Sleep lowers waking theta frequency in the rat hippocampus

Summary

Hippocampal theta oscillations coordinate computations underlying learning and memory. The frequency of theta varies with factors such as locomotion and anxiety, but the effect of an animal’s sleep history on theta frequency remains unknown. Using long-duration CA1 recordings in rats, we found that awake theta frequency progressively decreases following sleep but remains elevated during sleep deprivation. These changes were not accounted for by movement but were predicted by the proportion of sleep in the preceding 30 mins. In contrast, theta frequency remained relatively stable during rapid eye movement sleep. In aged rats, sleep-dependent frequency changes were less pronounced, likely due to sleep fragmentation. Systemic administration of the phosphodiesterase inhibitor rolipram during sleep deprivation reduced theta frequency, mimicking natural sleep. Collectively, these findings reveal a robust influence of sleep history on hippocampal theta frequency, with potential implications for understanding memory function, age-related sleep disruptions, and the potential for pharmacological interventions.

Graphical Abstract

Introduction

Neuronal oscillations in the theta frequency range (5–10 Hz) are a hallmark of the hippocampus across mammalian species, from rodents to humans ^1-3. These oscillations are widely considered to provide a clock that can entrain and coordinate multiple brain circuits, to allow them to perform computations that involve encoding and retrieval of information involving the hippocampus ⁴. Theoretical models initially proposed that a single cycle of the theta provides a computational unit, e.g. potentially accounting for the amount of information that can be maintained in a working memory buffer ⁵. Multiple lines of experimental evidence also indicate that distinct computations are performed within each cycle of the theta oscillation ^6-10, with the frequency of theta determining the system’s clock. Notably, stimulation at theta frequency is optimal for driving long-term potentiation in hippocampal circuits ^11,12 and neuronal ensemble firing patterns that occur during theta are selectively promoted for subsequent reactivation and replay during sleep ^6,13.

The theta clock frequency, however, is not entirely fixed but is shaped by both intrinsic and external factors affecting the hippocampus and can vary depending on the state and condition of the animal. Theta frequency is strongly impacted by movement ¹⁴ and varies linearly with the animal’s running speed ^15,16. It is also modulated by other factors, such as brain temperature ^15,17-19, the novelty of an animal’s environment ²⁰, and their level of anxiety ^15,21. The impact of these factors is likely mediated by the neuromodulatory tone of the hippocampus ^22-24. Based on these studies, we hypothesized that theta frequency may be influenced by the recent sleep history of the animal, particularly as it transitions between states of fatigue associated with prolonged waking and well-rested states following emergence from sleep.

To investigate this, we recorded the power and frequency of theta oscillations in animals before, during, and after emergence from sleep, and when they are kept awake by gentle handling followed by recovery sleep. We found that theta frequency is lower immediately after sleep but remains elevated during sleep deprivation, with an immediate drop following recovery sleep. When we performed similar studies in aged animals, we then found that these effects are relatively muted. Finally, we found that the phosphodiesterase inhibitor, rolipram, lowers theta frequency during sleep deprivation, consistent with its benefits for memory resilience under sleep loss ²⁵ and aging ²⁶.

Results

Awake theta frequency lowers with sleep

We first investigated peak theta frequency (Fig 1) in bouts of spontaneous waking in long-duration recordings from the rat CA1 region and observed a notable decrease in the frequency of theta oscillations starting with the onset of the light cycle in animals permitted ad-libitum sleep in their home cage (Fig 2A). Awake bouts (see Methods) were defined as periods of continuous quiet or active waking (QWAKE and AWAKE, respectively, with an average duration of 19.00 ± 2.84 s for AWAKE and 23.38 ± 3.46 s for QWAKE (see Fig S1 for additional details). In each waking bout, we calculated the power spectrum and examined the power of theta using Morlet wavelets (Fig 1A). We also estimated the peak theta frequencies and theta powers for each waking bout by fitting periodic and aperiodic components over the original spectrum ²⁷, and extracting the frequency of the peak periodic component in the 5-10 Hz theta frequency range. Over the 5 h of ad-libitum sleep in sample sessions (see Fig S1A for all recording sessions), a progressive decrease could be seen in the theta frequency starting at 7.6 Hz in a sample bout recorded at Zeitgeber time 1 (ZT; measured relative to the onset of the light cycle) near the start of the light cycle down to 5.5 Hz in a bout recorded 3 h later at ZT 4 (left subpanel in Fig 1B). This theta frequency reduction was consistent both for active awake states, in which theta oscillations were prominent (e.g. bout #1 vs #3 in Fig 1A), as well as for quiet awake states, in which theta was transient or not evident from visual inspection (e.g. bout #4 vs #2 in Fig 1A). Since animals spent the majority of the first 5 h of the light cycle in sleep, these observations suggested that sleep significantly influences theta frequency in subsequent waking periods. Additionally, inspection of these sessions suggested that spontaneous waking theta frequency changed according to the proportion of sleep preceding the bout. Notably, during this same period, power in the theta frequency band remained largely unchanged (Fig 1D).

Figure 1: Waking theta frequency drops following sleep.

(A) Five example wake bouts (#1-3 from a NSD session and #4-5 from a SD session) showing unfiltered hippocampal local-field potential (top left) and corresponding power spectra (bottom left) calculated using Morlet-wavelet transforms. Bouts #2 and #4 occurred during quiet wake (QWAKE), Bouts #1, #3, and #5 occurred during active wake (AWAKE). The right subpanels within each example bout show the power spectra (solid black) calculated by Welch's method along with the estimated full fit from FOOOF (“fitting oscillations & one over f”; pink) and its aperiodic sub-component (dashed black). Numbers above the peak indicate the theta frequency estimated from FOOOF. (B) Estimated theta frequency is shown for individual bouts (violet-gray for QWAKE, dark green for AWAKE) from a representative NSD (left) and a representative SD (right) session, with dot size representing duration and dot darkness indicating theta power. The average frequency in sliding 30-min windows is overlaid (NSD, blue; SD, red; similar results were obtained using 10-min windows). Individual examples depicted in panel (A) are numbered accordingly. Color bars above each panel show the proportion of time awake vs. sleep in the corresponding window. (C) Mean theta frequency (thick line) and SEM (shaded) across time in combined NSD (blue) and SD (red) sessions. Individual sessions are also overlaid (thin light lines). Color bars above display the average awake/sleep proportions across all SD and NSD sessions. Horizontal line along the x-axis indicates periods with significant differences (p < 0.001) between SD and NSD. A significant cluster spanned ZT 0–5 (p = 0.0002, clusterstat = 367.57, peak t = 6.19), indicating consistently higher theta frequency in the SD group. (D) Mean theta peak power (thick line) and SEM (shaded area) over time. Thin lines, bars above, and color codes are consistent with panel (C).

Figure 2: Stable theta frequency during maze running and rapid eye-movement (REM) sleep.

(A) Main experiments involved rest followed by either ad-libitum sleep (NSD, blue) or sleep-deprivation (SD, red), exposure to a novel maze (MAZE), and post-maze recovery sleep (color bar on top provides average sleep proportion in each group). Mean theta frequency (thick line, with shaded SEM) was significantly lower in sleep vs. sleep-deprivation based on a cluster-based permutation test (***p < 0.001 as in Fig 1C) but remained consistent across blocks that featured a similarly low proportion of sleep. There was no significant difference in theta frequency during SD relative to the REST baseline (ZT −1 to 0, red error bar plot). (B) During REM sleep, the theta frequency remained relatively stable in the NSD group, ranging from 6.5 to 7 Hz and was not noticeably affected by sleep deprivation in the recovery sleep period (right panel). Note that some discontinuities are present in the plot due to limited bouts of REM sleep at the beginning of the recovery block.

To test whether these effects were indeed due to sleep, as opposed to other factors such as the circadian rhythm entrained by the onset of the light cycle, on different days (counterbalanced in order) we kept the animals awake in their home cages for 5 h starting at ZT 0 using “gentle handling” (see Methods). This procedure involved an escalating series of steps (from cage tapping, to cage shaking, to disturbance of bedding materials) to keep animals awake whenever they displayed signs of transitioning to sleep. Animals in these sleep-deprivation (SD) sessions (left panels of Fig 1A-C) did not show a significant decrease in theta frequency over the course of SD. Instead, theta frequency remained consistently high across the 5-h period, comparable to levels observed at the end of the PRE period (Fig 2A). Although a brief apparent rise in theta frequency at the start of the session did not exceed baseline levels, it may reflect transient anxiety ²⁸ triggered by the experimenter entering the recording room at the onset of SD—a factor absent in the non-sleep-deprived (NSD) sessions. In contrast, the NSD group exhibited significantly lower theta frequency, consistent with a sleep-related decline (Fig 1C). This pattern was consistently observed across many sessions recorded from different animals, demonstrating the robustness of the sleep-related decrease in theta frequency (Fig 1C & Fig S1A). Comparing waking bouts across sessions also indicated that theta frequency tends to be lower in QWAKE compared to AWAKE, which is expected since AWAKE tends to feature more locomotion^14,16.

To quantitatively inspect this pattern while accounting for unequal numbers of waking bouts across conditions, as well as dependent measures in sessions from the same animal, we applied linear mixed-effects models with random intercepts for animal and for sessions nested within each animal (Fig S2). In a full factorial model (Model 1) that included waking State (QWAKE vs. AWAKE), Condition (NSD vs. SD) and TimeBin (First vs. Second and Third) we confirmed that theta frequency was significantly lower during QWAKE than AWAKE (Fig S2A, B), resulting in a main effect of State (mean difference = −0.27 Hz; t = −5.39, p = 7.4 × 10⁻⁸). Additionally, we observed a significant main effect of TimeBin (p < 10⁻¹³), indicating a robust decline in theta frequency for both across the time bins. Furthermore, an interaction between Condition and TimeBin (p = 5.5 × 10⁻⁴), indicated that the sleep-dependent decrease in theta frequency over time was significantly attenuated in SD animals. On the other hand, we observed no significant interactions between waking State and Condition and/or TimeBin, indicating that the effect of sleep and SD were consistent across QWAKE and AWAKE states.

A factorial model that pooled QWAKE and AWAKE (Fig S2C) but included EMG and ThetaPower likewise showed significant effects for Condition (NSD vs. SD), Timbin, and an interaction between the two. This model also confirmed a significant effect of ThetaPower on theta frequency, but not of EMG, indicating that ThetaPower, which we use to separate QWAKE and AWAKE (Methods), accounts for more of the variance in theta frequency during waking. Consistent with this, a factorial model for ThetaPower (Fig S2D) showed a significant effect of State, with consistently higher theta power during AWAKE vs. QWAKE. However, in contrast to theta frequency (Fig S2B), theta power did not vary significantly across TimeBins or Condition (see also Fig S2E). Based on these observations, we pooled QWAKE and AWAKE for the subsequent theta frequency analyses.

Theta frequency rebounds during maze running and is stable during REM sleep

Given the differences in theta frequency between NSD and SD, we hypothesized that these groups would display different theta during behavior on a maze. Therefore, at ZT 5 we placed animals from both groups on a novel linear track—to which they had not been previously exposed—to run for water rewards delivered at the track ends. During the resting block in the home cage in the dark cycle starting at ZT 21, 3 h before the dark-to-light transition, theta frequency was naturally similar in both groups of animals (SD: 7.38 +/− 0.29; NSD: 7.40 +/−0.42; Fig 2A). Subsequently theta frequency decreased significantly over 5 h of NSD. During the same period, the theta frequency in these animals was relatively constant, between 6.5 to 7 Hz, which was lower than the awake theta frequency observed in the resting block prior to ZT 0, but higher than the theta frequency seen during waking after sleep (Fig 2B). Upon exposure to the maze, however, the frequency of awake theta rebounded to PRE levels, with no significant differences between groups (Fig 2A, MAZE). Thus, contrary to our expectation, the prior 5-h period of sleep deprivation versus ad-libitum sleep did not have enduring effects on the frequency of theta when animals were exposed to a novel maze.

After the maze run, both sleep-deprived and ad-libitum sleep animals were left to sleep undisturbed in the home cage, though SD animals slept more vigorously. Upon this sleep, theta frequency significantly decreased in both groups, falling below 6.5 Hz (Fig 2A). During recovery sleep as well as during NSD, REM theta frequency was relatively constant between 6.5 and 7 Hz (Fig 2B). These observations suggest that the theta frequency drop in awake states following sleep has a different mechanistic origin than that of REM sleep. Further, the differential modulation of theta frequency across these states suggests a mechanism responsive to the animal's current state (i.e. during MAZE or REM), as well as its prior sleep.

Immediately preceding sleep resets theta frequency

Our observations thus far indicate a relationship between sleep history and theta frequency wherein theta frequency drops upon waking but increases as sleepiness wears off. We next asked how far back in time sleep history most strongly influences theta frequency. Pooling data from all ZT 0-5 sleep sessions, we used generalized linear models (GLMs) to examine the relationship between sleep proportion within time windows of different lengths, ranging from 1 min to 60 min prior to the onset of a waking bout, and the frequency of theta during the bout (Fig 3A). Among these history windows, the fraction of sleep in the preceding 30-min window best predicted the theta frequency of that bout (Fig 3A, B). We did not observe any further improvement by accounting for how much of this window contained REM or slow-wave sleep (SWS; Fig S3A, B), suggesting that both sleep states confer a similar effect. Consistent with this, the total sleep proportion within the preceding 30-min window was strongly and negatively correlated with waking theta frequency (Fig 3B; linear regression, R² = 0.17, p = 2.6 × 10⁻¹⁴²).

Figure 3: Influence of sleep history on awake theta frequency.

(A) Results of a generalized linear model (GLM) relating sleep history to theta frequency. Each point shows the main effect (±95% confidence interval) of sleep-state proportions computed over different preceding time windows. The 30-minute window showed the strongest negative association with subsequent theta frequency (R² = 0.185, RMSE = 0.749). (B) Fraction of sleep in the preceding 30-mins is significantly and negatively correlated with awake theta frequency (Pearson’s r = −0.41, p < 0.001). Group-level data from all non-sleep-deprived (NSD) sessions showing shifts in awake theta frequency following spontaneous bouts of sleep. Each dot represents an individual awake bout; dot size reflects bout duration and color indicates relative theta power (see legend). The color bar above the plot indicates the proportion of sleep over time.

Intercept but not slope of theta frequency—speed regression is impacted by sleep history

Earlier studies suggested that theta frequency correlates with the movement speed of the animal ^16,29,30. Although these studies measured movement speed on a track, which is much higher than what is possible in the animal’s cage, we nevertheless tested whether the animal’s movement speed in the cage could potentially account for theta frequency under ad-libitum natural sleep and sleep deprivation conditions. To do this, we focused on the subset of animals for which we had reliable position tracking in the home cage (see Table S1), calculated the mean motion speed for each AWAKE bout (Fig 4A) and modeled its relationship with theta frequency using a linear mixed-effects model (Fig 4B-D). The model included Speed, TimeBin (early, middle, late thirds of the 5h period), and Condition (NSD, SD) as predictors, with Session and Animal as random effects.

Figure 4: Dynamics of awake theta frequency and its correlation with movement.

(A) Instantaneous movement speed during bouts of quiet awake (purple shading) and active awake (green shading) over the first 5 h of the light cycle (ZT 0-5) in an example non-sleep-deprivation (NSD) session. No shading indicates sleep bouts. We split this 5 h period into three time bins corresponding to the beginning, middle, and end. (B) Movement speed and theta frequency were correlated in active awake bouts (red for sleep-deprivation (SD), blue for NSD; sized according to duration) in each of these blocks. The best-fit linear regression for each block is shown with a solid line. (C) Theta y-intercepts of the speed-theta regression lines are shown for each time bin. Error bars indicate 95% confidence intervals. Intercepts significantly decreased across time bins in NSD sessions (First vs Second: Δ = 0.44 Hz, p = 0.006; First vs Third: Δ = 0.34 Hz, p = 0.021), whereas no significant change was observed in SD sessions (all p > 0.24). Intercepts were significantly higher in SD than NSD during the second and third time bins (Second: Δ = 0.55 Hz, q = 0.0058; Third: Δ = 0.45 Hz, q = 0.011; FDR-corrected). (D) Estimated slopes of the speed–theta relationship (Hz per cm/s) are shown for each time bin. Slopes did not differ across time bins within either condition (all p > 0.16) and did not differ between SD and NSD in any bin (all q > 0.41), indicating that sleep lowers baseline theta frequency without altering its modulation by running speed.

Consistent with the previous reports, we observed a significant effect of movement speed on theta frequency (F(1, 1094) = 15.70, p = 7.9 × 10⁻⁵). Importantly, we still found a significant effect of TimeBin (F(2, 1094) = 5.88, p = 0.0029 (all bouts from all sessions in Fig 4B), indicating that the change in theta frequency across time in sleep (NSD) sessions was not explained by changes in movement speed. Instead, these changes were reflected in the intercepts of the speed-theta regression (Fig 4C), which progressively decreased across time bins during NSD sessions and were lower than those observed in SD sessions. In contrast, the slope of the speed-theta relationship did not differ across time bins or between SD and NSD conditions (all p > 0.16; Fig 4D), indicating that sleep primarily lowers the baseline theta frequency without altering its modulation by running speed. Given that the intercept of theta frequency versus movement speed has been associated with anxiety, with a lower theta frequency resulting from anxiolytics ^15,28, these observations suggest that the lower theta frequency we observed may reflect diminished anxiety and increased relaxation experienced upon waking up from sleep.

Resonances in neuronal spiking displays similarly consistent theta frequency patterns

Next, we asked whether theta frequency changes that we observed in the LFPs also had a similar effect on the simultaneously recorded units in our sessions. To examine the theta modulations of single-unit activities, we calculated the spike autocorrelogram for each unit in sliding 30-min time windows (with 25-min overlap). Using the time lag of the first peak in the autocorrelograms, we estimated the resonant theta frequency for each unit in that window and examined the evolution of this theta resonant frequency over the ZT 0-5 block (Fig S4A). The peak frequency of theta modulations in single units was generally higher than in the LFP (~7 Hz), consistent with previous reports ^31,32. Consistent with the LFP, a drop in the frequency of theta modulations in unit activities was observed over the 5-h block in both SD and NSD conditions (Fig S4B), though this effect appeared less pronounced than that in the LFP (Fig 1C). At the population level, theta frequency firing was significantly modulated by both condition and time (Fig S4C; LME ANOVA: Condition, F(1,16008) = 8.32, p = 0.0039; TimeBin, F(2,16008) = 72.80, p = 3.35 × 10⁻³²), indicating overall higher frequencies during SD and a robust decrease across time bins. Importantly, a significant Condition × TimeBin interaction (F(2,16008) = 4.62, p = 0.0099) indicated that the temporal evolution of theta frequency across the ZT 0–5 period differed between conditions.

Age-Related Attenuation in Theta Frequency Modulation During Sleep

These results indicated a robust relationship between sleep and theta frequency in subsequent awake states. As earlier studies showed that aged animals exhibit more interrupted sleep patterns than younger ones, we next asked whether similar theta frequency patterns would be observable in aged animals. Hybrid Fisher/Brown Norway rats aged 25.9—27.1 months obtained from the National Institute on Aging Rodent Colony were implanted with bilateral electrodes and underwent similar experiments as the adult rats (Table S1). In these aged animals (Fig 5A, B) theta frequencies ~ 7 Hz were observed during continuous awake periods (Fig 5A, REST, MAZE). During NSD in aged rats only transient reductions in theta frequency were observed, notably less than those in their younger counterparts. Similarly, during post-maze recovery sleep blocks, theta frequency drops were smaller, mostly staying above 6.5 Hz, in contrast to the larger drops we observed in adult animals (Fig 5A).

Figure 5: Theta frequency changes in aged animals under sleep deprivation and natural sleep conditions.

(A) Estimated marginal means (± SEM) of wake-theta peak frequency across three time bins for aged (left) and adult (right) animals, comparing SD and NSD. Estimates are derived from the mixed-effects model used in the main analyses. (B) Mean theta frequencies (thick lines) and SEMs (shaded) in aged animals, comparing sleep deprivation (SD; red) and ad-libitum natural sleep (NSD; blue) conditions. Segments represent the end of the dark cycle (REST), light-period sleep or sleep deprivation (SD/SLEEP), maze exploration (MAZE), and post-maze sleep (RECOVERY). Color bars above each panel show the proportion of time spent awake versus asleep in 30-min sliding windows. Dark horizontal bars and asterisks indicate significant differences between conditions (p = 0.041); light horizontal bars and “n.s.” denote periods that were significant in point-wise comparisons but not in cluster-based permutation tests. (C) Each dot represents an individual awake bout from all sessions, with size indicating bout duration and color intensity reflecting relative theta power. (D) The same bouts sorted by sleep proportion in the 30-min window preceding bout onset (see Fig 3 for the method). Increased sleep in the preceding 30 mins is associated with reduced theta frequency (R² = 0.04).

To test these effects, we again applied a linear mixed-effects model with Condition, TimeBin, and AgeGroup (adult vs aged) factors and random intercepts for Animal and Session nested within Animal. Marginal ANOVA tests revealed no significant main effects for Condition, TimeBin, or AgeGroup alone. However, there was a significant interaction between TimeBin and AgeGroup (F(2 ,8029.97) = 12.15, p = 5.4 × 10⁻⁶), as well as a significant three-way interaction between Condition, TimeBin, and AgeGroup (F(2,8336.59) = 3.03, p = 0.049. Post-hoc comparisons (false-discovery rate corrected) confirmed that theta frequency was significantly higher during SD relative to NSD in adult animals across all TimeBins (first: p = 0.0026; second: p = 7.3 × 10⁻¹⁶; third: p = 2.5 × 10⁻¹⁴). In contrast, no significant SD–NSD differences were detected in aged animals. Furthermore, during NSD in adults, theta frequency significantly declined from the first to later TimeBins (first vs second: p = 9.4 × 10⁻³²; first vs third: p = 3.0 × 10⁻³³), whereas these temporal changes were not significant in aged animals. A smaller but still significant decline in theta frequency was also observed during SD in adults (first vs second: p = 3.7 × 10⁻⁹; first vs third: p = 1.2 × 10⁻¹²). Together, these results indicate that theta frequency dynamics across time and sleep were markedly attenuated in aged animals.

Differences in sleep behavior between the two cohorts may contribute to this attenuation. Consistent with this, we observed altered sleep dynamics in the aged animals across the recording period (Fig S5A, C). During NSD, these aged animals demonstrated reduced sleep compared to adults whereas during SD they managed to occasionally sleep despite our attempts at sleep-deprivation; they appeared to be awake with eyes wide open, leading inadvertently to fewer gentle handling interventions, but post-hoc scoring of their brain activity was more consistent with sleep (Fig S5B). Analysis of sleep fractions before awake states in aged animals still showed a significant negative correlation between sleep fraction and theta frequency, with the 30-min pre-awake period remaining a crucial predictor (Fig 5D), though the variance explained was notably less than we saw in the adults (R² = 0.04 aged vs. R² = 0.17 adults). Overall, these observations suggest that theta frequency undergoes less modulation following sleep in aged animals, due to a combination of sleep fragmentation as well as a weaker effect of sleep on theta frequency.

Rolipram reduces theta frequency in awake sleep-deprived animals

Our data shows that sleep-deprivation sustains an elevated frequency of theta compared to ad-libitum natural sleep. It has been shown that systemic administration of a phosphodiesterase inhibitor can shield the rodent brain from the detrimental effects of sleep deprivation on synaptic plasticity and memory performance ^25,33,34 . We reasoned, therefore, that protective effects of rolipram could also be reflected in the frequency of awake theta oscillations during sleep deprivation. We performed intraperitoneal injections of rolipram (1 mg/kg) and saline controls during the 5-h SD period twice in each animal, at the 1 h and 2.5 h time points. Similar to the earlier experiments, theta frequency was high (>7 Hz) during awake rest and run blocks but dropped below 6.5 Hz after recovery sleep following sleep deprivation (Fig 6D). Remarkably, the administration of rolipram during SD also resulted in a significant decrease in theta frequency (< 6.5 Hz), mirroring changes in theta during natural sleep periods in non-sleep-deprived animals. To quantify these effects, we applied a linear mixed-effects model predicting theta frequency with Injection (ROL vs CTRL) and TimeBin (Baseline, Inj1, Inj2) as fixed effects and random intercepts for animal and session. Marginal ANOVA tests revealed a significant effect of TimeBin (F(2,5446) = 10.48, p = 2.9 × 10⁻⁵) and a strong Injection × TimeBin interaction (F(2,5446) = 88.05, p = 2.3 × 10⁻³⁸), indicating that the temporal dynamics of theta frequency differed markedly between rolipram and control conditions. Post-hoc comparisons confirmed that rolipram significantly reduced theta frequency following both injections during SD, relative to baseline and relative to saline controls (all p < 0.001; Fig 6C). In contrast, theta frequency in saline-treated animals remained relatively stable across time bins. These results demonstrate that rolipram administration during sleep deprivation produces a rapid and robust reduction in awake theta frequency.

Figure 6: Impact of rolipram on theta frequency during sleep deprivation.

(A) Changes in mean theta frequency (thick line) and SEM (shaded) across different experimental phases—homecage activity in the dark cycle (REST), novel maze exposure (MAZE), sleep deprivation in the light cycle (SD), and recovery sleep (RECOVERY)—following intraperitoneal injections of saline control (CTRL, blue) or rolipram (ROL, red). Red dashed vertical lines denote the timestamps of the two injections during the sleep-deprivation phase (at 1 h and 2.5 h). Under the control condition, theta frequency remained consistently high throughout the sleep deprivation phase. Conversely, a significant reduction in theta frequency was observed following rolipram administration at two time points during SD (p = 0.016, p = 0.028) and at one time point during recovery (p = 0.028). Dark horizontal bars and asterisks indicate periods with significant differences between conditions; light horizontal bars and “n.s.” denote periods that were significant in point-wise comparisons but not in cluster-based permutation tests. (B) Theta power remained generally comparable across conditions. (C) LME analysis of SD-period theta frequency using custom bins (Baseline: 0-1 h, Inj1: 1-2.5 h, Inj2: 2.5-4 h) with fixed effects Condition, Time Bin, and Condition × Time Bin, and random intercepts for Animal and Session nested within Animal. Model-estimated marginal means ± SEM are shown; horizontal brackets/asterisks indicate FDR-corrected post hoc pairwise contrasts. (D) Mean REM theta frequency during the recovery period (left), plotted across Zeitgeber time (ZT). Lines indicate the mean and shaded regions indicate SEM for control (CTRL, blue) and rolipram (ROL, red) conditions. Linear mixed-effects (LME) model-estimated awake theta frequency across successive time bins during recovery (right). Points indicate model-estimated marginal means and error bars indicate SEM for CTRL (blue) and ROL (red). Horizontal bars denote statistically significant pairwise differences between conditions across time bins.

Unexpectedly, the effects of rolipram on theta also continued into the REM sleep periods during the recovery sleep. Linear mixed-effects analysis of REM theta frequency revealed a significant Injection × TimeBin interaction (F(2,491) = 6.29, p = 0.002) during the recovery period, indicating that REM theta dynamics differed between rolipram and control conditions after the end of sleep deprivation. In particular, theta frequency in the rolipram condition increased across recovery bins and became significantly higher during the later recovery period compared with control sessions (Fig 6D). Post-hoc comparisons confirmed that REM theta frequency during the third recovery bin in the rolipram condition was significantly higher than in the control condition (Fig 6D, right panel, p = 0.033). While the underlying reasons for this effect are currently unknown, they may reflect enduring effects of rolipram on cAMP signaling during sleep^35,36. Overall, these observations suggest that rolipram’s potential to mimic sleep-like neural modulation may underly its reported capacity to provide resilience to the detrimental effects of sleep deprivation ²⁵.

Discussion

Theta oscillations and their frequency have been critically linked to the memory functions of the hippocampus ². As it has been posited that the theta cycle represents a single moment for cognitive processing, a lower frequency (i.e. a longer unit moment) would appear beneficial for computation ^5,28. This suggests a functional benefit for maintaining hippocampal theta frequency at or below a certain range. Consistent with this, optogenetic manipulations of the medial septum that increase the frequency of theta oscillations in the hippocampus have been found to impair memory encoding, whereas those that decrease theta frequency leave memory function intact ³⁷. Our study shows that the frequency of the hippocampal theta oscillation undergoes continuous modulation across sleep and wake cycles, with a strong lowering upon waking from sleep. In particular, we found that the proportion of sleep in the previous 30 mins was a strong predictor of theta frequency—theta frequency was at its lowest when animals first awoke from sleep but increased rapidly upon waking. This observation was true both when we looked at theta in transient bouts of quiet waking, as well as in more sustained bouts of active waking. The frequency of theta increased with movement, as expected ^15,16. However, changes in movement were not the underlying source of the theta frequency reduction that we observed.

Anxiolytic Effects of Sleep on Hippocampal Theta Frequency

Previous studies have suggested that the slope and intercept of the theta-frequency versus running speed correlation represent different aspects of the mechanisms underlying the generation of hippocampal theta oscillations. Notably, the intercept of the theta-frequency-running speed relationship has been associated with anxiety ^15,28,38. Drugs that reduce anxiety lower the intercept while anxiogenic drugs increase the intercept. In our study, the effects of sleep history were most evident in the intercept of the phase-movement speed relation, suggesting that sleep’s effects on theta frequency are consistent with an anxiolytic effect of sleep ³⁹. Interestingly, while awake theta frequency was elevated during sleep-deprivation, when compared to sleep, it nevertheless also showed a slight but still significant decline over the 5-h sleep-deprivation procedure (Fig 5A). This also suggests that sleep-deprivation through gentle-handling was not in itself anxiogenic, consistent with previous reports ^40,41.

The frequency of theta has also been linked to the brain’s metabolic rate ¹; higher theta frequency is observed in species that have a higher metabolism. Moreover, hippocampal pyramidal cell firing rates across the circadian cycle vary in a similar way to hippocampal theta frequency, suggesting that these systems are essentially linked ⁴². Sleep notably slows down brain metabolic activity ⁴³, and lowers firing rates in the hippocampus⁴⁴. Our study further demonstrates the frequency of theta is lower when emerging from sleep, consistent with these metabolic effects. Interestingly, however, within sleep itself, the theta frequency, which is only observable during the REM state, was remarkably consistent, and generally higher than the theta evidence upon waking. This suggests that the different mechanisms underlying theta oscillation generation during REM and waking are differentially affected by sleep, with only awake theta alternated by variations resulting from sleep.

Overall, these observations suggest that the lowering of theta frequency by sleep may reflect an important aspect of sleep’s effect on hippocampal function, and that this lowered theta frequency may be a signature of the well-rested brain. Resets of levels for different arousal-promoting neuromodulators—serotonin ^46,47, norepinephrine ^48,49 and/or acetylcholine ^50,51–may mediate this effect via metabotropic receptors distributed in the hippocampus and connected brain regions. Even though we observed some decrease in theta frequency in the sleep-deprivation sessions, this lowering was significantly weaker than under ad-libitum sleep conditions. This also indicates that the theta frequency effects were not due to the circadian rhythm alone (but see ⁴²). Nevertheless, in both SD and sleep conditions, exposure to a novel maze was sufficiently arousing to return theta frequency to elevated levels, indicating that animals remain capable of a rapid physiological response to novelty and exploration.

Higher Theta Frequency in Aging and Lower Theta Frequency with Rolipram

The lowering of theta frequency following sleep was also muted in aged animals. Some of this may be due to the overall fragmentation of sleep that is an unfortunate corollary to aging, including in our aged rat cohort. However, we saw only modest differences in sleep proportion between young and aged animals in the NSD condition (Fig S5B), indicating that sleep has a more modest effect on hippocampal theta frequency in the aged animals (compare also Fig 5D and Fig 3D). Collectively, these observations suggest that the muted theta-frequency reset may reflect a subtle inability of sleep in the aged brain to restore hippocampal function. Future experiments with a larger cohort and more stringent sleep-restriction protocols could help reveal significant effects of sleep vs. SD in aged animals as well.

Strikingly, administration of rolipram, which has been shown to help overcome the detrimental effects of sleep loss on memory ²⁵ and to improve memory function in aged animals ²⁶ by enhancing cAMP signaling, produced a lower theta frequency in sleep-deprived animals, mimicking the theta frequency obtained with sleep. It may be that this theta reflects rolipram’s propensity to induce nausea in rats ^52,53 by enhancing the presence of “type II” theta linked to fearful stimuli. However, evidence also suggests that type II theta is not strictly a response to negative stimuli, but reflects a more general arousal signal that can even be evoked by conspecifics of the opposite sex ^54,55. Moreover, it is precisely this type II theta that is suggested to be captured by the theta-frequency intercept at zero movement speeds^38,56. Interestingly, rolipram administration also resulted in increased theta frequency during REM sleep many hours after its administration. This suggests a sustained pharmacological impact on cAMP signaling during sleep^35,36, rather than a non-specific physical response to nausea alone. Overall, we interpret the lower theta frequency induced by rolipram as potentially reflecting its positive pharmacological impact on cognition and anxiety ^28,57.

Limitations of the Study

A previous study observed an increase in theta power over the course of sleep deprivation ⁴⁵ , but without an apparent corresponding change in theta frequency, and suggested that theta power can be a valuable predictor of sleep-propensity. The changes in theta power in this study were largely unique to the quiet waking epochs that were associated with low muscle activity. In our study, we did not detect a change in theta power over the course of either sleep or sleep deprivation, in either the quiet or active waking states. However, the theta frequency lowering was evident in both quiet and active waking periods. Some differences between the data in these studies could arise from the differences in experimental design, including the different sleep-deprivation procedures, particularly the change to a novel home cage that took place in that study ⁴⁵, which could have triggered additional spatial learning.

We also note that studies have also shown that brain temperature, which decreases during sleep, has a strong effect on brain metabolism and theta frequency ^17,18. A recent study further showed that modifying the temperature of the medial septum, a major source of extrinsic hippocampal theta, leads to corresponding changes in theta frequency ¹⁹, as well as in theta power. Our observations are also consistent with a drop in brain temperature over the course of sleep, leading to lower theta frequency, and a rise in brain temperature with waking, leading to a rebound in theta frequency.

In our aged cohort, our procedure for sleep deprivation was compromised by the ability of the aged animals to sleep with their eyes open. We regrettably only realized this in post hoc sleep scoring based on electrophysiology. Consequently, the blunted theta frequency modulation observed in the aged animals may partially reflect an inability to achieve complete sleep deprivation in the SD condition and the presence of fragmented sleep in the NSD condition. Finally, as noted above, rolipram has been found to induce nausea in rats ^52,53. Thus, we cannot rule out that some of the lowered theta frequency we observed following rolipram administration may have been due to the induction of an aversive state in these animals.

The Role of the Theta Cycle in Memory

The theta wave is considered to represent a single cycle for hippocampal neuronal computations in the service of memory. Theoretical work has suggested that the duration of the cycle sets limits on the amount of information that can be associated during memory encoding and recall ^58,59, and maintained in a working memory buffer ⁵. These notions have been well-supported by a large body of experimental studies ^6-10. Studies have found that the neuronal firing activities that take place in each cycle of theta are crucial in allowing these neurons to form into assemblies and promoting these assemblies for subsequent reactivation and replay during sleep ^6,13,60. In light of this, the changes in theta frequency following sleep may have important functional consequences; these findings suggest that memories formed upon emergence from sleep are most likely to be subsequently remembered.

STAR★Methods

Experimental Model and Study Participant Details

Animals

This study used rodent animal models only. In three separate experiments, a total of 16 rats were used, including adult Sprague Dawley rats, adult Long–Evans rats, and aged F344BN F1 rats. Animal sources, strain identifiers, and RRIDs are provided in the Key Resources Table. Both male and female adult rats were included, whereas the aged cohort included male F344BN F1 rats; sex-specific effects were not analyzed separately because the study was not designed to test sex-specific effects. Detailed information about the rats, including their distribution by strain, sex, age, and weight at the time of surgery, experimental condition/session as well as the specific probes used, and recording site is provided in Table S1.

Key resources table

REAGENT or RESOURCE	SOURCE	IDENTIFIER
Bacterial and virus strains
AAV2.9 CamKiiα-DmOctβ1R.HA	Havekes et al. (ref 64)	N/A; custom viral vector, University of Pennsylvania Viral Vector Core
Chemicals, peptides, and recombinant proteins
Rolipram	Sigma-Aldrich	Cat# R6520; CAS: 61413-54-5
Deposited data
Electrophysiology and behavioral data	This paper	Zenodo DOI: https://doi.org/10.5281/zenodo.17122450
Experimental models: Organisms/strains
Rat: Sprague Dawley	Envigo (Haslett, MI)	Hsd:Sprague Dawley SD; Order code 002; RRID:RGD_737903
Rat: Long–Evans	Envigo (Haslett, MI)	HsdBlu:LE; Order code 140; RRID:RGD_5508398
Rat: F344BN F1	NIA Aged Rodent Colonies / Charles River Laboratories	F344BN F1; F344CDFBN; RRID:SCR_007317
Software and algorithms
Custom MATLAB scripts	This paper	Zenodo DOI: https://doi.org/10.5281/zenodo.17122450
MATLAB	MathWorks	2025b
FOOOF	Donoghue et al. (ref 27)	Version 1.1.1
Buzcode / SleepScoreMaster	Buzsáki lab GitHub	https://github.com/buzsakilab/buzcode
SpyKING CIRCUS	Yger et al. (ref 74)	Version: 1.1.0
FieldTrip	Oostenveld et al. (ref 75)	Version: 20251201
Phy	Cortex Lab GitHub	https://github.com/cortex-lab/phy
CellExplorer	Petersen et al. (ref 76)	https://github.com/petersenpeter/CellExplorer
Motive tracking software	NaturalPoint, Inc.	Version 2.1.2
Other
Neuronexus Buzsaki32 probe	NeuroNexus	Model: Buzsaki32
Neuronexus A5×12 probe	NeuroNexus	Model: A5×12
Neuronexus Buzsaki64 probe	NeuroNexus	Model: Buzsaki64
Diagnostic Biochips P128-1 probe	Diagnostic Biochips	Model: P128-1
Diagnostic Biochips P128-8 probe	Diagnostic Biochips	Model: P128-8
Masmanidis 128K probe	Yang et al. (ref 72)	Model: 128K
Masmanidis 128L probe	Yang et al. (ref 72)	Model: 128L
Open Ephys acquisition system	Open Ephys; Siegle et al. (ref 73)	Version: 2.2
Intan RHD recording controller	Intan Technologies	C3008
OptiTrack Flex 13 camera tracking system	NaturalPoint, Inc.	Model: Flex 13
RatPack vector rat illustrations	Etienne Ackermann; Kemere Lab GitHub repository	GitHub: kemerelab/ratpack; License: CC BY-SA 4.0

Animals were wild-type/non-transgenic rats. In a subset of animals in the PDE4 inhibition experiment, AAV2.9 CaMKIIα-DmOctβ1R.HA was infused into the hippocampus 3–4 weeks before electrode implantation to express the Drosophila octopamine receptor, as described below. No genetically modified animal lines were bred for this study.

Animals were maintained in the University of Michigan animal facility under standard laboratory housing conditions. Food was available ad libitum, and water was available ad libitum except during behavioral training and recording periods requiring water restriction, as described below. Animals were handled before surgery, monitored during water restriction, allowed to recover after surgery, and maintained according to institutional veterinary and husbandry guidelines.

Ethical Compliance

All animal procedures were approved by the Animal Care and Use Committee at the University of Michigan, ensuring adherence to guidelines established by the National Institutes of Health.

Methods Details

Animal Handling and Training

Prior to surgical procedures, animals were handled for at least five days, 20 min each day, to familiarize them with human interaction. Animals were then placed on a water restriction regimen and trained in a small box to alternate between two wells to obtain water. During water restriction, animals were provided ad libitum access to water for at least 30 min daily and their weight was monitored to ensure it did not drop below 85% of the weight prior to water restriction. Water restriction was ended prior to electrode implant surgery and restarted 24h before recordings.

Surgical Procedures

All surgical procedures were conducted under isoflurane anesthesia (4-5% for induction and 1-2% for maintenance) in a stereotaxic frame. The surgical process began with the removal of hair from the head and cleaning of the incision area using alcohol and betadine. An incision was then made to expose the skull, and additional local anesthesia was applied using a lidocaine and bupivacaine cocktail. After cleaning the skull and applying hydrogen peroxide to remove extra tissues and blood, craniotomies were performed at AP: −3.36, ML: ±2.2 or AP: −4.50, ML: ±3.5, depending on the probe type, using a dental drill with a trephine burr. The dura was carefully removed with fine tweezers to expose the brain surface. Upon cessation of bleeding, silicon probes were implanted and the craniotomy was covered with DOWSIL silicone gel (3-4680, Dow Corning, Midland, MI) and wax. Signal quality was comparable between the different probes used with similar results across animals (see individual results in Fig S1 and Fig S2). To test whether the different probe locations used in different animals influenced the theta frequency we measured, we applied linear mixed-effects (LME) models that included probe location as a categorical fixed effect (anterior (AP −3.3-3.6, ML ±2.2) versus posterior (AP −4.5, ML ±3.5)). In the adult dataset, the model ThetaFrequency ~ Condition * TimeBin + ProbeLocation + (1∣Animal) + (1∣Animal:Session) probe location was not significant a significant factor (F(1,7829)=1.05, p=0.305), and estimated marginal means (averaged across Condition × TimeBin) were comparable: 6.96 ± 0.13 Hz for anterior sites and 6.73 ± 0.18 Hz for posterior sites. Similarly, in the combined aged/adult dataset, probe location was not a significant factor (F(1,8.31)=2.06, p=0.187) in the model ThetaFrequency ~ AgeGroup * Condition * TimeBin + ProbeLocation + (1∣animalID) + (1∣animalID:Session). Estimated marginal means were comparable, 6.94 ± 0.12 Hz for anterior sites and 6.72 ± 0.08 Hz for posterior sites (mean ± SEM, averaged across AgeGroup × Condition × TimeBin). Thus, we observed no significant effect of probe location on theta frequency, consistent with previous reports ^61,63.

Protection and electrical shielding for the implant were ensured by employing a combination of copper mesh and/or 3D printed plastic depending on the type or the probes used. Ground and reference screws were placed in the skull over the cerebellum, and all these components were securely attached to the skull using C&B Metabond^® Quick Adhesive Cement System and dental cement. Post-surgery, a topical Triple Antibiotic Ointment (BluePoint Laboratories) was applied to the incision site, and the oral analgesic meloxicam (1-2 mg/kg dose, 1.5 mg/ml in Meloxidyl; drops of meloxicam were added to Froot Loops cereal for ingestion) was given prior to and after the surgery. Animals were given a recovery period of at least five days in their home cages, during which the probes were gradually lowered to the target recording site in the hippocampal region, identified by electrode depth, characteristic sharp-wave ripple signals⁶² and corresponding unit spiking activities. Experimental recordings started once a good signal was obtained, typically seven days after surgery.

Behavioral

After recovery from surgery, animals were placed in different experimental conditions. At the end of the dark cycle, animals (6 adult rats, 3 aged rats) underwent 3 h of rest as a baseline recording in their home cage, followed by either 5 h of sleep deprivation (10 sessions) or ad-libitum sleep (9 sessions) starting with the onset of the light cycle (ZT 0). At this point, animals were then placed to run for water rewards at the two ends of a novel track for about an hour and subsequently returned to their home cage for another 3 h of observation. At this point, the 3 aged animals were also placed back on the same track for a second exposure and subsequently underwent another 9 h of recording in the dark cycle.

Seven animals were tested with PDE4 inhibitor rolipram (1 mg/kg, intraperitoneal; 7 sessions) or saline (4 sessions). Four out of these 7 (minus BG, BGU, and MR10) were infused with a viral vector, AAV2.9 CamKiiα-DmOctβ1R.HA, into the hippocampus 3-4 weeks before surgery to express the Drosophila octopamine receptor⁶⁴. In these experiments, following the 3 h baseline recording, animals were placed on the novel track for an hour prior to the end of the dark cycle. Starting with the onset of the light cycle, these animals were then sleep-deprived and received intraperitoneal administration of either rolipram (1 mg/kg) or saline/PBS, at ZT1 and ZT2.5 time points. The DmOctβ1R.HA infused animals also underwent testing with intraperitoneal administration of octopamine (1 mg/kg) prior to the rolipram/saline sessions, but due to uncertainty in receptor expression patterns, we examined only the rolipram and saline sessions here.

Sleep Deprivation Protocol

Sleep deprivation was carried out starting at the onset of the light cycle with animals in their home cages, following a commonly used 'gentle handling' procedure ^65-67. This method is widely adopted because it minimizes confounds due to of stress and forced locomotion ^41,68-71. The animals were first thoroughly habituated to the experimenter by being handled for more than 3 days, 20-30 mins/day before the surgery. During SD, interventions of increasing intensity were employed when the animals displayed signs of sleepiness, starting from tapping on the cage, to gently shaking the cage, to displacing the bedding materials. Following the 5 h of sleep deprivation, a recovery period of 48 h was allotted before another sleep deprivation session.

Data Acquisition

Different silicon probe configurations were used in these recordings: 4 shank Buzsaki32, 5 shank A5x12, or 8 shank Buzsaki64 probes (from Neuronexus, MI), 1 shank P128-1, or 8 shank P128-8 (from Diagnostic Biochips, MD), and 4 shank 128K or 4 shank 128L Masmanidis probes⁷² (from IDAX Microelectronics Labs, CA). See Table S1 for further details. The electrophysiological data were acquired using either OpenEphys ⁷³ or an Intan RHD recording controller, with a sampling rate of 30 kHz. For the analysis of local field potentials (LFP), the signals were downsampled to 1250 Hz. The tracking of the animal's position was facilitated by Optitrack (NaturalPoint, Inc., OR), which employs infrared cameras to detect 3D markers attached to the animal’s crown. In some sessions, due to suboptimal calibration for homecage, the animal’s positions were not usable; only the position data from 6 NSD and 5 SD sessions were used in the speed analysis.

Spike Sorting and unit-based analysis

Spike sorting began with filtering, thresholding, and automatic clustering using SpyKING CIRCUS ⁷⁴. Brief movement-related artifacts were detected using automated screening of continuous LFP data in FieldTrip. Artifact windows were identified with complementary detectors for jumps (ft_artifact_jump), clipping (ft_artifact_clip), z-value outliers (ft_artifact_zvalue), and amplitude-threshold events (ft_artifact_threshold) ⁷⁵. Detector outputs were converted to time windows and merged into a single artifact mask that was used during spike-sorting preprocessing. Most detected artifacts occurred during TRACK/maze epochs, whereas home-cage periods, which comprised the majority of the recordings, were comparatively artifact-free. Initial sorting was followed by thorough manual curation and reclustering using the Phy package (https://github.com/cortex-lab/phy). Putative neurons were classified into pyramidal cells and interneurons (wide and narrow) using Cell Explorer ⁷⁶. ⁷⁵For unit-based rhythmicity analyses (Fig S4), autocorrelograms (ACGs) were computed from spikes occurring within concatenated awake bouts inside sliding windows centered across Zeitgeber time ⁷⁷. In the current analysis, spikes were extracted from 60-min windows (±30 min around each window center). ACGs were calculated with a 1.4 s lag window using 1 ms bins, and positive lags were used for downstream visualization and analysis (Fig S4A). ACGs were smoothed with a 20 ms Gaussian kernel. Units were retained only if they showed sufficient spike-count support, defined as a mean ACG count of at least 5 within the 80-200 ms lag range. Theta frequency was quantified from the ACG using a local-maximum approach, defined as the dominant peak within the 100-200 ms lag range. In parallel, damped-oscillatory model fits were computed to assess rhythmicity and fit quality, and poorly fit unit-window estimates were excluded before summary analyses and mixed-effects modeling.

Sleep scoring and bouts

Following previous studies ^44,78-81 data were binned in 2-s overlapping periods with 1-s steps. Theta and slow-wave channels were selected using the automated Sleep Score Master, part of the Buzcode toolbox (https://github.com/buzsakilab/buzcode), which identifies channels based on spectral features by maximizing separation between theta and non-theta states. Briefly, channels were evaluated based on theta-band (5–10 Hz) power and bimodality of theta-related metrics across time, and the channel with the strongest and most stable theta oscillations was selected. A corresponding slow-wave channel was selected in parallel based on low-frequency spectral features and maximal separation of high vs low slow-wave activity. For each period, slow-wave slope, theta power, and electromyogram (EMG) were estimated using functions in Sleep Score Master, to categorize brain states into slow-wave sleep (SWS), quiet wake (QWAKE), REM sleep, and active wake (AWAKE). EMG activity was estimated by examining high-frequency (300-600 Hz) band cross-correlation values between spatially distant channels, as these correlation values strongly correlate with nuchal EMG ⁸². Utilizing irregular-resampling auto-spectral analysis, the slope of the aperiodic component of the power spectrum was used to measure slow-wave activity ^83,84.

Theta power was estimated based on the ratio of power at 5-10 Hz to 2-20 Hz. Thresholds were set at the trough of the resulting bimodal distributions to separate these variables into low and high periods ^81,85. First, high slow-wave activity and low EMG periods were classified as SWS; then, high theta/high EMG periods were classified as AWAKE while high theta/low EMG periods were classified as REM sleep. The remaining low theta/high EMG periods were categorized as QWAKE. To determine transitions between states, a Schmidt trigger was used to prevent brief threshold excesses and false detections due to rapid fluctuations. After automatic sleep scoring, results were reviewed manually. In particular, due to the lack of SWS during sleep deprivation, the threshold for bimodal slow-wave slope distribution was less clear, requiring further manual adjustment for those sessions.

Continuous periods belonging to any of the four brain states (QWAKE, AWAKE, SWS, REM) were defined as “bouts”. Many of our analyses were particularly focused on the bouts which were classified as awake (QWAKE and AWAKE). Each awake bout was characterized by its duration, theta peak frequency and power estimated from the periodic component of the power spectrum using FOOOF, median EMG, and median movement speed. Bouts with invalid spectral fits, in which no theta peak was detected in the 5-10 Hz range, were excluded (926 of 8,762 bouts). Unless explicitly stated, QWAKE and AWAKE states were combined for analyses (see also Fig S2). A total of 7,836 awake bouts were analyzed across 18 sessions from 6 animals (mean ± SEM = 486.8 ± 51.4 per session; 1,460.3 ± 279.4 per animal). Bout durations averaged 22.1 s across conditions (NSD: 19.5 ± 1.6 s; SD: 24.0 ± 2.0 s, mean ± SEM across animals). For the aged animals, QWAKE and AWAKE states were first combined, yielding a total of 742 awake bouts analyzed across 10 sessions from 3 animals (mean ± SEM = 74.2 ± 9.9 per session corresponding to 247.3 ± 9.5 per animal, with mean ± SEM bout durations = 114.7 ± 16.9 s in NSD and = 251.6 ± 62.5 s in SD sessions). For the rolipram experiments, a total of 6,956 awake bouts were analyzed across 11 sessions from 7 animals (mean ± SEM = 632.4 ± 37.5 per session; 993.7 ± 115.9 per animal, with mean ± SEM bout durations = 33.9 ± 3.5 s in CTL and = 31.7 ± 3.9 s, in ROL sessions). To capture local sleep-wake patterns, awake proportion was defined as the fraction of time in awake states in a 30-min sliding window centered on each time point.

Theta Frequency Analyses

All analyses of local field potentials (LFPs) and unit activity were performed using custom MATLAB scripts, available on our GitHub repository: https://github.com/diba-lab/Theta. Theta oscillations were analyzed in two main contexts: (1) at the level of individual bouts, such as represented by dots in Fig 1B and associated with power spectra as shown in Fig 1A. In this case, time–frequency representations were computed using Morlet wavelet transforms to capture transient theta dynamics. (2) For continuous tracking of theta frequency across time, state-specific bouts were concatenated in 30-min windows sliding in 5 min steps and frequency estimates were computed across these bouts using Welch’s method with 2-s windows at 1-s overlap. Similar patterns were observed when we used 10-min sliding windows instead of 30-min (data not shown). Relative theta power within (5-10 Hz) was isolated above the aperiodic component using a "knee" model in the 1-40 Hz range in FOOOF ²⁷, which parameterizes power spectra by separating periodic peaks from the aperiodic background. Theta frequency was defined as the frequency with maximum power within the theta band.

Quantification and Statistical Analyses

Cluster-based permutation testing

To assess time-resolved differences in theta frequency, peak power, or sleep proportions between sleep-deprived (SD) and non-sleep-deprived (NSD) conditions, or relative to a fixed control values like baseline, we used non-parametric cluster-based permutation tests implemented in FieldTrip ⁷⁵. This method controls for multiple comparisons by clustering adjacent time points with consistent effects and computing cluster-level statistics as the sum of t-values ⁷⁵. Between-condition comparisons used a two-tailed independent-samples t-test; comparisons against a fixed value used a dependent-samples t-test, with a synthetic dataset constructed from matched, constant-valued trials. For both analyses, significance was assessed via 10,000 permutations, using the maximum cluster statistic to build the null distribution. Test parameters were: method = 'montecarlo', statistic = 'indepsamplesT' or 'depsamplesT', correctm = 'cluster', clusteralpha = 0.05, alpha = 0.05, tail = 0, numrandomization = 10000.

Linear mixed-effects modeling

Statistical analyses using linear mixed-effects models (LME) were performed to account for repeated measurements nested within sessions and animals. All models included random intercepts for Animal and Session nested within Animal ((1∣Animal) + (1∣Animal:Session)) and were fit using restricted maximum likelihood. Fixed effects were evaluated using marginal ANOVA F-tests. Planned post hoc contrasts were computed from model coefficients and corrected for multiple comparisons using Benjamini-Hochberg false discovery rate (FDR). Continuous covariates were z-scored before modeling. Detailed model specifications are provided in Table S2.

For theta-frequency analyses, fixed effects included Condition (SD vs NSD reference) and Time Bin (First: ZT 0-1.67 h reference; Second: ZT 1.67–3.33 h; Third: ZT 3.33–5 h). The state-resolved model (Fig S2B) additionally included State (QWAKE vs AWAKE reference) and interaction terms to test state dependence. The movement- and power-controlled model (Fig S2C) included MedianEMG and FOOOF-derived theta power (PowerFooof) as covariates to test whether muscle tone and/or theta power captured the variance across awake states; under this model, theta power but not EMG was significant, supporting our state scoring methods. A separate analysis for theta power (Fig S2D) used the same hierarchical random-effects structure with fixed effects Condition, State, and TimeBin, showing a significant difference in theta power between QWAKE and AWAKE, but no changes across time in theta power. Pooling QWAKE and AWAKE here (Fig S2E) confirmed that MedianEMG correlates with theta power, as expected, but that this relationship does not vary across time bins.

Population-level analyses of unit theta frequency (Fig S4C) were performed using pooled single-unit data across sessions, with fixed effects Condition, Time Bin, and their interaction (Condition × Time Bin), using the same random-effects structure. This model quantified temporal changes in unit-level theta frequency across the ZT 0–5 h period and compared SD and NSD conditions.

Rolipram analyses (Fig 6C-D) included two LME models. The first model (Fig 6C) analyzed NSD AWAKE/QWAKE theta frequency using custom injection-relative bins (baseline: 0-1 h; inj1: 1-2.5 h; inj2: 2.5-4 h), with fixed effects Injection (Rolipram vs control), Time Bin, and Injection × Time Bin. The second model (Fig 6D) focused on analyzing REM theta frequency during recovery sleep, with the same Injection × Time Bin structure but using the three-bin time definition described above (First, Second, Third). Both models used the same random-effects structure and FDR-corrected post hoc contrasts.

Aged-versus-adult analyses (Fig 5A) were performed in a combined dataset using fixed effects AgeGroup (aged vs adult), Condition, and Time Bin with full interaction terms (AgeGroup × Condition × Time Bin) to test age-dependent differences in baseline theta frequency and SD/NSD temporal dynamics.

Theta frequency and speed

To investigate how theta frequency varies with locomotion speed, time of day, and experimental condition (Fig 4A,B), we fit a linear mixed-effects model using MATLAB’s fitlme function. Due to camera placement issues, movement speed was unavailable in some of the sessions (see Table S1); therefore, analyses involving movement speed were restricted to the remaining sessions (4 SD, 6 NSD sessions from 5 animals). The analysis was restricted to AWAKE bouts in which animals were moving at speeds > 1 cm/s. Theta frequency was modeled as a function of speed (continuous), time bin (categorical: First, Second, Third, by dividing each period into thirds), and Condition (categorical: SD vs. NSD), including all interaction terms: Theta Frequency ~ Speed × TimeBin × Condition + (1∣Animal) + (1∣Animal:Session). Random intercepts were included for Animal and Session to account for repeated measurements within the same subjects and sessions.

The model provided extrapolated intercepts for theta frequency at Speed = 0 for each Condition × TimeBin combination. For each combination, we also estimated the slope of the relationship between theta frequency and running speed, expressed as the change in theta frequency (Hz) per 1 cm/s of speed. These estimated slopes were then compared across TimeBins within each condition and between conditions within each TimeBin. Standard errors and 95% confidence intervals for intercepts, slopes, and contrasts were derived from the fixed-effect covariance matrix. P-values from post hoc tests were corrected using the Benjamini-Hochberg false discovery rate procedure.

GLM modeling of sleep history and theta peak frequency

To quantify how recent sleep history predicts waking theta frequency, we fit a generalized linear model (GLM) to individual waking bouts using MATLAB’s fitlm. The dependent variable was the FOOOF-derived peak theta frequency during each waking bout. Predictors were retroactively computed sleep fractions (total sleep, including SWS and REM) within logarithmically spaced time windows (1, 2, 4, 8, 15, 30, and 60 min) preceding the onset of each bout. The model was fit by ordinary least squares. Model performance was evaluated using the coefficient of determination (R²), adjusted R², and root mean squared error (RMSE). To visualize the temporal structure of the relationship, we plotted the estimated main effect of sleep proportion for each window along with 95% confidence intervals (Fig 3C). This analysis revealed that sleep in the preceding 30 min was the strongest predictor of waking theta frequency.

Asterisks in the figures indicate statistical significance: p < 0.05 (*), p < 0.01 (**), and p < 0.001 (***); “n.s.” indicates not significant (p ≥ 0.05).

Supplementary Material

Document S1. Figures S1–S5

Table S1. Summary of animals, recording sessions, and probe configurations, related to STAR Methods

Table S2. Linear mixed-effects models used for theta frequency and power analyses, related to STAR Methods