models in rodents estimate Process S purely on the basis of prior sleep–wake history and correlate the resulting level of Process S with the expressed SWA (Franken et al., 1991b, 2001; Huber et al., 2000; Vyazovskiy et al., 2007). In these simulations, the time course of S is determined iteratively on the basis of the vigilance states. During waking and REM sleep, S increases according to a saturating exponential function with an upper asymptote of 1 (Franken et al., 1991b; Huber et al., 2000) or an upper asymptote derived from the SWA data (Franken et al., 2001; Vyazovskiy et al., 2007). During NREM sleep, S decreases according to an exponential function with a lower asymptote of 0 (Franken et al., 1991b; Huber et al., 2000) or a lower asymptote derived from the data (Franken et al., 2001; Vyazovskiy et al., 2007). The time constants of the increase (τi) and decrease (τd), and the initial value at the start of the experiment (S0) are estimated by optimizing the linear correlation between S and SWA and minimizing the mean square of the difference between S and SWA on the basis of hourly values.
For mice, this approach was sufficient to reach an optimal fit in most strains (Franken et al., 2001; Huber et al., 2000). However, in the rat, an additional modulation of τd was needed (Franken et al., 1991b). SWA was consistently higher than S in the light period and lower than S in the dark period. Similarly, in a simulation of the effects of a 6-h SD at the start of the dark period, SWA was lower than S in the dark period in the rat (Vyazovskiy et al., 2007). Absence of light was shown to increase SWA in the rat (Alfoldi et al., 1990; Tobler et al., 1994) and therefore a higher τd was assumed in the light compared with in the dark period. This adaptation increased the success of subsequent simulations considerably (Franken et al., 1991b).
Besides the influence of light on sleep and SWA (Alfoldi et al., 1990; Tobler et al., 1994) it was proposed that the discrepancies between S and SWA could be caused by a difference in the duration of NREM sleep episodes between the light and dark periods. In addition, at the start of an NREM sleep episode, it takes a couple of minutes before SWA reaches an asymptotic level (AL) (Trachsel et al., 1989). When the increase rate differs between the light and dark periods, this will cause an under- or overestimation of Process S, depending on the time of day.
To eliminate the effect of light and other exogenous stimuli, animals were released in constant dark conditions for at least a week and a baseline day was recorded followed by an SD of 6 h and a recovery period of 18 h. The time course of SWA within an NREM sleep episode was analyzed and the hourly values of SWA were simulated with and without a circadian modulation of τd. The environmental conditions are, from a chronobiological point of view, adequate to rule out any environmental influence on daily modulation of vigilance states or EEG variables, which means that any daily modulation observed must be endogenous, e.g. from within the animal itself (Mistlberger and Rusak, 2005). The present conditions enable to determine whether under constant dark conditions: (1) a circadian modulation is still necessary in the simulation, (2) a circadian modulation is present in vigilance state episode frequency and duration, (3) a circadian modulation is present in the increase rate of SWA at the onset of an NREM sleep episode.
Materials and Methods
All experiments were performed under the approval of the Animal Experiments Ethics Committee of the Leiden University Medical Center. Male Wistar rats (n = 11), 300 g at the time of surgery, were implanted under deep anesthesia with EEG and electromyogram (EMG) electrodes. For the EEG, screw electrodes (Plastics One, Roanoke, VA, USA) were screwed through the skull on the dura over the right parietal cortex and the cerebellum. For the EMG, two wires with suture patches (Plastics One, Roanoke) were inserted between the skin and neck muscle tissue.
Electroencephalogram and EMG recording techniques were as described previously (Deboer et al., 2003, 2007). In short, the EEG and EMG were continuously recorded and amplified (amplification factor ∼2000), band-pass filtered (0.5–30 Hz, −40 dB/decade) and subjected to analog-to-digital conversion (sampling rate 100 Hz). All data were recorded simultaneously in 10-s epochs and stored on a computer hard disk.
The animals were connected to the recording system by a flexible cable and a counterbalanced swivel system, and then allowed to remain on the cable for at least 1 week (9–15 days) before the start of the recording. During that time and during the experimental recordings, the animals were maintained in continuous darkness. Drinking rhythms were continuously recorded and an estimate of the circadian phase was obtained by visual inspection of drinking onset. Under constant conditions, a 24-h baseline day was recorded. Subsequently, the animals were sleep deprived for 6 h, starting at rest onset (CT 0), followed by 18-h recovery.
During the 6-h SD, the animals were observed with an infrared camera in addition to the online EEG recording. Whenever the animals appeared drowsy or the EEG exhibited slow waves, they were mildly disturbed by moderate noise, by the experimenter entering the recording room, and, if necessary, by introducing fresh food, fresh drinking water or nesting material into the cage. The animals were never touched, and never disturbed during feeding and drinking.
Offline EEG power density spectra were calculated with a Fast Fourier Transform routine within the frequency range of 0.25–25.0 Hz in 0.1-Hz bins. EMG signals were integrated over 10-s epochs. Three vigilance states, waking, NREM sleep and REM sleep were determined on the basis of standardized EEG and EMG criteria for rats (Deboer et al., 2003, 2007; Franken et al., 1991a). Epochs containing artifacts in the EEG signal were excluded from the analysis of the spectrum.
All EEG power density data were standardized relative to the mean 24-h baseline value in NREM sleep (=100%). Hourly values of vigilance states and SWA in NREM sleep were calculated. To analyze changes in SWA at transition into NREM sleep, NREM sleep episodes lasting at least 7 min were selected based on episode duration criteria published previously (Deboer and Tobler, 1996; Huber et al., 2000). The analysis was performed on consecutive 6-h intervals of baseline (CT 0–6; 6–12; 12–18; 18–24) and recovery (CT 6–12; 12–18; 18–24). The time course of SWA within the NREM sleep episode was approximated by fitting a saturating exponential function (Eqn 1) to the empirical values (Trachsel et al., 1989):
where SWA is relative SWA, A is the asymptote, t is the time after an NREM sleep episode onset counted in 10-s epochs, T is the time constant of increase and SWA0 is the initial value of SWA at t = 0 (onset of NREM sleep). The parameters to be determined are A and T. The AL of SWA is the sum of A and SWA0.
In the simulation of Process S, the time course of S was determined iteratively on the basis of vigilance states (Franken et al., 1991b; Huber et al., 2000). In 10-s epochs scored as waking or REM sleep, S increased according to a saturating exponential function with an upper asymptote 1 (Eqn 2). In epochs scored as NREM sleep, S decreased according to an exponential function with a lower asymptote of 0 (Eqn 3). S was computed according to Franken et al. (1991b) and Huber et al. (2000):
where St and St+1 are values of S for consecutive epochs, τi and τd the time constants of the increase and decrease, respectively, and Δt the 10-s time interval of the iteration. For all animals, the same parameters were used. Initially, the time constants (τi = 8.6, τd = 3.2) and the initial value (S0 = 0.55) were taken from the publication by Franken et al. (1991b). Subsequently, the time constants τi and τd and the initial value S0 were estimated by optimizing the linear correlation between the hourly values of SWA in NREM sleep and S in baseline and recovery for all animals. Finally, τi and S0 were set to 8.6 h and 0.55, and τd was increased in the rest phase (CT 0–12) and reduced in the active phase (CT 12–24) according to the values provided by Franken et al. (1991b). To compare SWA and S, SWA was transformed according to a linear regression. For plotting purposes, data from Process S were standardized relative to the mean 24-h baseline values of S. Values of r presented are mean r-values over all animals after Fisher’s z transformation of the individual r-values.
Overall effects were analyzed by two-way anova with factors ‘time’ (1- and 6-h intervals) and ‘condition’ (baseline or recovery day). Contrasts were tested by post hoc two-tailed t-test only if the main factor or interaction of the anova reached significance.
The first simulation of Process S was based on the initial values and time constants obtained by Franken et al. (1991b). In this, τi = 8.6 h, τd = 3.2 h and S0 = 0.55. This resulted in a significant correlation between SWA and S (r = 0.555). However, SWA was consistently higher than S in the rest period and lower than S in the active period (Fig 1, top panel). Systematically varying τi, τd and S0 did not result in one single optimal solution (data not shown); however, a local maximum was obtained close to the values obtained by Franken et al. (1991b). It therefore was decided to continue with those values. Making τd variable by increasing τd in the rest phase (τdr) and decreasing τd in the active phase (τdr = 3.9, τda = 2.5, Franken et al., 1991b) reduced the amount of 1-h intervals with significant differences between S and SWA and increased the value of r to 0.682 (Fig. 1, middle panel). Subsequently, the difference in τd between the rest and active phases was iteratively increased, keeping the other variables (τi and S ) constant. This resulted in an optimal solution with τdr = 4.8, τda = 1.57. Only a few 1-h intervals still show a significant difference between S and SWA and the value of r increased to 0.749 (Fig. 1, bottom panel).
The average time course of SWA within the first 7 min after the start of a NREM sleep episode is shown in Fig. 2. SWA exhibited an initial rapid increase after NREM sleep onset and reached an AL within 2–5 min. During baseline, the AL (Table 1) decreased from the first 6 h (143%) to the second 6 h (100%), remained constant from the second to third 6-h period (93%) and increased again from the third to fourth 6-h period (127%). These changes in the AL over the baseline day were significant (P < 0.05, anova factor ‘time of day’). After the 6-h SD, the AL was significantly increased to 167% in the second 6-h period of the rest phase (CT 6–12) and then decreased progressively reaching levels significantly below that at baseline in the last 6 h of the active period (101%). The amount of waking interspersed in the NREM sleep episodes did not differ within the first 5 min after the start of the NREM sleep episodes across the circadian phase.
Table 1. Amount of vigilance states and the rise rate (T) and asymptote of SWA in the course of an NREM sleep episode in 6-h intervals
Significant differences from baseline (*P < 0.01, two-tailed paired t-test after significant anova).
The time constant T of the increase in SWA at the onset of NREM sleep changed significantly over the day (Table 1) with the slowest T in the first 6 h of the rest phase (2 min and 13 s). T was shorter in the second 6-h interval (1 min and 25 s) reaching the fastest T in the first 6 h of the active phase (40 s) and slowing after that (1 min and 33 s). The changes over the day in T were significant (P < 0.05, anova factor ‘time of day’); however, T was not influenced significantly by SD, reaching similar values in recovery after SD compared with that at baseline.
Slow-wave activity in NREM sleep was significantly increased for several hours immediately after SD (Fig. 1). Moreover, NREM sleep and REM sleep were increased above baseline levels for several 1-h intervals throughout the 18-h recovery period (Fig. 3). The first and second 6-h intervals after SD showed significant increments in NREM and REM sleep, compared with that at baseline (Table 1).
Waking episode duration was significantly shorter in the rest phase compared with that in the active phase (P < 0.05, anova factor ‘time of day’), but the frequency of waking episodes did not change over the day (Table 2). As a mirror image, NREM sleep episode duration was significantly longer in the rest phase compared with that in the active phase (P < 0.05, anova factor ‘time of day’). NREM sleep episode frequency decreased significantly from the rest to active phase (P < 0.05 anova factor ‘time of day’). Similarly, REM sleep episode frequency and duration decreased significantly from the rest to the active phase (P < 0.05 anova factor ‘time of day’). SD mainly influenced vigilance state episode frequency with less waking episodes and more NREM and REM sleep episodes in the recovery period (Table 2). Waking episode duration was significantly reduced in the first 6 h of the active phase of the recovery period.
Table 2. Episode frequency and duration of the different vigilance states in 6-h intervals
Episode duration (min)
Episode frequency (h−1)
*P < 0.05 or **P < 0.01 indicate significant differences from baseline (two-tailed paired t-test after significant anova).
The present analysis shows that SWA in the NREM sleep EEG needs time to come to full expression after the start of a NREM sleep episode. In our experimental conditions, it took 2–5 min before SWA reached plateau levels and this duration was a function of the time of day, but not of sleep pressure or previous time awake. A similar analysis at the end of a NREM sleep episode did not reveal an effect of SD or the time of day on the drop of SWA at the end of an NREM sleep episode (data not shown). In the simulation of Process S, τd is ‘on’ from the first scored 10-s NREM sleep epoch. The level of SWA is thought to represent the decrease rate of Process S. However, the present rodent models do not represent what is happening with SWA (and therefore the decrease rate of Process S) at the onset of a NREM sleep episode. This may be one of the reasons why there is a systematic circadian modulation of the difference between S and SWA in the initial simulation.
This is schematically drawn for the baseline situation in Fig. 4. τd of Process S (in gray) is here set to the AL of each NREM sleep episode in the 4.6-h baseline episodes obtained in Fig. 2. The actual mean values of SWA are plotted in front of it, relative to this AL. Because SWA needs time to build up to its full expression for several minutes, the simulation is systematically overestimating SWA during the first minutes of a NREM sleep episode. After optimizing of τd and τi, this will result in a systematic underestimation of τd. This by itself will not cause a circadian modulation in the difference between S and SWA. However, the rise rate of SWA at the onset of a NREM sleep episode is shown to change over the circadian day and therefore the amount of underestimation of τd also changes with the time of day. Fig. 4 clearly shows that the differences in the area under the curve between SWA and the ALs are larger in the first and last 6-h episodes compared with 6-h episodes between CT6 and CT18 and this difference is significantly changing with the time of day (P < 0.05, anova). This circadian change in T introduces circadian fluctuations in the accuracy of the simulation when a constant τd is applied.
The rise rates of SWA at the initiation of NREM sleep in the present experiment are considerably slower than those obtained previously by Trachsel et al. (1989). The main difference between the two experiments is the availability of light in the rest phase in the previous experiments (Trachsel et al., 1989). In the absence of light, rats are known to express more SWA during NREM sleep in the rest phase (Tobler et al., 1994). Possibly, the absence of light during the rest phase enables the increase in T. In that case, plateau levels will be reached later, resulting in an increase in SWA in the mean hourly values compared with SWA in the light condition. This finding is in accordance with the notion that the daily changes in the rise rate influence the success of the simulation. Longer rise rates in the present study, particularly at the beginning of the rest phase, are paralleled by a larger difference between τdr and τda compared to Franken et al. (1991b) where the animals were in a light–dark cycle.
A second modulating source could be NREM sleep episode duration, which also shows a circadian modulation with shorter episodes in the active phase compared with that in the rest phase. With shorter episodes, the relative contribution of the rising phase of SWA becomes larger.
The present method of simulation has been applied earlier in Sprague–Dawley rats (Franken et al., 1991b) and in three different mouse strains (Huber et al., 2000) kept under 12-h : 12-h LD conditions. Although the strain and LD conditions differed from Franken et al. (1991b), the present simulations were able to find a local maximum close to the values obtained by Franken et al. (1991b). That the simulations did not result in one single optimum solution may be caused by a difference in the increase rate of SWA at the entrance into NREM sleep, which was markedly slower compared with the values found by Trachsel et al. (1989) obtained under LD conditions. As mentioned previously, slower increase rate will increase the discrepancy between data and simulation and will reduce the fit between data and simulation.
Applying a different method, Franken et al. (2001) were able to successfully simulate Process S in mice. The latter may indicate a species difference between rats and mice. However, Huber et al. (2000) were able to apply the present method to C57/BL6 and the 129/SvJ mouse strain, but were not able to simulate the time course of SWA in the 129/Ola mouse strain, indicating that the applied simulation method may be an important factor as well. In addition, NREM sleep episode duration is more than 2 min shorter in 129/Ola mice compared with that in C57/BL6 and 129/SvJ mice (4.7, 7.1 and 7.1 min, respectively; Huber et al., 2000) supporting the notion that this variable may influence the success of the simulation. Whether 129/Ola mice display a slower increase rate of SWA at the entrance into NREM sleep remains to be determined.
It has been suggested that quality of waking also may cause differences in the sleep homeostatic response, with more exploratory behavior, or social stress inducing higher SWA in subsequent NREM sleep (Huber et al., 2006; Meerlo et al., 1997). As rats probably explore more during the active phase than during the rest phase, this also could induce a circadian modulation in the relation between simulation and data. Nevertheless, it is clear that the models applied in rodents do not fit the data at the initiation of an NREM sleep episode due to the time SWA needs to come to full expression.
In humans, it had been observed that the build-up rate of SWA within an NREM sleep episode is dependent on the prior duration of sleep and waking (Dijk et al., 1990). With longer previous waking, T is faster in humans. As this effect is similar to the effect of prior waking duration on SWA, this increase in T seems to be caused by increased sleep pressure. Therefore, a change in T has been implemented in the simulations of Process S and is coupled to the level of Process S at the time of initiation of an NREM sleep episode (Achermann et al., 1993). This refinement enables a detailed and quantitative prediction of the changes in SWA in the course of an NREM sleep episode in different experimental protocols.
With a similar approach in rats possibly the circadian adjustment of τd is no longer necessary. However, the present data seem to indicate a difference between rats and humans. In the rat, T is not influenced by changes in sleep pressure. After a 24-h SD, a clear increase in the AL was found, but T did not differ significantly from that at baseline (Trachsel et al., 1989). In the present experiment with a 6-h SD, a clear increase in the AL is visible (more than 66% above baseline). However, no significant change in T was found and SWA reached plateau levels after approximately 3 min in both conditions (Fig 2, CT6–CT12 condition).
The present analysis shows that under constant dark conditions SWA in NREM sleep is a function of prior waking duration, which is in accordance with the two process model of sleep regulation (Borbely, 1982; Daan et al., 1984). Remarkably, the constant conditions did not eliminate the necessity of a systematic circadian modulation in τd, which is therefore probably an endogenous property of rat sleep. The data suggest that this modulation may be caused by a circadian modulation in the rise rate of SWA at the onset of an NREM sleep episode; however, other factors influencing the circadian modulation, like NREM sleep episode duration or a difference in the quality of waking between the rest and active phases may also contribute to this phenomenon. Data obtained after SD indicate that in the rat, the rise rate of SWA at the onset of a NREM sleep episode is independent of the prior amount of sleep and wakefulness, indicating that incorporating this into the modeling of sleep homeostasis in a similar way as is done in humans (Achermann et al., 1993) is not possible in the rat.
The study was supported by the European Union (Grant LSHM-CT-2005-518189).