Homeostatic and Circadian Contribution to EEG and Molecular State Variables of Sleep Regulation

Abstract

Study Objectives:

Besides their well-established role in circadian rhythms, our findings that the forebrain expression of the clock-genes Per2 and Dbp increases and decreases, respectively, in relation to time spent awake suggest they also play a role in the homeostatic aspect of sleep regulation. Here, we determined whether time of day modulates the effects of elevated sleep pressure on clock-gene expression. Time of day effects were assessed also for recognized electrophysiological (EEG delta power) and molecular (Homer1a) markers of sleep homeostasis.

Design:

EEG and qPCR data were obtained for baseline and recovery from 6-h sleep deprivation starting at ZT0, -6, -12, or -18.

Setting:

Mouse sleep laboratory.

Participants:

Male mice.

Interventions:

Sleep deprivation.

Results:

The sleep-deprivation induced changes in Per2 and Dbp expression importantly varied with time of day, such that Per2 could even decrease during sleep deprivations occurring at the decreasing phase in baseline. Dbp showed similar, albeit opposite dynamics. These unexpected results could be reliably predicted assuming that these transcripts behave according to a driven damped harmonic oscillator. As expected, the sleep-wake distribution accounted for a large degree of the changes in EEG delta power and Homer1a. Nevertheless, the sleep deprivation-induced increase in delta power varied also with time of day with higher than expected levels when recovery sleep started at dark onset.

Conclusions:

Per2 and delta power are widely used as exclusive state variables of the circadian and homeostatic process, respectively. Our findings demonstrate a considerable cross-talk between these two processes. As Per2 in the brain responds to both sleep loss and time of day, this molecule is well positioned to keep track of and to anticipate homeostatic sleep need.

Citation:

Curie T; Mongrain V; Dorsaz S; Mang GM; Emmenegger Y; Franken P. Homeostatic and circadian contribution to EEG and molecular state variables of sleep regulation. SLEEP 2013;36(3):311-323.

INTRODUCTION

The timing and quality of both sleep and wakefulness are thought to result from the fine-tuned interaction of two processes.¹ One of these two processes keeps track of the time spent awake and asleep and is referred to as the sleep homeostat. The other sets internal time of day and is referred to as the circadian process. Because misalignment between the two processes significantly and negatively affects our daytime functioning,² such as experienced during jet-lag and shift work and reported for the blind,^3,4 the study of their interaction is of direct relevance to obtain a better understanding of the mechanisms determining cognitive performance and contributing to quality of life. The study of this interaction is, however, rendered difficult by the fact that most sleep related variables and cognitive performance measures are affected by both processes, necessitating the use of intricate protocols to quantify the contribution of each.⁵ Nevertheless, such experiments revealed that changes in the electroencephalogram (EEG)-derived variable EEG delta power, which quantifies the delta oscillations (1-4 Hz) characteristic of the EEG during NREM sleep, are mainly sleep-wake driven in nature (i.e., homeostatic),⁵ while variables such as core body temperature and plasma melatonin serve as reliable phase markers of the circadian process.⁶

With the discovery of the molecular substrate of circadian rhythms, steady-state mRNA levels of core clock genes, notably that of the Period homolog genes 1 and 2 (Per1 and -2), have become widely used as additional circadian state variables. This enabled the measurement of circadian rhythms not only in the central circadian pacemaker; i.e., the suprachiasmatic nuclei (SCN), but also in peripheral tissues, tissue explants, cell cultures, and in blood and buccal samples.^7–10 It has, however, become evident that clock genes are not exclusively “circadian” genes, as they are involved in a variety of other behaviors and functional pathways including the cell cycle, metabolism, and courtship song.^7,11–13 Our own work and that of others suggest a role for clock genes in the homeostatic regulation of sleep.¹⁴ Specifically, evidence of altered sleep homeostasis was found in mice and flies lacking functional core clock genes including Bmal1 (Arntl or aryl hydrocarbon receptor nuclear trans-locator-like) and its fly homolog Cyc (Cycle), Clock (Circadian locomotor output cycles kaput), Npas2 (Neuronal PAS domain protein 2), and the Cryptochome genes (Cry1 and -2).^15–19 In addition, we reported that sleep deprivation elevates Per1 and Per2 mRNA levels and decreases the expression of the clock controlled gene D-site albumin-promoter binding protein (Dbp) in the brains of mice and rats.^17,20 Moreover, the sleep-wake dependent changes in Per2 expression are modified in mice lacking Npas2¹⁸ or both Cry1 and -2,²¹ and sleep loss decreases the DNA-binding of BMAL1, CLOCK, and NPAS2 to the E-box enhancers of the Dbp and Per2 promoter in the cerebral cortex.²² Together, these observations suggest that the homeostatic need for sleep is not only affected by but also affects the machinery comprising the core molecular circadian clock. From this, it follows that the rhythmic changes in clock genes in peripheral organs (including brain areas outside the SCN) could, at least in part, be sleep-wake driven instead of strictly circadian driven, thereby compromising their utility as circadian state variables.

This dual aspect of the regulation of Per2 expression suggests that Per2 integrates both circadian and homeostatic information. The study of Per2 expression in relation to time of day and sleep-wake dependent factors could therefore be exploited to learn, at a molecular level, about the interaction between the two processes that govern sleep and wake quality and timing. We focus on Per2 because its expression is most reliably increased by sleep deprivation and we have assessed its dynamics in several protocols and mouse lines.^17,20,23 Most studies evaluated the effect of sleep deprivation at one time of day only, and the interaction between the effects of sleep loss and the ongoing circadian changes in Per2 mRNA levels has thus far not received much attention. The aim of the present study is therefore to quantify the contribution of time of day to the sleep-deprivation-dependent changes in the molecular and electrophysiological measures used to index sleep regulatory processes in the mouse. We performed sleep deprivations at four different times of day in three different inbred strains of mice known to respond differently to sleep deprivation both in terms of their increase in EEG delta power and Per2 expression.^20,24 We found that the effects of enforced wakefulness on clock gene expression strongly depended on time of day, both in direction of change and magnitude. This nonlinear relationship between circadian and homeostatic aspects on clock gene expression could be reliably modeled mathematically. We further determined to what extent recognized electrophysiological (i.e., delta power) and molecular (i.e., Homer1a expression^25,26) markers of sleep homeostasis reflect prior sleep-wake history independent of time of day.

METHODS

Animals, Housing Conditions, and Sleep Deprivation

All animals were kept under a 12 h-light/12 h-dark cycle (12:12 LD; lights on at 09:00, 110 lx) and were singly housed with food and water available ad libitum. We use zeitgeber time (ZT) to indicate time of day, with ZT0 (or ZT24) marking light onset and ZT12 dark onset. Room temperature was kept at 25°C. In all experiments animals were sleep deprived for 6 h by “gentle handling.”²⁷ Mice of 3 inbred strains [C57BL/6J (B6), AKR/J (AK), and DBA/2J (D2)] used to quantify gene expression were purchased from Jackson Laboratory (Bar Habor, ME). The B6 mice used in the EEG and corticosterone experiments were purchased from Charles River (Lyon, France). The experiments were approved by the Ethical Committee of the State of Vaud Veterinary Office, Switzerland.

Quantitative PCR

Mice from the 3 inbred strains AK, B6, and D2 were submitted to a 6-h sleep deprivation initiated at four different times of day (ZT0, -6, -12, and -18). After 5.5 h of sleep deprivation, mice were killed by cervical dislocation within the following 30 min, together with their non-sleep-deprived controls (males, 3 months old, n = 9/time point/condition [i.e., sleep deprivation and controls)/strain; total n = 216]). Brains were rapidly removed and frozen at -80°C. The same tissues were previously used for micro-array analyses²⁵ and are used here for quantitative PCR (Taqman) assessment of the steady state expression levels of Per1, Per2, Cry1, Cry2, Dbp, and Homer1a and the housekeeping control genes GusB, Tbp, and Rps9 (Table S1).

RNA from whole brain was isolated and purified with the RNeasy Lipid Tissue Midi kit (Qiagen, Hombrechtikon, Switzerland) and DNase-treated. RNA quantity was assessed with a NanoDrop ND-1000 spectrophotometer (ThermoScientific, Wilmington, DE, USA). RNA quality was controlled on Agilent 2100 bioanalyzer chips (Agilent Technologies, Basel, Switzerland). For cDNA synthesis, 1 μg of total RNA was reverse-transcribed using random hexamers and Superscript III reverse transcriptase (Invitrogen, Basel, Switzerland) according to standard procedures. The cDNA equivalent of 20ng of total RNA was PCR-amplified in an ABI PRISM 7900 detection system (Applied Biosystems, Switzerland). Forward, reverse primers and probes sequences were chosen from the coding regions of the genes of interest and were determined using Primer Express version 1.0 software (Applied Biosystems, Switzerland). To confirm specificity of the nucleotide sequences chosen for the primers and probes and the absence of DNA polymorphisms, BLASTN searches were conducted against the dbEST and nonredundant set of GenBank, EMBL, and DDBJ databases. Primers (Invitrogen) and probes (Eurogentec, Seraing, Belgium) sequences used are listed in Table S1. Three technical replicates were analyzed. Expression levels were calculated using the modified ddCt method from qBase²⁸ and normalized relative to the 3 above-mentioned housekeeping genes selected with gNorm software.²⁹

Mathematical Modeling of Clock Gene Expression

The dynamics of Per2 and Dbp expression after enforced wakefulness were reminiscent of a driven harmonic oscillation (see Results section). We implemented an iterative solution using a 4th-order Runge-Kutta method. The algorithm was adapted from the one provided by Dr. Daniel Suson (School of Engineering, Mathematics, and Sciences, Purdue University; “oscillator.c” available at http://physics.tamuk.edu/∼suson/html/4390/DiffEq.html). The model allows for testing how different “driving” forces, in our case the sleep-wake distribution (minutes of waking or sleep/5-min intervals taken from experiment described below) and corticosterone levels (see below), alter Dbp and/or Per2 expression. At 0.01-s increments, velocity and position of the body in oscillation were calculated based on the conditions of the preceding 0.01 s and eventual momentary external forces (sleep-wake and/or corticosterone) that were exerted. The system was damped (consistent with friction proportional to the speed of the body in motion), such that without periodic force, rhythms gradually (asymptotically) revert to singularity. A natural frequency of 23.5 h was assumed consistent with the endogenous circadian period of a mouse generally being shorter than 24 h, while the period of the driving force under entrained conditions of the experiments was 24 h. Because we were interested in reproducing the relative changes in gene expression only, parameter optimization was performed on z-transformed empirical and simulated data (i.e., both were converted to a standard normal distribution). As the force and mass in the simulation affect the amplitude but not the time-dependent relative profile, both were set to unity and not considered as free parameters. While successful for Dbp, simulations of baseline data revealed that the sleep-wake distribution is not sufficient to explain the observed phase position of Per2 expression in the brain. Adding our baseline corticosterone data as a driving force resulted in the desired phase for Per2. Maximal driving force for corticosterone during baseline was set to 1.0N, to peak at ZT11, and re-occurring every 24 h under our entrained conditions. Except for the 6-h sleep deprivation starting at ZT0,²³ for the remaining three sleep deprivations, information concerning the increase in corticosterone and how the effects of corticosterone on Per2 expression compares to those of extended waking per se, is lacking. For this initial attempt, it sufficed to assume that the combined force was constant during the sleep deprivation and did not vary with the time of day the sleep deprivation was performed. Parameter optimization was achieved by minimizing the mean square of the differences between the predicted values and the average expression levels (i.e., eight data points averaged over the three strains such that total n = 27/time point/ condition [baseline vs. sleep deprivation]).

Baseline Time-Course of Plasma Corticosterone Levels

Male B6 mice were used to construct a mean baseline time course of corticosterone (2.5-3.0 months old; n = 12). Mice were handled during the 3 days prior to the start of the experiment. The experiment consisted of four days during which blood from each mouse was sampled twice a day, with ≥ 12 h between subsequent samples. Mice were divided into 3 groups (n = 4/group). Each subsequent day samples were taken 3 h later and each subsequent group was sampled 1 h later, resulting in a 24-h baseline time course for each mouse at 3-h intervals (eight samples/individual) and an overall time course at 1-h intervals (n = 4/interval). Before each sampling, mice were briefly anesthetized (10-15 s; isoflurane, 4.5%). A small tail incision was made and blood collected in heparin-containing (10 μL) tubes. After sampling, mice were immediately placed back in their home cage and left undisturbed until the next sampling. Samples (volume 34.6 ± 1.6 μL; n = 96) were centrifuged (5 min at 8,000 rpm), and supernatants were frozen and stored at -80°C. Corticosterone was quantified by an enzyme immuno-assay (EIA kit; Enzo Life Sciences AG, Lausen, Switzerland) according to manufacturer instructions. Test samples were diluted 40 times in the provided buffer, and optical density was measured (λ = 405 nm).

EEG Recording and Analysis

EEG/EMG surgeries were performed according to the methods described previously^30,31 with minor changes. Briefly, EEG and EMG electrodes were implanted under deep ketamine/ xylazine anesthesia (intraperitoneal injection, 75 and 10 mg/ kg, at a volume of 8 mL/kg). Two gold-plated screws (diameter 1.1 mm) served as EEG electrodes and were screwed through the skull over the right cerebral hemisphere (frontal electrode: 1.7 mm lateral to midline, 1.5 mm anterior to bregma; parietal electrode: 1.7 mm lateral to midline, 1.0 mm anterior to lambda). Four additional screws were used as anchor screws. Two semi-rigid gold wires were used for EMG electrodes and were inserted into the neck musculature along the back of the skull. The four electrodes were soldered to a connector and cemented to the skull. After recovery from surgery (4-7 days), mice were connected to a swivel contact through recording leads to which they could habituate for 7 days prior to the experiment.

Mice (B6, males, 3 months old) were recorded for 96 continuous hours, of which the first 48 h served as baseline, followed by 6 h of sleep deprivation initiated at four different times of day (ZT0 [n = 7], -6 [n = 8], -12 [n = 9], and -18 [n = 9]) and recovery. EEG and EMG signals were amplified, filtered, analog-to-digital converted (2 kHz), and down-sampled and stored at 200 Hz. The behavioral states wakefulness (W), rapid eye movement (REM) sleep, and non-REM (NREM) sleep were visually assigned for consecutive 4-s epochs as described previously.^30,31 EEG signals were subjected to a discrete Fourier transform (DFT) to determine EEG power density in the delta frequency range (i.e., EEG delta power, 1-4 Hz) for 4-s epochs scored as NREM sleep. Individual differences in absolute levels of delta power were accounted for by expressing it as a percentage of the mean delta power over the last 4 h of the 2 baseline light periods. Delta power was averaged for 12 intervals to which an equal number of NREM sleep epochs contributed (i.e., percentiles) during the 12-h light periods, for six intervals during the 12-h dark periods, and for eight intervals during the 6 h immediately following sleep deprivation (recovery). Choice of the number of percentiles per recording segment depended on the amount of NREM sleep present. Sleep onset latency after the sleep deprivation was calculated as the time elapsed between the end of the sleep deprivation and the first sleep episode lasting ≥ 1 min and not interrupted by more than two 4-s epochs scored as wakefulness.³²

EEG power spectra were calculated to assess levels of theta activity reached during the sleep deprivation. Because the dominant theta frequency (theta peak frequency) was found to vary in relation to the time of day the sleep deprivation was performed, we determined theta power at the central frequency (peak theta power) rather than calculating average theta power using a fixed band width, as is usually done. Theta peak frequency and absolute peak theta power were individually calculated based on the average EEG spectra (0.25 Hz resolution; 0-90 Hz) for all artifact-free 4-s epochs of wakefulness during the last 1.5 h of the sleep deprivation according to published criteria.³⁰ The number and duration of NREM sleep episodes occurring during the sleep deprivation were quantified as a proxy for the number of intervention needed to keep the animals awake. The number of NREM sleep episodes scored off-line based on the EEG and EMG signals is likely to underestimate the true number of interventions needed to keep the animals awake.

Expected levels of EEG delta power were calculated individually using previously published parameter estimates.¹⁸ In these simulations, the time course of EEG delta power is predicted based solely on the sleep-wake distribution by assuming that a homeostatic need for sleep (“Process S”) increases according to a saturating exponential function when the animal is awake (or in REM sleep) according to S_t+1 = UA − (UA − S_t)*e^-dt/τi, and decreases exponentially when animals are in NREM sleep according to S_t+1 = LA + (S_t − LA)*e^-dt/τd; where S_t+1 and S_t are consecutive values of Process S (time resolution of iteration dt = 4s), which varies between an upper (UA = 282%) and lower (LA = 55%) asymptote with time constant τi (= 7.9 h) and τd (= 1.9 h) for the increase and decrease, respectively (for details see²⁴; parameter estimates taken from¹⁸).

The dynamics of Homer1a seemed to follow similar dynamics as EEG delta power and was therefore, as a first attempt, simulated using the same rules as for delta power. As for the Per2 and Dbp simulations, parameter optimization was achieved by minimizing the mean square of the differences between the predicted values and the average Homer1a expression levels (n = 27/time point/condition [baseline vs. sleep deprivation]). Parameters to be optimized were the lower and upper asymptote and the 2 time-constants.

Statistics

To assess the effects of time of day, condition (sleep deprivation vs. control), and genetic background (inbred strains B6, AK, and D2), 1-, 2-, or 3-way analyses of variance (ANOVAs) were performed. Significant effects and interactions were decomposed using post hoc (paired) t-tests, Tukey HSD test, or simple effect analysis (contrasts). “Regular” and partial Pearson correlations were used to quantify relationships between variables. Statistical analyses were performed using SAS (SAS Institute Inc, Cary, NC, USA) or Statistica (Statsoft Inc, Tulsa, OK, USA). Cutoff for statistical significance was set to P = 0.05, and results are reported as mean ± SEM. SigmaPlot 12 (Systat Software Inc., Chicago, IL, USA), and GraphPad Prism 4 (GraphPad Software Inc., San Diego, CA, USA) was used for graphing and nonlinear fitting of Gaussian and exponential saturating functions.

RESULTS

Time of Day Modulates the Effects of Sleep Deprivation on Per2 and Dbp mRNA Levels

It now has become well established that enforced wakefulness changes the expression of clock genes in the brain.^17,18,20,23 In these studies, sleep deprivation was, however, initiated at light onset (ZT0) when sleep need is high and after which the main sleep phase starts in most mouse strains.³³ Here we studied the interaction of the effects of sleep deprivation with the ongoing changes in the expression of clock genes Per1, Per2, Cry1, and Cry2, and the clock-controlled gene Dbp. These 5 transcripts have in common that their transcription can be activated by the heterodimeric transcription factors CLOCK::BMAL1 and NPAS2::BMAL1 as part of the transcriptional-translational feedback loop underlying circadian rhythm generation.⁹ In addition, expression of the activity-induced transcript Homer1a, that we previously identified as a molecular marker of sleep need,²⁵ was assessed. Sleep deprivations, each 6 h in duration, were performed at four different times of day (ZT0-6, ZT6-12, ZT12-18, and ZT18-24) in 3 inbred strains of mice (AK, B6, and D2). Because we have previously reported on strain differences in the homeostatic regulation of sleep and in the changes in gene expression during sleep deprivation for these 3 strains,^{20,21,24,25,32} and because the similarities in the effects of sleep deprivation and time of day on gene expression among strains outweigh strain differences, we do not report in detail on the effects of genotype.

Under undisturbed control conditions, whole brain levels of all six transcripts significantly varied as a function of time of day (Figure 1A). Maximum mRNA levels were reached either at ZT12 (for Dbp, Per1, and Cry2) or 6 h later at ZT18 (for Per2, Cry1, and Homer1a). Minimum mRNA values were reached at ZT6 for all transcripts except for Dbp, for which lowest values were already observed at ZT0. Amplitude of change was largest for Dbp (3.0-fold; i.e., the ratio of mean highest and lowest values), followed by Homer1a and Per2 (2.8- and 2.4-fold), and smallest for Cry2 (1.2-fold).

Figure 1.

Effects of sleep deprivation on clock gene expression in the forebrain of three inbred strains of mice as a function of time of day. (A) qPCR quantifi cation of Dbp, Per1, Per2, Cry1, Cry2, and Homer1a (top to bottom panels, respectively) mRNA levels after 4 different 6-h sleep deprivations (SDep; ZT0-6, ZT6-12, ZT12-18, and ZT18-24 in AK [left], B6 [middle], and D2 [right panels] mice). Mean (± SEM; n = 9/data point) expression in baseline (BSL; gray circles and lines, values at ZT24 replotted at ZT0) and after each sleep deprivation (red circles and lines). Note that SEMs are often smaller than symbol size. Characters near gray baseline symbols denote signifi cant differences from other strains at the time point considered (A = AK; B = B6; D = D2; post hoc Tukey, P < 0.05). (B) Histograms show mean (± SE of the ratio) fold change after each sleep deprivation for each strain (AK: white, B6: black, D2: brown vertical bar) calculated by contrasting values reached at sleep-deprivation-end to corresponding (i.e., same ZT) baseline levels. Red triangles indicate signifi cant sleep-deprivation-to-BSL differences (post hoc, t-tests, P < 0.05). Red asterisk indicates signifi cant strain difference in the effect of the ZT6-12 sleep deprivation observed for Homer1a (AK > B6, D2: post hoc Tukey, P < 0.05). Please note logarithmic scaling of y-axes.

Against this background of ongoing baseline changes, we assessed the effect of sleep deprivation and its interaction with time of day. Sleep deprivation did not significantly affect Cry2 expression in the brain (Figure 1A, B) consistent with our published results.¹⁷ Although significant at some times of day (i.e., sleep deprivations ZT0-6 and ZT18-24), also for Cry1 the effects of sleep deprivation were modest (< 1.2-fold; Figure 1B). The sleep-deprivation-induced increase in Per1 mRNA levels after the ZT0-6 sleep deprivation matched our previous observations,²⁰ although now only for D2 mice was a significant increase reached. At other times of day, sleep deprivation did not consistently affect Per1 expression. Robust effects of sleep deprivation were observed for the remaining 3 transcripts Dbp, Per2, and Homer1a and will be focused on here.

Sleep deprivation consistently decreased Dbp expression and increased Per2 and Homer1a expression in all 3 inbred strains with the exception of the sleep deprivation ending at ZT18 (Figure 1B). At this time, deviations from corresponding baseline values were significantly smaller for all 3 transcripts and strains, and remained significantly different from baseline for Homer1a only. Although at first glance similar, the time of day and sleep-deprivation-dependent dynamics that contributed to the decreased effect (or lack thereof) after the ZT12-18 sleep deprivation greatly differed among the 3 transcripts. As is the case here (Figure 1B), effects of sleep deprivation on gene expression are usually assessed by comparing the levels reached after the sleep deprivation with levels attained at the same time of day during baseline conditions. Because we have suggested a role for Per2 and Homer1a in the homeostatic regulation of sleep, it is important to also evaluate the levels reached after sleep deprivation relative to the level at which the sleep deprivation was initiated. If indeed indexing homeostatic sleep need, a transcript should consistently and monotonically increase (or decrease in the case of Dbp) over the course of the sleep deprivation irrespectively of the level at which the sleep deprivation was initiated (unless saturation levels are reached; i.e., ceiling effect). The time course of Homer1a clearly illustrates this; i.e., its expression always increased independent of the time the sleep deprivation occurred (Figure 1A). The degree by which Homer1a increased was, however, not constant, and the levels reached seemed to saturate such that the magnitude of the increase was larger when sleep deprivation started at low baseline expression levels and smaller when starting at higher levels. This relationship, quantified by linear regression, could explain 80% of the variance observed in the increase over the course of the sleep deprivation (Figure 2, lower right panel). Consistent with the prediction of such dynamics, we observed that amplitude of change over the day in the Homer1a levels reached after the four sleep deprivations was significantly reduced compared to that in baseline levels (1.3-fold vs. 2.8-fold; Figure 1A; 2-way ANOVA: interaction factors “ZT” (0-, 6-, 12-, 18h) and “Condition” (sleep deprivation, baseline); P < 0.0001), which points to a ceiling effect or, in modeling terms, the presence of an upper asymptote.

Figure 2.

Correlations between the slope of the ongoing baseline change in gene expression, the gene expression at sleep deprivation onset, and the sleep-deprivation induced change in gene expression. Depicted are linear regression lines (solid) and their 95 % confidence interval (delimited by paired dashed lines) for the partial correlations of Dbp, Per2, and Homer1a transcripts (top to bottom panels, respectively) calculated for the dependence of the sleep-deprivation (SDep)-induced change in gene expression on either the ongoing baseline change in expression (i.e., “slope,” left panels, green symbols), or the expression at sleep-deprivation-onset (right panels, blue symbols). The effect of the level of expression at sleep-deprivation-onset was removed for assessing the effect of slope on the effect of sleep deprivation and vice versa (i.e., partial correlations). Analyses are based on the mean values obtained in the 3 inbred strains (n = 3/sleep deprivation, total n = 12; see Figure 1). Partial correlation coefficients are indicated (r_par; P-values in parentheses). Note that for Homer1a the sleep-deprivation-induced increase depends only on its expression at sleep-deprivation-onset, while for Dbp and Per2, the sleep-deprivation-induced change depends almost exclusively on the ongoing change in expression under baseline conditions (or “slope”). Further note that the data points can no longer be directly compared to those in Figure 1, as these are adjusted according to the partial correlations.

The time of day dependent changes in the sleep-deprivation-induced effects on Per2 and Dbp expression clearly differed from that of Homer1a. There was no indication of the presence of an upper asymptote (or lower asymptote in the case of Dbp) that could explain the lack of or reduced effect of the sleep deprivation ending at ZT18 (Figure 1A). Furthermore, Per2 expression decreased with respect to its level at sleep deprivation onset when the sleep deprivation was initiated at ZT18. This effect was robust and observed in all 3 inbred strains. Similarly, the expression of Dbp increased when the sleep deprivation was initiated at ZT0. Closer inspection revealed that the direction and magnitude of change in the expression of these 2 transcripts during the sleep deprivation depended on the ongoing change during baseline, such that when sleep deprivation was performed during the decreasing phase of Per2 expression, the increase was smaller or even negative, and, when sleep deprivation was performed during the increasing phase, a larger relative change was observed. Changes in Dbp followed a similar (albeit opposite) pattern. The quantification of this relationship by linear regression demonstrated that the slope of the ongoing change in baseline predicted > 80% of the variance in the change in expression over the course of the sleep deprivation (Figure 2, upper and middle left panels). In contrast to the dynamics underlying Homer1a expression, the level of expression at sleep-deprivation onset did contribute less (for Per2) or not at all (for Dbp; Figure 2, upper and middle right panels). These results support the idea that in brain areas outside the SCN, the expression of the circadian genes Per2 and Dbp vary both in relation to time of day (circadian) and in relation to the sleep-wake distribution (homeostatic), while Homer1a is mainly activity (or waking) induced.

Predicting the Time Course of Per2, Dbp, and Homer1a Expression: A Model Approach

That the effect of enforced wakefulness on Per2 and Dbp expression in the brain depends on the ongoing direction and rate of their change in baseline is reminiscent of the phase-dependent effects of a force exerted on a body in oscillation, such as in a pendulum or a spring-mass system. To test this, we assumed that the expression of both transcripts behave according to a driven harmonic oscillator with damping in proportion to the velocity of the oscillation. We implemented an iterative solution using the common 4^th-order Runge-Kutta approximation, enabling the instantaneous assessment of the effects of a driving force exerted at any given time (see Methods). Since we think that the expression of these transcripts in the brain is, at least in part, determined by the sleep-wake distribution, we used, as a starting point, the sleep-wake distribution as the driving force. Using data obtained in mice recorded in the sleep experiment presented below, we determined time spent asleep and awake for consecutive 5-min intervals during baseline recordings and during the four sleep deprivations performed at the four different zeitgeber times. Because extended waking suppresses Dbp and increases Per2 expression, maximal force (set to 1.0N) was exerted when the mouse was asleep or awake for the entire 5 min of a given interval, for Dbp and Per2, respectively. For Dbp the sleep-wake distribution initiated an oscillation with a phase matching that observed in baseline (Figure 3, upper panels). Effects of the four sleep deprivations were also reliably reproduced. Specifically, the increase of Dbp during the ZT0-6 sleep deprivation and its varying decrease during the 3 other sleep deprivations could be explained with this model. The fit was optimized by systematically varying the damping constant and comparing z-transformed predicted versus observed data; i.e., Dbp expression levels at the four time points under baseline and sleep deprivation conditions averaged over the 3 inbred strains. Optimal fit was reached with a damping constant of 2.25 kg/s. Correlation analysis revealed that 94% of the variance in the data could be accounted for by the simulation (r = 0.972, P < 0.0001, n = eight data points).

Figure 3.

Simulation of the dynamics of Dbp, Per2, and Homer1a expression. (A) Simulation of the time course of Dbp (upper), Per2 (middle), and Homer1a (lower panel) expression in the brain. For Dbp and Per2, a driven and damped harmonic oscillator was assumed with as periodic driving force either the sleep-wake distribution (for Dbp: dark-gray signal at bottom of panel indicates minutes spent asleep in consecutive 5-min intervals) or the changes in plasma corticosterone levels (for Per2: dark-gray signal at bottom of panel, amplitude set to 1.0; see Figure 4). These recurrent forces initiate and set the phase of the circadian expression pattern in Dbp and Per2 (gray line) in baseline (see Methods and Results for details). For Dbp the force exerted during the four 6-h sleep deprivations (SDep; ZT0-6 orange; ZT6-12: yellow; ZT12-18: green; ZT18-24: blue) is zero as no sleep was present. For Per2 it was assumed that the force was the same for the 4 sleep deprivations and to follow a square-wave function, the amplitude of which was optimized by fitting to the empirical expression data. Simulations were run for 10 days prior to sleep-deprivation-onset in order to reach steady state oscillations (days 1-8 not shown). Changes in Homer1a expression were simulated according to the same assumption as EEG delta power (see Methods and Figure 5); i.e., expression increases during 4-s epochs scored as wakefulness and REMS and decreases during 4-s epochs scores as NREM sleep according to exponential saturating functions (gray line). The simulation presented was performed using the sleep-wake distribution of an individual mouse (dark-gray signal at bottom of graph; min of waking/5min interval). Gray and red symbols are the predicted expression levels at the timepoints the empirical samples were taken during baseline and after sleep deprivation, respectively (see Figure 1 and panels B). Light gray areas denote the dark periods. (B) Comparison of the predicted (left) and observed (right panel) expression levels for Dbp, Per2, and Homer1a. Empirical data were averaged for the 3 inbred strains (see Figure 1) during baseline (gray lines and symbols) and sleep deprivation (red dashed lines and symbols).

With the same assumptions we then simulated the dynamics of Per2 expression in the brain but now with waking, instead of sleep, providing the positive force. The phase position of the resulting oscillation in baseline was, however, delayed by about 6 h relative to the one observed (analysis not shown). A well-established zeitgeber for Per2 expression in peripheral tissues is circulating corticosterone.^34–38 We therefore used the time course of the baseline changes in plasma corticosterone levels measured in B6 mice to initiate and set the phase of Per2 rhythmicity in the brain. In the simulation, the maximum force (set to 1.0) exerted by corticosterone occurred at ZT11 according to our data (Figure 4) and consistent with the literature.³⁹ The phase of the resulting oscillation now matched the one observed (Figure 3), supporting the idea that corticosterone sets the phase of Per2 expression in the brain.³⁸ We previously reported that sleep deprivation increases Per2 expression not only through extending wakefulness but also through the sleep-deprivation-associated increase in corticosterone.²³ This combined action was included in the simulation as being the same constant force for the duration of each of the four sleep deprivations. The amplitude of this force (relative to the baseline force), in addition to the damping constant, were optimized by minimizing the square of the differences between the predicted and observed z-transformed data. Best fit was obtained with a damping constant of 0.65N/s and a sleep deprivation force 2.50 times greater than maximal forces exerted during baseline. With these assumptions and parameter settings, the observed effects of the four sleep deprivations on Per2 expression could be reliably reproduced (Figure 3). Specifically, the decrease of Per2 during the ZT18-24 sleep deprivation and its varying increase during the 3 other sleep deprivations could be explained in detail with this model. As for Dbp, the simulation of Per2 accounted for almost all of the variance in the data (r = 0.973; P < 0.0001; n = eight data points).

Figure 4.

Baseline time course of plasma corticosterone levels. Mean (± SEM; n = 4/time point; 8 samples/mouse; total n = 12; see Methods) time course of changes in plasma corticosterone (black symbols and line; left y-axis). Gray line indicates best fit Gaussian function (r = 0.86, P < 0.0001, n = 24 data points; estimated peak time 11.0 ± 0.3 h; nonlinear regression). Fit values were used as the force driving for the baseline changes in Per2 expression (Figure 3A, middle panel). Values were normalized to fit a 0 to 1 scale (right y-axis). Gray areas delineate the dark period.

Finally, to contrast these 2 transcripts that combine information concerning time of day as well as time spent awake, we simulated the expression of Homer1a. As for Dbp, the simulation was based solely on the sleep-wake distribution, but unlike for Dbp (and Per2) we used saturating exponential functions to estimate its dynamics similar to established methods to predict the dynamics of EEG delta power (see Figure 5),^18,24,40,41 and consistent with Homer1a being an activity-induced transcript.⁴² In each 4-s epoch scored as wakefulness (or REM sleep), Homer1a was assumed to increase, and in each 4-s epoch scored as NREM sleep its expression was assumed to decrease. These changes were delimited by upper and lower asymptotes that, in addition to the 2 time constants defining the rate of change of the 2 exponential functions, were the free parameters to be optimized in the simulation. Optimal fit was obtained with an upper asymptote of 5.82 and a lower asymptote of 0.55 (expressed in the same relative units as in Figure 1) and time constants of 2.85 and 0.70 h for the increase and decrease of Homer1a, respectively. Also this simulation reliably recapitulated the main features observed for the dynamics of Homer1a; i.e., its time course in baseline, the fact that it always increases during sleep deprivation, the dependence of the magnitude of increase during sleep deprivation on its initial level, and the reduced amplitude of the changes in the levels reached after the sleep deprivation compared to those observed in baseline (r = 0.981; P < 0.0001; n = eight data points).

Figure 5.

Effects of sleep deprivation on NREM sleep, EEG delta power, and sleep-onset latency as a function of time of day. (A) Mean (± SEM) time course of EEG delta power during NREM sleep (triangles; % of the last 4 h of the baseline light periods), simulated values of “Process S” (lines; right y-axis), and time spent in NREM sleep (circles; min/ recording h; left y-axis) during 48-h baseline (gray symbols and lines) and during and after four 6-h sleep deprivations (SDep) starting either at 48 h (ZT0: orange), at 54 h (ZT6: yellow), at 60 h (ZT12: green), or at 66 h (ZT18, blue) after the start of the recording. Gray areas delineate the dark periods. Note that for baseline, all 4 experimental groups were pooled (n = 33), rendering SEM smaller than symbol size. (B) Loss of time spent in NREM sleep varied among the 4 sleep deprivations. Vertical bars represent mean (± SEM) difference between NREM sleep during the sleep deprivation and during the corresponding 6-h interval during baseline and thus reflect mainly the distribution of NREM sleep during baseline. Asterisks mark significant differences among sleep deprivations (post hoc Tukey; P < 0.05; ZT0 = ZT6 > ZT18 > ZT12). Color coding for sleep deprivation timing as in panel A. ZT times indicated refer to the start of the sleep deprivations. (C) Sleep onset latency, calculated from the end of the sleep deprivation to the first consolidated NREM sleep bout, importantly varied among sleep deprivations. See panel B for details. (D) Differences between empirical and simulated levels of EEG delta power calculated for the first 20 min of NREM sleep after sleep deprivation. Asterisk indicates significant differences between observed and predicted values (post hoc, paired t-tests; P < 0.05). See panel B for details.

Time of Day Modulates the Effect of Sleep Deprivation on EEG Delta Power

In addition to providing the sleep-wake data to base our gene expression simulations on (see previous section), the sleep EEG experiment allowed us to determine whether a sleep deprivation performed at different times of day differently affected EEG delta power, a measure thought to exclusively index homeo-static sleep need with circadian factors having negligible influence.¹ Although this issue was addressed in various mammalian species,^5,43–46 experimental data in the mouse were lacking.

During the 2 baseline days, the typical sleep-wake distribution of B6 mice was observed with a clear preference for sleep during the light periods, lowest levels of sleep in the first half of the dark periods, and a transient increase in sleep time in the second half of the dark period (Figure 5A).³³ This nycthemeral distribution of sleep gave rise to the equally typical dynamics of delta power reaching highest levels during sleep immediately following the initial period of sustained wakefulness in the dark period, followed by a gradual decline as a function of the presence of NREM sleep, and reaching lowest levels in the last 4 h of the light periods. Because of the baseline distribution of sleep and waking, the four 6-h sleep deprivations, scheduled at four different times of day, deprived mice of varying durations of sleep, ranging, on average, from 40 to 200 min (Figure 5B).

All four sleep deprivations raised delta power well above the highest levels reached during baseline (Figure 5A; post hoc paired t-test, P < 0.01), but its level significantly varied according to the time of day recovery sleep was initiated, with highest values reached after sleep deprivations initiated at ZT12 (242 %) and lowest for sleep deprivations initiated at ZT0 and ZT18 (194% and 201%; 1-way ANOVA factor ZT P < 0.01; post hoc Tukey; ZT12 > ZT18 and ZT0; P < 0.05). Several factors are likely to have contributed to these differences in EEG delta power reached after the four sleep deprivations. For example, the initial conditions of the four sleep deprivations differed; i.e., sleep need at the onset of the ZT18-24 sleep deprivation is higher compared to that at which the ZT6 and ZT12 sleep deprivations were initiated because animals had been awake for most of the preceding 6 h. Moreover, sleep onset latency; i.e., the time between the end of the sleep deprivation and the start of recovery sleep, differed such that mice deprived of sleep from ZT12-18 remained awake about 2.5 h longer than the other 3 sleep deprivation conditions (Figure 5C). We addressed these 2 specific issues by performing a simulation analysis that predicts the level of delta power by taking the 4s-by-4s individual sleep-wake distribution over the 96-h recording time into account, similar to that performed for Homer1a (see above). The simulation was carried out using the exact same model parameters determined previously in a sleep deprivation experiment starting at ZT0 in the same inbred strain (see Methods section).¹⁸ The simulation could predict with high accuracy the empirical levels of delta power throughout the experiment (Figure 5A); in particular, its values reached in the first 20 min of recovery NREM sleep after the ZT0-6 sleep deprivation (Figure 5D); i.e., the condition for which the parameters were previously optimized. Also the observed values reached after the ZT12-18 and ZT18-24 sleep deprivations did not significantly deviate from expected levels and were under- and overestimated, respectively, by only 4% (Figure 5D). However, the empirical values reached after the ZT6-12 sleep deprivation were significantly higher (12%) than could be expected based on the sleep-wake distribution, suggesting that time of day modifies the dependence of delta power on the sleep-wake distribution.

Another contributing factor, which was not accounted for by the simulation, was the “quality” of wakefulness induced by the sleep deprivation. The theta content of the waking EEG is known to increase over the course of extended waking periods^27,47 and has been reported to predict delta power in subsequent NREM sleep.⁴⁸ We therefore quantified theta power reached in the last 90 min of the sleep deprivation. For all four sleep deprivations, the waking EEG showed a clear theta component (Figure 6A), although its magnitude and frequency significantly varied among sleep deprivations. Theta oscillations were slower for the 2 sleep deprivations performed during the light phase compared to the dark and, against expectation, during the ZT6-12 sleep deprivation, which was followed by above expected levels of delta power, lowest theta power levels were reached (Figure 6B). We further noted that of the four sleep deprivations, the ZT6-12 sleep deprivation was clearly the most difficult to perform. This was reflected by the higher number of NREM sleep episodes occurring during this sleep deprivation (Figure 6C), resulting in more NREM sleep accrued during the ZT6-12 sleep deprivation than the other 3 sleep deprivations (ZT0, -6, -12, and -18 sleep deprivation: 4.3 ± 1.3, 8.1 ± 1.2, 2.3 ± 1.0, and 1.7 ± 0.5 min, respectively; 1-way ANOVA P < 0.0005; post hoc Tukey: ZT6 > ZT0 = ZT12 = ZT18 sleep deprivation; P < 0.05).

Figure 6.

EEG theta activity and the number of NREM sleep episodes during the sleep deprivation. (A) Mean waking EEG spectra during the last 90 min of the four 6-h sleep deprivations (SDep) starting at ZT0 (orange), -6 (yellow), -12 (green), or -18 (blue line). For comparison the mean spectral profile for waking calculated of the 48-h baseline is depicted (gray line). Baseline spectral profiles did not differ among the 4 sleep-deprivation groups. (B) Theta peak power (left) and frequency (right panel) did differ among the 4 sleep deprivations (post hoc Tukey; P < 0.05; peak theta power: ZT0 = ZT18 > ZT18 = ZT12 = ZT6; frequency: ZT12 = ZT18 > ZT6 = ZT0). Color coding for sleep-deprivation timing as in panel A and ZT times indicated refer to the sleep-deprivation start. (C) The number of NREM sleep episodes obtained during the ZT6-12 sleep deprivation was highest (post hoc Tukey; P < 0.05; number of episodes: ZT6 > ZT0 = ZT12 = ZT18). See panel B for details.

DISCUSSION

The study of circadian rhythms and sleep homeostasis critically depends on variables that reliably reflect either one of these two processes. Here we demonstrate that an acute, short-lasting sleep deprivation immediately influences the expression of the circadian clock gene Per2, widely used as a circadian state variable, and of the clock-controlled gene, Dbp, in a time of day dependent manner. Moreover, the sleep-deprivation-induced increase in EEG delta power, a measure thought to be exclusively determined by the sleep-wake history, displayed a time of day modulation. These findings add to a growing body of evidence pointing to a considerable cross-talk between these two processes at various levels of organization.¹⁴ Finally, our results illustrate that no definitive insight into the relationship between sleep, waking, and gene transcripts can be gained by performing a single sleep deprivation, and that the effects should be evaluated in light of the ongoing dynamics at the time the sleep deprivation is performed. Using quantitative models such as the ones presented here could help delineate the nature of these interactions.

Per2 Integrates Information Concerning Time of Day and Time Spent Awake

Clock genes importantly contribute to the generation of circadian rhythms and engage in transcriptional-translational feedback loops resulting in rhythmic expression of their mRNA and protein levels in most tissues.⁹ Other factors can, however, affect the expression of clock genes (Figure 7). For instance, sleep loss is known to change the expression of the clock genes Per1-3, Npas2, Rev-Erbα, and the clock controlled genes Dbp and E4bp4 (Nfil3).^{17,18,20,23,25} Of the remaining core clock genes Clock, Bmal1, Cry1, and -2 expression seem less or not affected by elevated sleep pressure (see our current data and those of Wisor [2002],¹⁷ but also see Wisor [2008]²¹). The sleep-deprivation-induced increase in Per2 expression in the brain was mediated, at least in part, through the molecular circadian clock because in Npas2 knock-out mice and in Cry1,2 double knockout mice, this increase was significantly reduced and augmented, respectively.^18,21

Figure 7.

Summary of the molecular mechanisms by which sleep deprivation could alter clock gene expression in the forebrain. A negative feedback loop underlies circadian rhythm generation with, as the positive arm, NPAS2 (or CLOCK)::BMAL1 heterodimers activating the transcription of Per and Cry (only Per2 shown) through their E-box enhancers. PER and CRY proteins then increase (green arrow) and, upon nuclear entry, associate with the NPAS2::BMAL1 complex to inhibit their own transcriptional activation thus providing negative feedback (red arrow). PER and CRY proteins then decrease resulting in a removal of this inhibition allowing the cycle to restart. As a result NPAS2::BMAL1 target genes, such as Per2, cycle with a near 24-h period in many tissues. Expression of other genes, including Dbp and E4bp4, are similarly regulated. Besides this circadian regulation, Per2 expression is regulated by other factors through which sleep deprivation might act: e.g., the cAMP response element (CRE), glucocorticoid response element (GRE), and D-box enhancers through which phosphorylated CRE binding protein (pCREB), ligand-bound glucocorticoid receptors (GR), and DBP can induce Per2 expression, respectively, while E4BP4, also acting on the D-box, can repress Per2 expression. Sleep deprivation, besides extending waking, also activates the HPA axis and metabolism, evidenced by its induction of corticosterone (CORT), increased CREB phosphorylation and Npas2 and E4bp4 expression (green dashed arrows), and decreased Dbp expression (red dashed arrow). In addition, sleep-deprivation-induced changes in metabolic state as evidenced by changes in NAD⁺, can directly affect NPAS2 mediated transcriptional activation and the SIRT1-mediated deacetylation (Ac) of PER2. These “non-circadian” changes in Per2 could impinge on the ongoing circadian oscillation as conceptualized in the model presented in Figure 3. See text for references.

Another factor importantly contributing to the changes in Per2 expression is the sleep-deprivation-associated increase in corticosterone.²³ Corticosterone can directly control Per1 and -2 expression through glucocorticoid responsive elements (GRE) in their promoter,^38,49,50 and is known to be important in setting the phase of circadian rhythms in the periphery.^34,36–38 The importance of corticosterone in setting the phase of Per2 expression in the brain was further underscored in the present simulation analysis. Moreover, extended periods of wakefulness are known to augment levels of phosphorylated cAMP response element (CRE) binding protein (pCREB) in the cerebral cortex,^51,52 which could have contributed to the observed increase in Per2 expression through binding to the CRE element in its promoter.⁵³ Tumor necrosis factor α (TNFα), which also increases with sleep deprivation,⁵⁴ seems to affect Per2 expression through the same signaling pathway.^55,56 Other likely contributions concern the activation of Per2 transcription through its D-box elements to which DBP and E4BP4 are known to bind, although E4BP4, which is increased by sleep deprivation,²³ is a suppressor of Per2,⁵⁷ while Dbp, which is decreased by sleep deprivation (current data and^17,20,23,25), activates Per2 transcription.^57,58–60

This dual aspect of the control of Per2 expression; i.e., through circadian and “activity induced” factors summarized in Figure 7, could also play a role in explaining why two CLOCK/NPAS2:BMAL1 target genes (i.e., Per2 and Dbp) can be affected in opposite ways by sleep deprivation. If indeed activation of Per2 expression through corticosterone and/or CREB phosphorylation causes PER2 protein levels to increase during the sleep deprivation, then PER2 could suppress Dbp expression through interference with CLOCK::BMAL1 and/or NPAS2::BMAL1 complexes. Consistent with this is the observation that the increase in Per2 expression during a sleep deprivation precedes the decrease in Dbp expression.²⁰ In this scenario, the activation of Per2 expression by these non-circa-dian factors should outweigh the suppression by PER2 of its own “circadian” transcription. Our recent findings that sleep deprivation reduces DNA binding of CLOCK, NPAS2, and BMAL1 onto both Per2 and Dbp fit this reasoning.²²

Modeling Gene Expression in the Brain

The model approach proposed here is a first attempt to gain insight into the dynamic coupling of the homeostatic and circadian aspects of sleep on gene expression at the level of a tissue; i.e., the brain. The data and analyses presented in Figures 1 and 2, intuitively suggested the use of a driven harmonic oscillator with the sleep deprivation exerting a driving force on oscillations in Per2 and Dbp expression. In circadian biology, limit-cycle oscillators in which the amplitude of the oscillation is preserved and is independent of forces exerted on the system, are often preferred in modeling to accommodate the self-sustained aspect of circadian rhythms.⁶¹ Nevertheless, even at the level of individual cells, including fibroblasts and SCN neurons, both linear-damped oscillators and self-sustained limit-cycle oscillators seem to describe the data equally well.⁶² Moreover, at the tissue level, circadian rhythms in clock gene expression in brain areas outside the SCN behave as damped oscillators in vitro⁶³ and, under various experimental conditions, follow the sleep-wake (or rest-activity) distribution in vivo,¹⁴ consistent with our model and data. The specific effects of the four sleep deprivations on Dbp and Per2 expression could be reproduced with surprising accuracy and illustrates how the dual (circadian and activity induced) aspect of the control of the expression of these two transcripts interact and explains how the same intervention (i.e., sleep deprivation) can either increase or decrease the expression of a gene. Further, studies could test the model under the various conditions known to alter both the sleep-wake distribution and clock gene expression in the brain, while leaving rhythms in the SCN unaffected (e.g., food restriction, circadian splitting, methamphetamine administration; reviewed in¹⁴). Our recently submitted work could already confirm one prediction of the model; i.e., when sleep and wakefulness are homogenously distributed over the 24-h day, such as is the case in SCN-lesioned mice, circadian rhythms in PER2 protein in peripheral tissues, including the brain, are lacking (T. Curie, S. Maret, Y. Emmenegger, and P. Franken; In vivo imaging in peripheral tissues reveals sleep-wake dependent and circadian factors driving PER2 protein levels, Submitted), notwithstanding the fact that ex vivo and in vitro studies have demonstrated that these tissues do have the intrinsic capacity to generate circadian rhythms.^8,64

Besides its accuracy in reproducing the results the model was also straightforward in that only one (damping constant for Dbp) or two (damping constant and magnitude of force provided by the sleep deprivation relative to the baseline driving force for Per2) parameters had to be optimized. Both maximal driving force and weight were set to unity and, as only the relative changes of sleep deprivation were considered (z-scores), were no longer free parameters. Likewise, the intrinsic period of the system (set to 23.5 h) is not a critical parameter under the entrained conditions the model was tested (analysis not shown). The model was used to predict changes in mRNA levels and could be extended to predict protein levels. The sleep-deprivation-incurred changes in Per2 expression could be coupled to those of Dbp given the earlier argument that increases in PER2 could contribute to inhibiting Dbp transcription. Such inhibition is likely to affect the damping constant in the model which was found to be higher for the simulation of Dbp expression than for Per2. Clearly, other assumptions, such as the uniform force provided by the sleep deprivation used to predict the sleep-deprivation-induced changes in Per2, require validation. At present, only for the ZT0-6 sleep deprivation the respective contribution of corticosterone and wakefulness (40% and 60%) to the increase in Per2 expression can be estimated.²³

The model describing Homer1a expression followed the established methods of predicting the sleep-wake dependent changes in EEG delta power in mammals,^40,65 including mice.^24,41 The baseline time course and the different effects of the four sleep deprivations could be captured in detail. The optimal time-constant of the build-up rate of Homer1a during wakefulness estimated here in the simulation (2.9 h) is close to the one that can be empirically obtained from the dynamics of Homer1a expression in the brain after 0-, 1-, 3-, and 6-h sleep deprivations in the same three inbred strains (3.2 h; nonlinear regression analyses assuming an saturating exponential rise).⁶⁶ Obviously, data sampled at a higher time resolution could help test the model's predictions and the assumption that both waking and REM sleep similarly activate Homer1a.

Does Time of Day Modulate the Dynamics of EEG Delta Power?

EEG delta power is widely used to index homeostatic sleep need because most of its changes in baseline and after short-term acute sleep deprivations can be readily predicted based on the prior sleep-wake history in mammals.^{24,40,41,65,67} Studies in SCN-lesioned rats⁶⁸ and mice⁶⁹ and studies in arrhythmic Siberian hamsters⁷⁰ revealed no large impact of the loss of circadian regulation on the rebound in delta power after sleep deprivation. Nevertheless, simulation studies of the time course of delta power during baseline and after a sleep deprivation in the intact rat revealed a significant and systematic time of day variance that could not be accounted for by the sleep-wake distribution or the light-dark cycle.^40,43 Although simulation studies in the mouse did not reveal a similar time of day variance in the dynamics of delta power,^24,41 empirical data on such modulation in this model species were lacking.

Levels of delta power reached after each of the four 6-h sleep deprivation varied with highest levels reached after the sleep deprivation that started with the onset of the active phase; i.e., the ZT12-18 sleep deprivation. After this sleep deprivation, mice did not initiate sleep for another 2.8 h, thereby spontaneously extending sleep deprivation to almost 9 h. Previous efforts to keep mice awake for 9 h during the rest phase were unsuccessful in further elevating delta power compared to a 6-h sleep deprivation because, towards the end, sleep drive was so great that mice accrued considerable amounts of NREM sleep despite the almost continuous interventions aimed at keeping the mice awake.²⁴ This powerfully illustrates that circadian wake promotion can overcome homeostatic drive and that 9 h of sleep deprivation is still within the physiological range of periods of extended wakefulness that mice can sustain. Of note, sleep onset latency after the ZT6-12 sleep deprivation, which thus coincided with dark (and activity) onset, did not differ from sleep onset latencies observed after the ZT0-6 and ZT18-24 sleep deprivations, excluding the lighting condition as an important factor delaying sleep onset. If indeed circadian factors underlie the strikingly long sleep onset latency after the ZT12-18 sleep deprivation, then we also have to accept that the circadian wake-promoting signal is still not important at ZT12, and that other factors [e.g., low homeostatic sleep drive, high corticosterone levels, cessation of a circadian sleep promoting drive (see below), and/or dark onset when under LD conditions] contribute to initiating wakefulness at this time of day. Similarly, strongest circadian wake promotion in humans does not occur at wake onset in the morning but, paradoxically, just prior to habitual sleep time.^1,5 Along these lines, the difficulty of keeping mice awake and engaging them in active waking behavior accompanied by theta during the ZT6-12 sleep deprivation, despite their low sleep homeostatic drive (i.e., EEG delta power levels have reached lowest levels by ZT6), might point to an active sleep promotion by the SCN enabling mice to maintain asleep during this part of the day. Evidence for active circadian sleep promotion during the early morning hours has also been reported in humans.⁷¹

The simulation indicated that the high levels of delta power reached after the ZT12-18 sleep deprivation can be fully accounted for by the longer time spent awake, as simulated and empirical levels do not differ (Figure 5D). With the help of the simulation we could establish that, instead, the rebound in delta power after the ZT6-12 sleep deprivation was higher than expected, demonstrating that factors other than homeostatic factors contribute to its expression. When compared to the ZT0-6 sleep deprivation, the ZT6-12 sleep deprivation did not differ in sleep onset latency and the lighting condition under which the sleep deprivation was performed but did differ in the level of sleep need at which the sleep deprivation started, which was lower judged by the level of EEG delta power. Thus, if anything, lower delta power levels after the ZT6-12 sleep deprivation could be expected compared to the ZT0-6 sleep deprivation. Similarly, the extra time spent in NREM sleep and the lower EEG theta levels reached should equally have contributed to a lower delta power in subsequent recovery sleep.⁴⁸ In the rat, delta power tends to be higher when sleep takes place during darkness,⁷² an effect that could have contributed to the higher than expected levels reached after the ZT6-12 sleep deprivation. No evidence of such effect was, however, observed for recovery sleep occurring at ZT18. Nevertheless, we are currently investigating the effects of light on the time of day dependent effects of sleep deprivation on delta power. In summary, apart from assuming a circadian modulation of delta power,⁵ a straightforward explanation for this effect is not easily obtained. It is, however, interesting to note that the ZT6-12 sleep deprivation, apart from driving a delta power response above predicted levels, also produced the strongest increase in Per2 expression.

CONCLUSION

Extended periods of wakefulness can affect Per2 expression in the forebrain through both circadian and non-circadian mechanisms. Per2 thus combines activity induced and circadian aspects known to be central to sleep-wake regulation. Moreover, Per2 seems the only core clock gene that can be driven by both systemic cues and peripheral oscillators,⁷³ suggesting a central role in integrating information at different levels. Our model is a first attempt to gain insight into the dynamic coupling of these two aspects in the forebrain. Of obvious interest for a functional role of clock-genes in sleep homeostasis is their direct relation to energy metabolism both at the systemic and cellular levels,⁷⁴ including recent data linking intracellular redox state to clock genes such as the NAD⁺-dependent activity of the deacetylase Sirtuin 1 (SIRT1), which modulates CLOCK-mediated chromatin remodeling and promotes deacylation and degradation of PER2 (Figure 7).^75–77 Functionally, the coupling between energy balance and clock genes in tissues peripheral to the SCN, would allow adapting to and anticipating to conditions that challenge homeostatic need, such as food restriction,^78–84 and, conceivably, sleep loss.¹⁴

DISCLOSURE STATEMENT

This was not an industry supported study. Dr. Mang received a stipend from Novartis, Basel during his Master's thesis work. The other authors have indicated no financial conflicts of interest.

SUPPLEMENTAL MATERIAL

Table S1

Primer and probe sequences used for real-time qPCR