pii: sp-00406-14

http://dx.doi.org/10.5665/sleep.4656

SLEEP-WAKE BEHAVIOR DECOUPLED FROM DELTA POWER IN SLEEP-RESTRICTED RATS

Behavioral Sleep-Wake Homeostasis and EEG Delta Power Are Decoupled By Chronic Sleep Restriction in the Rat Richard Stephenson, PhD; Aimee M. Caron, BSc; Svetlana Famina, BSc Department of Cell and Systems Biology, University of Toronto, Toronto, Ontario, Canada

Study Objectives: Chronic sleep restriction (CSR) is prevalent in society and is linked to adverse consequences that might be ameliorated by acclimation of homeostatic drive. This study was designed to test the hypothesis that the sleep-wake homeostat will acclimatize to CSR. DESIGN: A four-parameter model of proportional control was used to quantify sleep homeostasis with and without recourse to a sleep intensity function. Setting: Animal laboratory, rodent walking-wheel apparatus. Subjects: Male Sprague-Dawley rats. Interventions: Acute total sleep deprivation (TSD, 1 day × 18 or 24 h, N = 12), CSR (10 days × 18 h TSD, N = 6, or 5 days × 20 h TSD, N = 5). Measurements and Results: Behavioral rebounds were consistent with model predictions for proportional control of cumulative times in wake, nonrapid eye movement sleep (NREM) and rapid eye movement sleep (REM). Delta (∆) energy homeostasis was secondary to behavioral homeostasis; a biphasic NREM ∆ power rebound contributed to the dynamics (rapid response) but not to the magnitude of the rebound in ∆ energy. REM behavioral homeostasis was little affected by CSR. NREM behavioral homeostasis was attenuated in proportion to cumulative NREM deficit, whereas the biphasic NREM ∆ power rebound was only slightly suppressed, indicating decoupled regulatory mechanisms following CSR. Conclusions: We conclude that sleep homeostasis is achieved through behavioral regulation, that the nonrapid eye movement sleep behavioral homeostat is susceptible to attenuation during chronic sleep restriction and that the concept of sleep intensity is not essential in a model of sleepwake regulation. Keywords: allostasis, chronic sleep restriction, EEG delta power, proportional control model, sleep deficit, sleep deprivation, sleep homeostasis, sleep intensity, sleep regulation, two-process model Citation: Stephenson R, Caron AM, Famina S. Behavioral sleep-wake homeostasis and EEG delta power are decoupled by chronic sleep restriction in the rat. SLEEP 2015;38(5):685–697.

INTRODUCTION In recent decades Western societies have witnessed deterioration in the quality of sleep and a corresponding rise in excessive daytime sleepiness, a trend that has been linked to a variety of adverse health consequences for individuals, and to major economic costs for society at large.1–5 It is often claimed that a significant fraction of the North American population lives with a chronic sleep debt,5 or a sleep disorder,6 although the true extent of the problem remains a matter of debate.7 The ability of individuals to cope with inadequate sleep will depend in part on whether the sleep regulatory system can acclimate to the chronic stress of chronic sleep restriction (CSR). Such acclimation would be expected to lessen the effect of excessive daytime sleepiness8 and perhaps mitigate other potential health consequences of sleep loss. Sleep propensity is regulated in part by an interval-timer mechanism, which mediates the well-known increase in propensity for sleep as a function of excess time spent awake.9 Borbély10 hypothesized that this mechanism serves as a “sleep homeostat” that defends a minimum daily sleep requirement,

and that it works in conjunction with a circadian clock to influence the daily quantity and timing of sleep in mammals. These ideas were formalized as a two-process model of sleep regulation,11 which still represents the conceptual foundation for most current theories in sleep regulation. It was noted,10,12 on the basis of the available data, that acute total sleep deprivation (TSD) is rarely followed by a rebound in sleep time that fully compensates for the duration of lost sleep (here a “rebound” is defined as a post-TSD increase in sleep above corresponding baseline levels). Such apparent shortfalls in sleep compensation have been reported in many studies of animals and man12–26 and represent a major problem for a hypothesis of sleep homeostasis, leading to ancillary concepts such as “sleep intensity” 10,12 and “core sleep.” 27 Hence, the two-process model proposes that rebound sleep is more “intense” than baseline sleep and that compensation for a sleep deficit consequently takes place more efficiently in the interval immediately following extended wakefulness. Earlier research28–30 had suggested that the power in the delta (∆) band (0.5–4 Hz frequency range) of the human electroencephalogram (EEG) is regulated in a way consistent with a homeostatic mechanism during stage 4 nonrapid eye movement sleep (NREM), and Borbély adopted ∆ power as an index of NREM sleep intensity in the two-process model.10,11 Since then, the homeostatic regulation of sleep and that of EEG ∆ power have generally been conceptualized, either explicitly or implicitly, as one and the same,31–33 although not without criticism.22 We suggest that the conflation of behavioral and EEG processes is unnecessary in the context of sleep-wake regulation, and support this by showing that cumulative sleep time is regulated by a long-term homeostatic control system

A commentary on this article appears in this issue on page 661. Submitted for publication June, 2014 Submitted in final revised form September, 2014 Accepted for publication September, 2014 Address correspondence to: Richard Stephenson, PhD, University of Toronto, Department of Cell and Systems Biology, 25 Harbord Street, Toronto, Ontario, M5S 3G5, Canada; Tel: (416) 978-3491; Fax: (416) 9788532; Email: [email protected] SLEEP, Vol. 38, No. 5, 2015

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error signal (Y0; deviation of cumulative time in state from set-point, termed wake excess, NREM deficit, and rapid eye movement sleep [REM] deficit) declines progressively as recovery proceeds, which in turn should induce a proportional decrease in the propensity for sleep, and hence in the rate of rebound, yielding a monotonic return of sleep-wake expression toward baseline values (Figure 1). The characteristic rate of rebound can therefore be quantified as the exponential time constant (τ) of the response. If the accumulated sleep deficit is great enough to exceed the maximum compensatory capacity of the system, then the completed response will leave a residual (uncompensated) sleep deficit (i.e., a sleep “debt”), quantifiable as a response offset (T0 ), as shown in Figure 1B. Under such circumstances, T0 should increase in direct proportion to the supramaximal TSD stimulus. Thus, four key parameters (τ, Rspan, Y0 and T0 ) are sufficient to provide a complete quantitative description of the rebound response and to evaluate whether the response acclimates to chronic sleep deficit. MATERIALS AND METHODS Subjects All procedures were performed in accordance with the guidelines established by the Canadian Council on Animal Care and were approved by the animal care committee at the University of Toronto (permit #: 20006771, 20007848). Male SpragueDawley rats (N = 23) were maintained at 21–23°C under a 12:12 h light-dark (LD) cycle. They had free access to food (standard laboratory rodent chow) and water throughout the study. Twelve rats (484 ± 14 g at baseline) were subjected to acute TSD (18 h in three rats and 24 h in nine) to establish the plausibility of the proportional control model of behavioral homeostasis and quantify the key variables. Two additional groups of animals were subjected to CSR. The first group (CSR18, N = 6, 516 ± 20 g at baseline) was exposed to 10 consecutive days of TSD for 18 h per day. The second group (CSR20, N = 5, 516 ± 39 g at baseline) was exposed to 5 consecutive days of TSD for 20 h per day. CSR18 is an entirely new analysis of data recorded in a previously published study.35 CSR 20 is a replication of the CSR schedule used by others.33,36 In all groups of rats, TSD and CSR were preceded by 2 undisturbed baseline days and followed by 3 undisturbed recovery days.

Figure 1—Quantitative analysis of cumulative time in state reveals a monotonic rebound in total sleep following acute 24 h total sleep deprivation (TSD). (A) Cumulative time in total sleep (tNREM and tREM combined) recorded over 4 w in one rat shows baseline stability before and after 24 h acute TSD (gray bar). Inset illustrates progressive return toward the extrapolated baseline linear regression (dotted black line) immediately following the end of TSD. (B) Net (detrended) cumulative sleep time exhibits a monotonic rebound response with superimposed diurnal rhythms. Proportional control model parameters (Rspan, τ, T0, Y0 ) are quantified by nonlinear exponential regression (black curve; see text for details).

independent of an intensity dimension. We further show that the post-TSD rebound in cumulative ∆ power (∆ energy) follows a different time course to that of sleep behavior. We suggest that sleep-wake state and EEG ∆ power are each regulated by separate, but correlated, controllers. Finally, we present evidence that CSR can lead to dissociation of the two control mechanisms, because CSR induces pronounced suppression of the behavioral homeostat, but little change in the biphasic ∆ power rebound during NREM recovery sleep. Our approach is based on the premise that homeostasis of sleep-wake behavioral state is mediated by a closed-loop proportional control system.34 Briefly, we assume that a physiological mechanism tracks (integrates) the time spent in sleep-wake states and acts to maintain a balance between sleep and wakefulness within a restricted range (“set-point”) over a timescale spanning hours to days. The proportional controller elicits a compensatory response (sleep rebound) when wakefulness is prolonged because of external disturbance (TSD). To be considered a true homeostat, the magnitude of the cumulative sleep rebound (Rspan ) should be directly proportional to the cumulative TSD stimulus, within a limit determined by the maximum compensatory capacity of the system. In a simple first-order system, this characteristic of direct proportionality should be evident not only between TSD episodes of differing duration, but also within each response. The latter derives from the model assumption that, following the end of TSD, the state-specific SLEEP, Vol. 38, No. 5, 2015

Surgical Procedures Details on the surgical procedure are reported elsewhere.35 Briefly, animals were anesthetized using isoflurane (1–2% in air/ O2 mix), and implanted intra-abdominally with a multichannel radio transmitter (model TL10M3-F50-EET, Data Science International, St. Paul, MN) to enable continuous recording of EEG and electromyogram (EMG) used in the scoring of sleepwake state. Multistranded stainless steel electrodes were tunneled subcutaneously to the head and neck, respectively. Bipolar (differential) frontoparietal EEG electrodes were implanted in the skull (coordinates, expressed relative to bregma, AP+2mm, ML2mm and AP-4mm, ML2mm) using stainless steel screws (size 080). EMG was recorded using bipolar electrodes embedded in the right dorsal trapezius muscle. EEG and EMG signals were referenced to a common “floating ground” electrode implanted over the left parietal cortex (AP-2mm, ML2mm). 686

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Rats were administered analgesic (buprenorphine, 0.015 mg.kg−1 subcutaneously [s.c.], or ketoprofen, 3 mg.kg−1 s.c.) during surgery, and for 2 subsequent days. They were allowed a minimum of 7 days to recover before experiments began.

constant”) and IQR is the interquartile range (Q3–Q1). Statistical quantiles were based on 24-h records (≤ 17,280 epochs). This method was preferred over standard parametric techniques because amplitudes of EEG and EMG signals were strongly skewed. Artifacts were filtered before and after state scoring, as follows. Prior to sleep scoring, epochs containing artifacts were identified in baseline recordings in the following sequence: 1. Movement artifact: caused by gross body movements and characterized by simultaneous large deflections in EEG and EMG signals. Epochs were scored as artifacts when both ∑EEG and EMG amplitude exceeded their respective FU. ∑EEG is the sum of amplitudes (μVrms) of the ∆ , θ, α, β, and γ bands. 2. Broadband EEG artifact: caused by external radio interference and characterized by increases in amplitude in all EEG frequency bands. Visible on raw traces mainly as high frequency “white noise,” but shown in conditioned data to affect the full spectrum of recorded frequencies. Epochs not filtered by [1] above, were scored as artifacts when amplitudes of both ∆ and γ bands exceeded their respective FU. 3. Signal dropouts: epochs in which the radio signal was lost, characterized by isoelectric EEG. Epochs not filtered by [1 and 2] above, were scored as artifacts when amplitudes of θ and γ bands simultaneously registered signal amplitude < 0.1th percentile. 4. Low-frequency EEG artifacts: epochs in which the EEG signal fluctuated at low frequency (< 6 Hz) about the mean without concurrent excessive noise in the EMG channel. Epochs not filtered by [1, 2, and 3] above, were scored as artifacts when amplitudes of both EEGlo and ∆ bands exceeded their respective FU. In each rat, data from all baseline days were subjected to the aforementioned four-stage artifact filter and the mean baseline threshold values (FU) were recorded for each stage. The entire data set (baseline, TSD/CSR, and recovery days) was then filtered using mean baseline FU values. Finally, after state scores were assigned, any residual EEG outliers were excluded from EEG power analyses by a final application of Tukey method to each frequency band separately, using the more conservative “outer fence” criterion (k = 3). This ensured that a few individual artifacts did not have disproportionate weight in the calculation of EEG energy. Prescore artifacts comprised 2.4 ± 0.7% of epochs in baseline, 12.8 ± 3.4% during TSD, and 2.8 ± 1.0% in recovery. Postscore outliers in baseline, TSD, and recovery, respectively, were (% of epochs); ∆, 0.06 ± 0.03%, 4.22 ± 2.27%, 0.09 ± 0.04%; θ, 0.2 ± 0.06%, 0.17 ± 0.06%, 0.13 ± 0.04%; α, 0.3 ± 0.14%, 0.56 ± 0.19%, 0.26 ± 0.13%; ß, 0.37 ± 0.08%, 10.3 ± 2.5%, 1.13 ± 0.55%; γ, 0.44 ± 0.09%, 12.1 ± 3.0%, 1.70 ± 0.86%. As mentioned, we measured the epoch mean amplitude (μVrms) of the frequency bands in the rat EEG. In the absence of a DC offset (i.e. zero-mean signal, as was the case in these standard AC-coupled EEG recordings), the root mean square voltage is mathematically equivalent to the square root of variance, and is therefore proportional to EEG power and, by extension, cumulative amplitude is proportional to EEG energy. Hence, for convenience the terms “power” and “energy” are

Experimental Protocol After recovery from surgery, animals were familiarized with a walking wheel (diameter 35 cm, width 16 cm, 3.5 rpm; see Caron and Stephenson35 for details) for several hours on each of 3 days. They were then housed in the wheel apparatus for the remainder of the TSD or CSR protocols. Baseline and recovery data were recorded with the wheel locked to allow ad libitum sleep. During the TSD intervals, the wheel was activated intermittently (8 sec on, 8 sec off) to enforce wakefulness while allowing brief resting periods to facilitate eating, drinking, and grooming behaviors. During 24-h TSD, the wheel was active from ZT0–24. During the 18-h TSD and CSR18 protocols, the wheel was active from ZT6–24. During the CSR 20 protocol, the wheel was active from ZT4–24. Thus, sleep opportunities and full recovery began at ZT0 in all cases. Data Acquisition and Sleep Scoring Data acquisition protocols were as described previously.35,37 Briefly, EEG and EMG signals were acquired by wireless technology to minimize the likelihood of instrumentation-related alteration of sleep-wake behavior.38 AC-coupled data from an analog receiver-decoder (models RPC1 receiver and DL-10 module; Datasciences International, Saint Paul, MN) were digitized at 400 Hz sampling frequency (16-bit data acquisition board, model PCI 6031E, National Instruments, Austin, TX) and conditioned and recorded using custom software (LabVIEW v.7.0, National Instruments). Digital filters (fifth order Butterworth) were used to extract frequency band-specific signal amplitudes (μVrms), which were recorded continuously in 5-sec epochs. EEG signals were filtered into the following bands39: very low frequency (EEGlo, < 1.5 Hz), delta (∆, 1.5–6 Hz), theta (θ, 6–9 Hz), alpha (α, 10.5–15 Hz), beta (β, 22–30 Hz), and gamma (γ, 35–45 Hz). The EMG signal was conditioned with bandpass (10–100 Hz) and notch (58–62 Hz bandstop) digital filters. Sleep-wake states were scored by off-line automated analysis, verified by visual analysis of subsamples of data, as described in detail elsewhere.37 In visual analyses, epochs were scored as wake when the EEG waveform was predominantly low voltage and high frequency and the EMG waveform featured high and variable voltages; as NREM when the EEG contained high amplitude, low frequency waves with low to moderate amplitude EMG; and as REM if the EEG was of low amplitude with prominent theta waves together with very low-amplitude EMG. Modifications were made to the artifact rejection component of the automated sleep-scoring system. Specifically, the artifact-index described previously37 was replaced with a multistage filter based on Tukey nonparametric outlier detection protocol40: FU = Q3 + k · IQR, where, FU is the upper outlier threshold, Q3 is the third quartile (75th percentile), k is a constant (1.5; Tukey “inner fence SLEEP, Vol. 38, No. 5, 2015

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used hereafter. Because of the occurrence of artifacts in some epochs, it was not possible to perform a simple integration of the signals for the calculation of EEG energy. We therefore obtained mean state-specific ∆ power within consecutive 2-h intervals and multiplied those values by the corresponding cumulative times spent in each state (yielding wake ∆ energy, NREM ∆ energy and REM ∆ energy), as well as ∆ energy across all behavioral states (total ∆ energy). EEG energy was also calculated in the same way (state-specific and total) for the θ, α, β, and γ bands. If present, long-term drift in transmitter signal strength was corrected by linear regression. However in the CSR 20 group, unresolved technical difficulties caused slow nonlinear fluctuations of power in the EEG signal, and this group was therefore not included in analyses of EEG power and energy. These slow changes in EEG signal strength did not affect sleep scoring because the sleep-scoring algorithm was designed to accommodate such problems.37 Behavioral analyses of the CSR 20 group are therefore included.

were performed using Tukey test or Dunnett test, as appropriate. Independent data were compared using unpaired t-test or ordinary one-way ANOVA, with Holm-Sidak post hoc multiple comparisons test. Nonparametric tests were used when transformations failed to normalize the data; Mann-Whitney U test, Friedman rmANOVA on ranks, or Kruskal-Wallis oneway ANOVA on ranks were used as needed with post hoc Dunn test. One-sample t-test was used to compare samples against a fixed value. Tests used are indicated in the Results section. Unless indicated otherwise, values are expressed as means ± standard error of the mean for normally distributed data, or median and interquartile range, as appropriate. The fiducial level of statistical significance was set at P ≤ 0.05. RESULTS Sleep-Wake State is Regulated by a Behavioral Homeostat Preliminary long-term recordings in four rats confirmed that baseline sleep was reasonably stable, corroborating previous observations under these experimental conditions,41 and that 3 days of recovery (encompassing > 80 % of the total response in these animals) were sufficient for regression analysis of sleep rebound response curves. Figures 1A and 1B show data recorded from one of these rats. Hence, analyses were conducted on 2 baseline days and 3 recovery days in all animals. The group mean behavioral rebound response following 24-h TSD (N = 9) is shown in Figure 2A. It was found in all 12 TSD animals that an exponential nonlinear regression provided a better fit to the post-TSD behavioral recovery data than a linear regression or a biexponential regression (as judged by AIC), which is consistent with the basic premise of the first-order proportional control model; i.e., that rate of response decreases in proportion to error signal. The model assumption of proportionality of steady-state response across trials could be confirmed for tREM. However, it was found that acute TSD of 18–24 h duration exceeded the maximum response capacity of the behavioral homeostat for tWAKE, tSLEEP and tNREM, as indicated by correlation and regression analyses of T0 and Rspan against sleep deficit/wake excess (Y0 ), the results of which are shown in Figure 3. In tWAKE, tSLEEP (Figure 3A) and tNREM (Figure 3B), T0 was significantly correlated with Y0 (wake excess or sleep deficit) with a slope that did not differ significantly from 1 (all R2 > 0.5, F1,10 < 1.1, P > 0.3). Thus, the corresponding Rspan did not change significantly with wake excess or sleep deficit over the recorded range for tWAKE, tSLEEP and tNREM (Figure 3A and 3B). The x-intercept of the linear regression of T0 versus Y0 was 404 min for tWAKE (and tSLEEP), and 355 min for tNREM, similar to the corresponding mean Rspan values (445.5 ± 22.8 and 371.2 ± 25.5 min, respectively). These values represent an estimate of the maximum capacity of the wake and NREM behavioral homeostats and an estimate of the threshold for onset of a permanent NREM sleep debt. In contrast, Figure 3C shows that the tREM deficit resulting from a day of TSD did not exceed the maximum capacity of the REM homeostat; T0 remained unchanged (R2 = 0.005, F1,10 = 0.05, P = 0.824) over the imposed range of REM deficits and the corresponding tREM Rspan therefore increased as a function of REM deficit with a slope (0.89 ± 0.47) that was not significantly different from 1

Model Parameter Analysis Cumulative sleep and wake times were recorded at a 2-h time resolution in order to filter ultradian variability.41 A mean rate of state expression was obtained for baseline days by linear regression (Figure 1A), and the data were expressed relative to mean baseline by subtraction of the extrapolated regression (Figure 1B), to obtain net cumulative sleep times (tNREM and tREM ) and net cumulative wake time (tWAKE ). Note that quantitative changes in cumulative total sleep (tSLEEP = tNREM + tREM ) are the additive inverse of tWAKE, so that all parameter values and statistical results reported for tWAKE apply also to tSLEEP. Beginning at the end of TSD or CSR, the recovery data were fit by exponential nonlinear regression: [tNREM, tREM] = Rspan · (1 − exp[−t / τ]) + Y0, and tWAKE = Rspan · exp[−t / τ] + T0 where Rspan is the difference between initial value (Y0, sleep deficit or wake excess at the end of TSD or CSR) and response asymptote (full rebound), τ is the response time constant (h, time to complete 1/e ≈ 0.632 of Rspan ), t is time since recovery onset, and T0 is an asymptotic offset. Regressions were constrained to originate at Y0. Statistical Analysis Statistical analyses and curve fitting were performed using Prism version 6.0 (Graphpad Software Inc., La Jolla, CA). Model selection and comparisons of goodness-of-fit in nonlinear regression, were assessed using Akaike information criterion (AIC).42 Goodness-of-fit in linear regression was quantified by the coefficient of determination (R2 ). Parametric tests were applied when data conformed to the assumptions of normal distribution (D’Agostino omnibus K2 test) and homoscedasticity (Brown-Forsythe test). Paired t-test or one-way repeated-measures analysis of variance (rmANOVA) was used for comparisons of nonindependent data. Geisser-Greenhouse ε was used to correct for nonsphericity (corrected degrees of freedom are presented), and post hoc multiple comparisons SLEEP, Vol. 38, No. 5, 2015

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Figure 3—Behavioral responses to acute total sleep deprivation (TSD) expressed as parameter values of a model of proportional control. Behavioral responses, 18 h TSD, N = 3; 24 h TSD, N = 9; electroencephalographic ∆ responses, 18 h TSD, N = 2; 24 h TSD, N = 8. Rspan (black symbols) is the full magnitude of the rebound, and T0 (white symbols) is the deviation from full compensation (steadystate error). These are plotted against Y0, the state-specific excess or deficit accumulated during TSD for wakefulness and total sleep (A), nonrapid eye movement (NREM) sleep (B), and rapid eye movement (REM) sleep (C). Correlations, quantified by linear regression, show that Rspan is directly proportional to Y0 for REM sleep, whereas T0 is directly proportional to Y0 for NREM sleep and wakefulness. X-axis intercept of the T0 regression (dashed vertical gray line) is interpreted as an estimate of the maximum compensatory capacity of the behavioral tNREM and tWAKE homeostats. (D) Rate of behavioral rebound response (τ) is significantly faster in REM sleep (tREM, dark gray), than in NREM sleep (tNREM, white) or wakefulness (tWAKE, black). Total ∆ energy response (striped gray) was as rapid as the tREM behavioral response, and significantly faster than both the tNREM behavioral and NREM ∆ energy (light gray) rebounds. NREM ∆ energy rebound was faster than the tNREM behavioral rebound, highlighting the influence of the biphasic rebound in NREM ∆ power on ∆ energy dynamics (see text for discussion). *P < 0.05; **P < 0.01; ***P < 0.001; °P < 0.1.

Figure 2—Behavioral and EEG energy responses to acute 24 h total sleep deprivation (TSD). (A) Mean (± standard error of the mean [SEM]) net cumulative time in state before (2 days baseline, BL1–2), during (blue bar, TSD) and after (3 days recovery, R1–3) 24 h TSD (N = 9 rats). All vigilance states conformed to the predictions of a first-order proportional control model of behavioral homeostasis. Wakefulness (tWAKE, blue), nonrapid eye movement (NREM) sleep (tNREM, green), rapid eye movement (REM) sleep (tREM, red), black curves indicate exponential regression through recovery data. (B) Mean (± SEM) state-specific and total net ∆ energy before, during and after 24 h TSD (N = 8 rats). ∆ energy responded to TSD with monotonic rebounds (black curves) in each of wake (blue), NREM (green) and REM (red). Note the relatively rapid response of total ∆ energy (gray). (C) Mean (± SEM) net total EEG energy before, during and after 24 h TSD in each of the θ (red), α (blue), β (violet), and γ (green) frequency bands. Those frequency bands that accumulated net deficit during TSD (α and β) responded with a monotonic rebound toward baseline during recovery, consistent with the prediction of a proportional control model of homeostasis. The frequency bands that accumulated net excess during TSD (θ and γ) did not respond with a return to baseline. In all frequency bands, the trajectory of the post-TSD response was determined primarily by the behavioral homeostat. Blue bars indicate TSD.

The time constant (τ) of the behavioral rebound differed between tREM and the other states (rmANOVA of log-transformed data, ε = 0.517, F1.034, 11.37 = 7.495, P = 0.018; Figure 3D); tWAKE (and tSLEEP), τ = 24.5 ± 1.2 h; tNREM, τ = 31.3 ± 3.2 h; tREM, τ = 12.1 ± 2.6 h, indicating that a full response (i.e., > 99 %, estimated as 5τ) took approximately 5 days for wake and sleep, > 6 days for NREM, and > 2 days for REM. CSR Induces State-Dependent Attenuation of Behavioral Sleep Homeostasis Net cumulative time in state is shown before, during, and after CSR in Figure 4. The post-CSR behavioral rebound appears attenuated in both CSR groups compared to the TSD group (Figure 2A), and this impression was confirmed by quantitative analysis. Relative to the TSD group, the cumulative NREM and REM deficits and wake excess were variable, reflecting interanimal differences in both the baseline rates of state expression

(R2 = 0.195, F1,10 = 0.05, P = 0.824), consistent with the assumption of proportional response in this state (Figure 3C). The accuracy of the behavioral homeostat is indicated by the extent to which the TSD-induced sleep deficit (Y0 ) is compensated upon completion of the recovery response (Rspan ). Expressed as the percent rebound, R% = 100 · Rspan / Y0, we found accuracy to be statistically indistinguishable across the three states (rmANOVA, F2,22 = 0.459, P = 0.64); wake = 76.4 ± 5.1 %, NREM = 85.3 ± 8.7 %, REM = 74.2 ± 11.5 %. SLEEP, Vol. 38, No. 5, 2015

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and the efficiency of TSD by wheel walking. This can be seen in Figure 5, where there is appreciable spread of the CSR18 and CSR20 group data along the abscissae. This variability proved fortuitous because it facilitated evaluation of correlations between sleep rebound response parameters versus cumulative deficit. Trendlines, obtained by least-squares linear regression through the pooled data (TSD, CSR18, and CSR20 combined), highlight the significant negative correlations of Rspan against cumulative excess/deficit (Y0) for tWAKE, tSLEEP (Figure 5A) and tNREM (Figure 5B), suggesting that CSR causes progressive attenuation (acclimation) of the responses in these states. In contrast, the tREM homeostatic parameters were not significantly correlated with cumulative REM deficit (Figure 5C), indicating that REM behavioral homeostasis was only slightly suppressed by the CSR protocols used in this study. It should be noted, however, that REM Rspan was not proportional to REM deficit following CSR, in contrast to the rebound following TSD (Figure 3C). Further insight into acclimation of the behavioral sleep homeostat was obtained from analysis of sleep opportunities in the CSR days (Figure 6). In prerestriction baseline, the CSR18 rats were awake for 32% of the ZT0–6 interval (115.4 ± 12.3 min) and the CSR20 rats were awake for 30% of the ZT0–4 interval (71.7 ± 5.8 min). These wake times represent the maximum rebound available to the rats during their respective sleep opportunities in the CSR days. We found that both groups of rats exploited only a small fraction of this potential extra sleep time, corroborating similar results in other studies.8,33,36,43–46 Indeed, over the course of the entire 10- and 5-day CSR protocols, the rats utilized only 1.5 ± 12.9 % and 13.8 ± 2.7% of the potential additional sleep opportunity in the CSR18 and CSR20 groups, respectively. Although this overall result may imply failure (during the early L photophase) of the behavioral sleep homeostat during CSR, closer examination of the data revealed evidence of differential changes in the homeostatic regulation of REM and NREM sleep behavior (Figure 6). The most consistent finding was that tREM increased approximately twofold above the corresponding intervals in baseline (x2.1 ± 0.4, rmANOVA, ε = 0.259, F2.59, 12.93 = 4.742, P = 0.0223 in CSR18, and x1.9 ± 0.3, ε = 0.484, F2.42, 9.67 = 3.201, P = 0.0796 in CSR20), an effect that was sustained across the CSR protocols. In both groups of rats, the increase in tREM occurred at the expense of both tWAKE and tNREM. In the CSR18 group, during the first 2 days of CSR, tWAKE decreased and tNREM remained at baseline levels whereas on subsequent days tWAKE returned to baseline levels and tNREM tended to decrease, although these trends were statistically equivocal because of high variability in response across days and between animals (tWAKE, rmANOVA, ε = 0.234, F2.34, 11.68 = 1.94, P = 0.185; tNREM, ε = 0.317, F3.17, 15.85 = 4.19, P = 0.022). In CSR20, tWAKE and tNREM decreased in approximately equal measure during sleep opportunities, although again high variability in response was a prominent feature and firm statistical conclusions were elusive (tWAKE, rmANOVA, ε = 0.418, F2.09, 8.36 = 2.25, P = 0.165, but post hoc Dunnett test, P = 0.016 on day 5; tNREM, ε = 0.5.18, F2.59, 10.36 = 2.33, P = 0.139, but post hoc Dunnett test, P = 0.0007 on day 3).

Figure 4—Behavioral and electroencephalographic (EEG) ∆ energy rebound responses are attenuated following chronic sleep restriction (CSR). Mean (± standard error of the mean [SEM]) net cumulative time in state for each of wakefulness (tWAKE, blue), nonrapid eye movement (NREM) sleep (tNREM, green) and rapid eye movement (REM) sleep (tREM, red), with recovery responses fitted by exponential nonlinear regression (black curves). During CSR, enforced wakefulness intervals and daily sleep opportunities are indicated by blue and red bars (abscissa), respectively. (A) Net cumulative time in state in CSR18 group (N = 6), 2 baseline days of unrestricted sleep, 10 consecutive days of total sleep deprivation (TSD) at ZT6–24, and 3 recovery days of unrestricted sleep. (B) Net cumulative time in state in CSR20 group (N = 5), 2 baseline days, 5 days of TSD at ZT4–24, and 3 recovery days. (C) Mean (± SEM) net ∆ energy (CSR18 group) in each of wakefulness (DWAKE, blue), NREM sleep (DNREM, green) and REM sleep (DREM, red), and total (DTOT, all states combined, gray), with recovery responses fitted by exponential nonlinear regression (black curves). (D) Magnitude (Rspan) of the total ∆ energy rebound versus deficit accumulated. Response to acute TSD (black circles, N = 8) was proportional to deficit (line of identity, red dashed line). Proportionality was absent following CSR18 (white circles, N = 5). (E) Rates of rebound (τ) of total ∆ energy were equivalent following TSD and CSR18. Red error bars, median and inter-quartile range. Unsteady EEG power signals (slow nonlinear drift) precluded analyses of ∆ energy rebound in the CSR 20 group. SLEEP, Vol. 38, No. 5, 2015

Acute TSD is Followed by Sequential Positive and Negative Rebounds in NREM ∆ Power Mean state-specific EEG ∆ power before, during, and after 24-h TSD (n = 9) is shown in Figure 7A. The TSD episode was 690

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Figure 5—Behavioral rebound (Rspan ) is differentially suppressed by cumulative sleep deficit or wake excess (Y0 ). Strength of correlation is estimated by linear regression (dashed lines) through data pooled from three groups of rats (total sleep deprivation [TSD], black symbols; CSR18, white symbols; CSR 20, gray symbols). Suppression of the homeostatic rebound was pronounced for wakefulness (A) and nonrapid eye movement (NREM) sleep (B) but negligible for rapid eye movement (REM) sleep (C). Note that the CSR 20 stimulus (5 consecutive days of partial TSD for 20 h per day) was only marginally sufficient to elicit acclimation (“allostasis”) of the NREM homeostat (B). CSR = chronic sleep restriction.

associated with a small (5 %) nonsignificant increase in ∆ power in wake (paired t-test, mean baseline versus mean TSD, P = 0.107), a small (15 %) decrease in ∆ power in NREM (P = 0.037), and no change in ∆ power in REM (P = 0.472). Post-TSD responses included an immediate prominent positive rebound (overshoot) in ∆ power during NREM (Figures 7A, 7C, and 7E) followed by a decrease (undershoot or “negative rebound”) below baseline (rmANOVA daily peak versus day, ε = 0.789, F2.37, 26.02 = 41.81, P < 0.0001, post hoc Dunnett test, P < 0.001 for recovery days 1 and 2 versus baseline). The latter began in the first recovery D phase and then intensified in the L phase of recovery day 2, before returning to baseline near the end of the D phase of recovery day 2. When measured as the difference from baseline at corresponding times of day, the deviation of NREM ∆ power in the positive rebound was of similar (paired t-test, P = 0.77) magnitude (but opposite sign) to that of the negative rebound (Figure 7C). The Biphasic NREM ∆ Power Response Was Slightly Attenuated, but Not Abolished, by CSR EEG ∆ power across the CSR18 study is shown in Figure 7B. Positive peaks in NREM ∆ power were evident in each daily sleep opportunity (rmANOVA, ε = 0.189, F2.46, 12.29 = 10.44, P = 0.0015), although statistical significance was demonstrable only in the first four sleep opportunities using Dunnett post hoc test. However when the data were expressed relative to baseline it was apparent that the sleep opportunity NREM ∆ power also exceeded the baseline levels on the final CSR day and first recovery day, as indicated by the 95% confidence intervals in Figure 7D. The post-CSR positive rebound, calculated as the mean deviation from baseline NREM ∆ power over the interval ZT 0–6, on recovery day 1 (immediately following the 18-h sleep restriction on the final CSR day) was smaller in the CSR18 group than in the TSD group (2.85 ± 0.89 versus 3.86 ± 0.86 μVrms). However, this difference was not statistically significant (MannWhitney U test, P = 0.779), indicating that CSR did not strongly suppress the positive rebound in NREM ∆ power. In contrast, the negative rebound in NREM ∆ power on recovery day 2 was significantly smaller in the CSR18 group than in the TSD group (−1.37 ± 0.57 versus −3.98 ± 0.75 μVrms, Mann-Whitney U test, P = 0.001). Thus, the negative rebound in NREM ∆ power was attenuated, but not abolished, following CSR18. SLEEP, Vol. 38, No. 5, 2015

Figure 6—Rapid eye movement (REM) sleep time increases at the expense of wake and nonrapid eye movement (NREM) times in daily sleep opportunities during chronic sleep restriction (CSR). (A) CSR18 (N = 6); 6 h sleep opportunities were available from ZT0–6 in each of 10 CSR days. (B) CSR 20 (N = 5); 4 h sleep opportunities were available from ZT0–4 in each of 5 CSR days. In both (A) and (B), bars denote mean (± standard error of the mean) cumulative time in each of wakefulness (tWAKE, black), NREM sleep (tNREM, white) and REM sleep (tREM, gray), expressed as change from corresponding baseline values. Statistical significance was assessed using repeated-measures analysis of variance (*P < 0.05; **P < 0.01; ***P < 0.001) or one-sample t-test ( † P < 0.05). Note that in (A), day 13 is the ZT0–6 interval immediately following the final CSR episode and therefore also constitutes the beginning of post-CSR18 recovery. Likewise in (B), day 8 represents both the final sleep opportunity and the beginning of post-CSR 20 recovery.

The Biphasic NREM EEG Power Response is Not Unique to the ∆ Frequency Band We recorded power (as μVrms) in the θ, α, β, and γ frequency bands and found that they all followed post-TSD patterns of response qualitatively similar to that described 691

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Figure 7—Responses of nonrapid eye movement (NREM) ∆ power to total sleep deprivation (TSD) and chronic sleep restriction (CSR). Mean (± standard error of the mean) electroencephalographic (EEG) ∆ power before, during and after (A) 24 h TSD (N = 9) and (B) CSR18 (N = 6) in wake (blue), NREM (green), and REM (red). Abscissa blue bars, enforced wakefulness; red bars, sleep opportunities. Peak NREM ∆ power in ZT 0–2 of each CSR sleep opportunity and recovery day were compared with the mean of 2 baseline days (repeated-measures analysis of variance with Dunnett post hoc multiple comparisons test; *P < 0.05, °P < 0.1). Rebound responses to TSD (C) and CSR18 (D), calculated as mean NREM ∆ power in the interval ZT0–6, expressed as difference from baseline. Columns show mean ± 95% confidence interval (*P < 0.05, °P < 0.1, one-sample t-test for null hypothesis mean = 0). (E) EEG power in each of the ∆ (black), θ (red), α (blue), β (violet), and γ (green) frequency bands during 3 recovery days following acute TSD. Data expressed as percent difference from baseline at corresponding times of day. Mean values (N = 12) are shown; error bars are omitted for clarity of presentation. Sequential positive and negative rebounds are evident, with a qualitatively similar pattern of response in all frequency bands, although statistical significance was found in ∆, θ and α bands only (see text). (F) EEG power in each of the ∆ (black), θ (red), α (blue), β (violet), and γ (green) frequency bands during 3 recovery days following CSR18. Although slightly attenuated relative to TSD, the biphasic pattern of response remained statistically significant following CSR18 in ∆, θ, and α bands.

Rebound of Total ∆ Energy is Mediated by Behavioral Homeostasis Following Acute TSD Mean net ∆ energy of the 24-h TSD group is shown in Figure 2B. Recovery data were analyzed by nonlinear least squares exponential regression to quantify Rspan, τ and T0, in the same way as was described for behavioral responses (Figure 2A). Wake ∆ energy followed a monotonic recovery profile, which was solely a consequence of the recovery of wake behavior (tWAKE); the small rise in wake ∆ power during TSD was not compensated by a commensurate undershoot of wake ∆ power during recovery (Figure 7A). Hence, τ of the wake ∆ energy recovery was equivalent to that of the tWAKE response (paired t-test after log transformation, P = 0.79). Likewise, the monotonic REM ∆ energy rebound (Figure 2B) was a direct result of the tREM response (Figure 2A) with no EEGspecific component (P = 0.203, Figure 7A). Goodness-of-fit of

for ∆ power (Figure 7E). However, the positive and negative rebounds were statistically significant only for ∆, θ, and α (one-sample t-tests, respective positive rebounds P = 0.009, 0.007, 0.016, and negative rebounds P = 0.0002, 0.0012, 0.0099). There were statistically significant differences between EEG frequency bands in the magnitudes of positive rebounds (rmANOVA, ε = 0.380, F1.52, 13.69 = 14.55, P = 0.0008) and negative rebounds (rmANOVA after log transformation, ε = 0.420, F1.68, 15.13 = 69.04, P < 0.0001) following TSD. The positive rebound in ∆ power was greater than those of all other frequency bands (Tukey multiple comparisons test, all P < 0.02), whereas the negative rebounds in ∆, θ, α, β, and γ power all differed from each other (Tukey, all P < 0.022, except β versus γ, P = 0.066). A similar broad-spectrum biphasic pattern was also present during recovery NREM sleep after CSR18 (Figure 7F). SLEEP, Vol. 38, No. 5, 2015

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DISCUSSION This study demonstrates behavioral homeostasis of sleepwake state, independent of “intensity,” in the rat. The behavioral sleep-wake homeostat has a finite capacity to correct perturbations in the controlled variable, a property it shares with all other known homeostatic control systems. We estimate that the maximum compensatory capacity of the rat behavioral homeostat for tNREM is limited to less than 400 min, which is approximately the amount of NREM sleep in a single 12-h L phase.48 In contrast, the maximum capacity of tREM behavioral homeostat was undefined in the current study, and may far exceed that of tNREM.22,49 However, the limited scale of the current study can provide only an approximation and a detailed dose-response analysis is needed for a definitive quantification of the full response capacity of the behavioral sleep-wake homeostat. The observed response characteristics of the behavioral homeostat, including residual steady state error (partially incomplete response, T0 > 0) and slow monotonic time course, are consistent with a low gain/overdamped proportional control system.34 It is possible that the present analysis overestimates the magnitude of the steady-state error of the behavioral homeostat because of the aforementioned saturation of the tNREM response, and our assumption that the set-point of the controller corresponds to the baseline mean rates of sleepwake as determined by linear regression (Figure 1). The latter assumption might be too conservative and a broader “set zone” bounded by upper and lower limits may be more appropriate (i.e., a “dual intervention” model50). We estimate (by extrapolation of the recovery regression curves to 5τ) that full behavioral recovery following 24-h TSD requires nearly a week in the rat, which is longer than is generally assumed for rodents51 and human subjects.13 We suggest that this discrepancy between studies can be ascribed in large part to differences in the analytical procedures used. Specifically, our assumption of a simple proportional control system required that we quantify behavior using a regression analysis of net cumulative time in state, whereas the conventional approach is to express post-sleep deprivation sleep-wake times as a “rate” within arbitrary time intervals (e.g., % of time or min per hour). The latter method of quantification (essentially an analytical model of time integration with periodic reset) has the disadvantage of relatively low statistical power because short-term sleep-wake expression is highly variable due to the probabilistic properties of state transition that vary over a range of timescales.52,53 Of particular importance in this context is the fact that ultradian rhythms in sleep-wake state are quasi-periodic in the rat,41 which means that there is substantial day-to-day variability in state expression even at the same time of day. Thus, the progressively diminishing post-sleep deprivation behavioral recovery profile is rapidly lost in statistical noise when data are compared against baseline in the conventional way. Monotonic behavioral rebound responses were observed in all three states of wake, NREM, and REM following acute TSD, but recovery of tREM was significantly faster than those of tNREM and tWAKE (Figure 3D). Previous studies have reported divergent homeostatic responses of NREM and REM following acute TSD and REM-specific deprivation, suggesting that there may be separate, perhaps competitive, regulatory systems for

the exponential regression model was inferior for NREM ∆ energy in comparison to wake, REM, and total ∆ energies (AIC values compared by rmANOVA, ε = 0.460, F1.38, 12.41 = 24.87, P = 0.0001). This is to be expected given that, unlike the other states, NREM ∆ energy is the product of an exponential behavioral response (Figure 2A) and a biphasic NREM ∆ power response (sequential positive and negative rebounds; Figure 7). In contrast, total ∆ energy (∆ power accumulated in all states over time) was well described by an exponential regression in 10 of 12 animals (statistically linear in two rats), with relatively low T0 and fast τ. Indeed, the rate of response of total ∆ energy (median τ = 6.2 h, IQR 3.3–11.4 h) was significantly faster than those of tNREM, tWAKE, and tSLEEP behaviors (rmANOVA on log transformed τ data, ε = 0.519, F1.56, 15.56 = 10.92, P = 0.0019), and was similar to the rapid rate of response of tREM described earlier (Figure 3D). After acute TSD, the ratio total ∆ energy Rspan / total ∆ energy deficit was not significantly different from unity (ratio = 1.29 ± 0.27, one-sample t-test, P = 0.321), which conforms to the assumption underlying the proportional control model for homeostatic control of total ∆ energy (Figure 4D). In contrast, NREM ∆ energy did not satisfy this criterion, both when tested against NREM ∆ energy deficit (ratio = 0.69 ± 0.07, P = 0.0011) and against total ∆ energy deficit (ratio = 2.96 ± 0.65, P = 0.0143). This implies that total ∆ energy is a better candidate for homeostatic regulation than NREM ∆ energy. ∆ Energy Rebound is Strongly Attenuated Following CSR State-specific and total ∆ energies are shown for the CSR18 rats in Figure 4C and illustrate the limited overall recovery of ∆ energy following CSR. Total ∆ energy deficit (black) was only 21% of the NREM ∆ energy deficit (green) owing to excess wake ∆ energy (blue), which substantially offset the deficit in NREM ∆ energy over the course of the CSR18 study, confirming previous predictions.47 Despite this relatively small overall deficit (error signal) in total ∆ energy, the ∆ energy rebound response was attenuated (abolished in one animal) and not proportional to total ∆ energy deficit following CSR18 (Figure 4D). However, the time constants of the residual total ∆ energy rebound responses (τ) did not differ significantly (unpaired t-test, P = 0.657) between TSD and CSR18 groups (Figure 4E). Total α and β Energies Conform to a Model of Homeostatic Regulation Following Acute TSD, but Total θ and γ Energies Do Not Net total α energy and net total β energy accumulated a deficit during TSD, which was followed by a monotonic return to baseline during recovery (Figure 2C). The small absolute magnitude of the biphasic rebounds (Figure 7E) in α power and β power had negligible effects on respective cumulative energies, and the rebound responses in these frequency bands were secondary to the homeostatic regulation of sleep-wake behaviors. In contrast, there was a large increase in θ power in wake during TSD, which was not compensated by a decrease in θ power in subsequent recovery, and hence total θ energy remained completely uncompensated (Figure 2C). A similar result, of smaller magnitude, was observed for net γ energy. SLEEP, Vol. 38, No. 5, 2015

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each sleep state.22,51,54 It is possible that the wake response is a passive consequence of active NREM and REM responses (i.e., a zero-sum property), but because some wake-dependent behaviors support homeostatically regulated functions (e.g., energy balance, thermoregulation), it seems likely that wake, as a homeostatic behavior, will itself be subject to behavioral homeostasis. Our data suggest that the sleep-wake homeostat serves to balance the expression of all behavioral states over time, rather than simply to defend a minimum requirement for sleep.10 Such a system (i.e., an equilibrium or settling-point model50) might explain the paradoxical “ceiling effect” on recovery sleep that occurs immediately following TSD and in the daily sleep opportunities during CSR in rats.8,21,33,55 An assumption implicit in contemporary theories of sleep regulation10,56 holds that a sleep homeostat effects concurrent regulation of time in state and intensity of state (∆ power). This implies that the homeostatically regulated variable is the time integral of ∆ power (∆ energy, an extensive quantity) and not ∆ power per se (an intensive quantity). Thus, ∆ power is an effector mechanism within the two-process model and not in itself a homeostatically regulated variable, which explains why ∆ power is marked by a conspicuous lack of stability (Figure 7). Although ∆ power is amplified and adjustable mainly in NREM, our data support suggestions that the ∆ power expressed in all states is of quantitative importance in a model of ∆ energy regulation.22,33,56 Total ∆ energy exhibited relatively high accuracy and rapid monotonic response following acute TSD (Figure 2B). The rapidity of the response (Figure 3D) was a direct consequence of the biphasic rebound in NREM ∆ power. That is, the positive rebound in NREM ∆ power contributed to a high initial rate of response in total ∆ energy, and the negative rebound prevented a subsequent overshoot during the ongoing (slower) behavioral tNREM rebound. These results and interpretation appear to reaffirm the classical concept of sleep homeostasis as a process regulating a combination of sleep duration and NREM ∆ power.11,56 However, our data also provide reasons to question the plausibility of this interpretation. We confirm previous reports22,55 that the positive and negative rebounds in NREM ∆ power quantitatively negate each other and therefore contribute little to R span of the total ∆ energy rebound following TSD. Thus, the rebound in ∆ energy is a secondary consequence of behavioral homeostasis. This point was demonstrated clearly after CSR in the current study, when behavioral homeostasis and ∆ energy rebound were both strongly attenuated (Figure 4), whereas a substantial NREM ∆ power response was retained (Figure 7). The retention of a NREM ∆ power negative rebound (albeit of reduced magnitude) following CSR, and after prolonged TSD,22 when total ∆ energy is severely undercompensated, is not compatible with feedback regulation of NREM ∆ power in a closed loop homeostatic controller of total ∆ energy. A sustained positive ∆ power rebound would be predicted under such circumstances. This observation of decoupled sleep behavior and EEG ∆ power during CSR is consistent with an alternative hypothesis that the two variables are regulated by at least partially independent control mechanisms and that acclimation of the two mechanisms to sustained sleep deficit occurs at different rates. SLEEP, Vol. 38, No. 5, 2015

The hypothesis that CSR might provoke acclimatory (“allostatic”) adjustments in the sleep regulatory system was supported in a study by Kim et al.36 of 5-day CSR 20 in the rat. However, Leemburg et al.,33 replicating the experimental design of Kim et al.36 with minor methodological and analytical modifications, concluded that the function of the sleep homeostat is preserved at normal levels during CSR 20. The data described in these two studies are less disparate than their opposing conclusions imply, and we suggest that much of the apparent discrepancy can be reconciled in light of the data and analysis in the current study. Both of these prior studies presented evidence of a small rebound in tNREM and a stronger rebound in tREM (especially during daily sleep opportunities) following 5 days of CSR 20. Furthermore, Kim et al. observed a biphasic rebound in NREM ∆ power, albeit with a relatively small positive rebound restricted to the first 2 h of recovery, whereas Leemburg et al.33 reported a stronger positive rebound in NREM ∆ power but without evidence of a subsequent negative rebound. These results are in broad agreement with our major findings; attenuation of the NREM behavioral sleep homeostat following CSR and smaller effect of CSR on NREM ∆ power and REM behavioral rebounds. We determined that the 5-day CSR 20 protocol is a marginally sufficient stimulus for onset of “allostasis”; a cumulative NREM deficit of at least 1,600–2,000 min was required before attenuation of NREM Rspan became apparent (Figure 5). This might explain why the rats studied by Leemburg et al. were largely unaffected by their CSR method (disk over water, NREM deficit approximately 1,500 min), in comparison with those exposed to a more effective method (continuous wheel walking, NREM deficit 1,722 min) in the Kim et al. study. Neither Kim et al., nor Leemburg et al. placed emphasis on the differential effect of CSR on behavior and ∆ power, highlighting instead their combined responses in ∆ energy. It remains to be determined whether REM sleep and NREM ∆ power are refractory to acclimation, or merely require a greater threshold of cumulative stimulus through prolongation or intensification of the CSR protocol. That the latter may be true for ∆ power is suggested by reports of strong suppression of positive rebounds following prolonged TSD in rats.22,49 In contrast, the tREM behavioral homeostat remains robust following prolonged TSD in rats.22,49 However, the current study indicates that there may also be some degree of acclimation of the tREM homeostat during CSR because proportionality of Rspan to REM deficit was absent following CSR (Figure 5C). These differences between the effects of CSR and prolonged TSD raise the possibility that the mechanisms underlying acclimation may be more sensitive to the rate of accumulation of the homeostatic error signal (wake excess, sleep deficit) than to absolute levels of sleep deficit.35 This general concept has recently been elaborated and evaluated in quantitative detail in a model of human neurobehavioral performance.57,58 Other studies in rat8,33,36,44–46,59 and mouse43 are consistent with our conclusion that an adequate CSR stimulus can induce acclimation most readily in the NREM behavioral homeostat of the rat, whereas the REM behavioral homeostat and EEG Δ power are less susceptible. CSR induced by 5 days of sustained 12-h wakefulness in the L or D diurnal phases45 produced a modest cumulative sleep deficit (of similar magnitude to that 694

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reported by Leemburg et al.33) with no evidence of acclimation in sleep-wake behavioral homeostasis and a small progressive decline in peak NREM ∆ responses over CSR days, supporting the suggestion that a minimum effective stimulus is required. Machado et al.59 exposed rats to 21 days of CSR18 using the platform technique. We calculate that their procedure induced a cumulative NREM deficit of approximately 1,800 min, similar to that of the 5-day CSR wheel-walking protocol used by Kim et al.8,36 and the current study. However, the postCSR (4 days) tNREM rebound (approximately 450 min59) was at full capacity as determined in the current study (Figure 3B). This contrasting result is again consistent with the hypothesis that acclimation may be sensitive to rate of accumulation of NREM deficit, although other factors relating to differences in protocol cannot be ruled out. The 21-day platform deprivation procedure induced a large cumulative REM deficit of approximately 1,200 min, which was followed by a suppressed tREM response including a small negative rebound after 2 days of recovery.59 This further supports the hypothesis that the tREM homeostat might also exhibit suppression during CSR (but not prolonged TSD22) if cumulative REM deficit is of sufficient magnitude. Clearly, there is a need for further research to define the relevant properties of the CSR schedule that induce acclimation in the NREM and REM behavioral homeostats. There is indirect evidence that human subjects might exhibit responses to CSR that parallel those described in the rat, although differences in protocol (e.g., time in bed is usually constrained) and analysis (e.g., Δ power is rarely integrated across all four NREM stages) preclude a direct comparison. Webb and Agnew60 subjected eight male students to a sleep restriction protocol of 8 consecutive days with 3 h of sleep per night in a study that provided the first clue that homeostatic responses may be weak following CSR. The subjects accumulated a TSD of approximately 2,000 min and regained virtually none of that during the first recovery night. The main response was an increase in stage 4 NREM sleep during the first 3 h of the night, such that total time spent in that stage was unchanged across the nights of the study. However this increase in early-night stage 4 NREM sleep occurred mainly at the expense of stage 3, resulting in an accumulated deficit of over 3.5 h of slow wave sleep time across CSR nights, only 3 min of which was recovered in the first recovery night. Subsequent studies have reported generally similar results,58,61–65 including maintenance of stage 4 sleep during CSR and rapid return of EEG and behavioral variables to baseline rates during recovery (implying limited cumulative rebound responses). A recent large study of the first recovery night in sleep restricted subjects66 described a weak behavioral rebound amounting to less than 1 h of extra sleep in 27 subjects scheduled to 10 h time in bed. This represents less than 4% of the cumulative sleep deficit, which we calculate from data reported in that study to be approximately 23.5 h. CSR has also been found to induce deficits in neurobehavioral performance that are inversely proportional to time in bed (i.e., to rate of accumulation of sleep deficit/wake excess).58,62 Furthermore, subjective sleepiness (as judged using the Stanford Sleepiness Scale) rises rapidly to a plateau during CSR days, implying subjective acclimation to progressive sleep deficit.9,58,62,67 Whether functional deficits and subjective sleepiness are causally linked to acclimation of SLEEP, Vol. 38, No. 5, 2015

the sleep-wake homeostat is unknown, although such a link has been assumed.57,66,68,69 Acute recovery of neurobehavioral performance was found to proceed rapidly following 5 days of restriction to 4 h time in bed, with full functional recovery requiring only 1–2 nights of sleep.66 However, in a forced desynchrony protocol, long-term susceptibility of performance to CSR increased (dependent on circadian phase) to an asymptote over 2 w despite acute recovery following 10 h sleep opportunities every 42.85 h. This is consistent with a model of fatigue, in which performance is modulated by two state variables representing short- and long-term effects.57,69 These functional responses to CSR correlate with recent observations of acclimation of the sleep regulatory system in animal studies.36,44 In the current study, we find in rats that CSR led to differential degrees and rates of suppression, with NREM behavior more affected than REM behavior and NREM ∆ power. This highlights the need for a better understanding of the dynamic interactions between CSR-induced changes in human neurobehavioral function and the various components of the sleep-wake regulatory mechanism. The quantitative approach taken in the current study may yield valuable insights into human responses to CSR if implemented in combination with recent models of neurobehavioral performance.57 For example, a dose-response study of long-term unrestricted recovery sleep (including daytime naps) in sleep restricted subjects would facilitate a fuller understanding of the dynamics of recovery of sleep regulation and neurobehavioral function. Finally, it should also be noted that a settling point model50 of proportional control mentioned earlier provides an alternative to “allostasis” as a potential explanation for the apparent suppression of the behavioral homeostatic responses following CSR in rats. That is, the settling point model predicts that rebounds would appear suppressed if sustained cumulative wake excess were to increase the “need” not only for sleep, but also for wakefulness. There are data that indirectly support this apparently paradoxical proposition. For example, in rodents and human subjects, CSR and prolonged TSD promote increased appetite and hyperphagia.70,71 The drive to eat is associated with sustained arousal through shared neuroendocrine mechanisms, including the hypocretin/orexin system.72,73 Thus, in a settling point model of proportional control, a chronic deviation of cumulative time in state from the baseline equilibrium may induce simultaneous increases in the drives for wakefulness and sleep, which would be predicted to blunt the net output (but not the actual magnitude) of the compensatory homeostatic drives of the individual states. Thus, this alternative model admits the possibility that the homeostatic drive for NREM may not necessarily decline in absolute terms during CSR, but may rise less rapidly than those of wake and REM. Studies such as the current one, which measure the final outputs of the control system (i.e., behavior), cannot distinguish between allostasis and the settling point hypotheses. Such a test would require independent manipulation of state-specific homeostatic drives during recovery from CSR. In conclusion, this study validates a key assumption of the two-process model of sleep regulation by providing evidence for homeostatic regulation of sleep-wake behavioral states. However our data cast doubt on the secondary assumption that regulation of NREM ∆ power is synonymous with regulation 695

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of sleep. Although the conceptual construct of sleep intensity has been a prominent feature of the two-process model since its inception,10,11 its exclusion does not invalidate the core principle of the two-process model and we suggest that there may be fresh insights to be gained from a new perspective within this general model framework. We have shown that the behavioral sleep-wake homeostat can be modeled as a simple closedloop proportional controller and the two-process model can be considered to be a special case within this class of control system. It is important to recognize that the primary regulated variables are not behavioral state per se, but underlying neurophysiological mechanisms whose activities vary as a function of time in state and whose effects include alteration of the probabilities of behavioral state transitions. Neuromodulators, including (but not limited to) extracellular adenosine,8,43,74 cytokines,75 prostaglandin D2,76 and nitric oxide,77 all are potential candidates for this regulatory role. This perspective rationalizes the role of “Process S” within a model of behavioral sleep-wake regulation10,11 by identifying it with regulatory mechanisms instead of a presumed functional output variable (∆ power). Behavioral homeostasis of sleep-wake state can be viewed as a mechanism that ensures adequate opportunity for the execution and regulation of physiological functions that are favored by a given behavioral state (i.e., “state-dependent” functions). By demonstrating that sleep-wake state is regulated by a behavioral homeostat we suggest that, within the narrow context of sleep-wake regulation, the concept of sleep intensity may be redundant. We further suggest that NREM sleep is “permissive” of ∆ power regulation, and that ∆ power might be just one of many processes that is regulated preferentially in sleep, rather than a process of sleep.

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DISCLOSURE STATEMENT This was not an industry supported study. Financial support: Dr. Stephenson, Natural Science and Engineering Research Council of Canada (NSERC) Discovery Grant; Ms. Caron, NSERC and Ontario Graduate Scholarships. The authors have indicated no financial conflicts of interest. REFERENCES

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