Neuronal firing rates diverge during REM and homogenize during non-REM

Neurons fire at highly variable intrinsic rates and recent evidence suggests that low- and high-firing rate neurons display different plasticity and dynamics. Furthermore, recent publications imply possibly differing rate-dependent effects in hippocampus versus neocortex, but those analyses were carried out separately and with potentially important differences. To more effectively synthesize these questions, we analyzed the firing rate dynamics of populations of neurons in both hippocampal CA1 and frontal cortex under one framework that avoids the pitfalls of previous analyses and accounts for regression to the mean (RTM). We observed several consistent effects across these regions. While rapid eye movement (REM) sleep was marked by decreased hippocampal firing and increased neocortical firing, in both regions firing rate distributions widened during REM due to differential changes in high- versus low-firing rate cells in parallel with increased interneuron activity. In contrast, upon non-REM (NREM) sleep, firing rate distributions narrowed while interneuron firing decreased. Interestingly, hippocampal interneuron activity closely followed the patterns observed in neocortical principal cells rather than the hippocampal principal cells, suggestive of long-range interactions. Following these undulations in variance, the net effect of sleep was a decrease in firing rates. These decreases were greater in lower-firing hippocampal neurons but also higher-firing frontal cortical neurons, suggestive of greater plasticity in these cell groups. Our results across two different regions, and with statistical corrections, indicate that the hippocampus and neocortex show a mixture of differences and similarities as they cycle between sleep states with a unifying characteristic of homogenization of firing during NREM and diversification during REM.

sharp-wave ripples and sleep spindles during NREM sleep 11 , and incorporated over the course of REM sleep 11,16 and in the neocortex, triggered by alternating cycles of UP/DOWN states 22,23 . In Miyawaki and Diba 11 and Watson et al. 10 , we took trouble to evaluate firing rate changes between different epochs of the same state (e.g. NREM i and NREM i+1 epochs in sleep) to avoid confounds of state-dependent neuromodulation. However, some questions remain regarding how firing patterns of neurons of differing excitabilities change within each of these states and on transitions between these states, and how these compare between hippocampal and neocortical neurons. In particular, low and high firing neurons, with presumed low and high levels of excitability, are expected to be affected differently by activity-driven homeostasis and appear to bear differing levels of plasticity 2,9,24,25 . While this question was addressed to some extent in our previous work, understanding such effects is complicated by regression to the mean (RTM), for which the null hypothesis allows that firing rates of low-firing neurons should increase and those of high-firing neurons should decrease across any two comparative periods. A careful consideration of RTM is therefore necessary for a proper statistical evaluation of differential changes in low and high-firing cells.
In this report, we investigate changes in firing rates of neurons while accounting for RTM across both hippocampus and frontal cortex and both within and across transitions between different stages of sleep. We find that transitions to REM and NREM sleep states differentially affect low-firing and high-firing neurons in each state. In both hippocampus and frontal cortex, we find that REM sleep is marked by increased inhibition, and the spread between low-and high-firing neurons increases, while NREM results in a more homogenized and narrowed distribution of rates. These observations may help provide insights into the function and effects of sleep states on cortical networks of neurons.

Differential effects of REM and NREM on higher-and lower-firing rate hippocampal neurons.
We previously recorded from populations of CA1 pyramidal cells and interneurons over multiple sleep and awake cycles 11 . Based on these data, we showed that mean firing rates in hippocampal pyramidal cells increased within NREM but decreased through transitions between NREM and REM, and such zig-zag change resulted in a net decrease across sleep 11,16 . However, it was not clear whether or not transitions between sleep states affect lower and higher firing pyramidal cells uniformly. To address this question, we sorted the pyramidal cells into five quintiles based on their rank-ordered firing rates (Fig. 1A) and investigated their changes within and across NREM and REM sleep epochs ( Fig. 1B-G). Hereby, all analyses of neurons in these quintiles refer strictly to the pyramidal/principal cells, and interneurons are treated separately. To overcome potential confounds from RTM, here cells were sorted according to their firing rates over the entirety of the periods shown in each panel (see Methods for further details). Although all quintiles showed gradual firing increases within NREM and sudden decreases at the transitions to REM, the relative magnitudes of changes were different in lower-and higher-firing quintiles. Upon transitions to REM, lower firing cells showed large drops in activity, while higher firing cells showed little change (Δfiring rate = −41.5 ± 3.3%, −31.0 ± 2.8%, −14.6 ± 2.9%, −5.9 ± 2.5%, and 11.4 ± 1.9% for low to high firing quintiles from last 1/3 of NREM to first 1/3 of REM, F (4) = 59.2, p = 1.1 × 10 −45 , one-way ANOVA; Fig. 1B), effectively widening the distribution of firing rates and producing an increased coefficient of variation in the firing rates across neurons (ΔCV = 0.189 ± 0.011, p = 1.0 × 10 −35 , Wilcoxon signed-rank test; Fig. 1B,D). Interneuron firing increased at the transition to REM (Δfiring rate = 38.8 ± 61.2%, p = 1.1 × 10 −25 , Wilcoxon signed-rank test), consistent with a more competition-driven network 26 . Within REM, firing rate changes were similar across quintiles and the CV did not change significantly (Fig. 1B,E,F). Upon the transition from REM to NREM, firing rates initially dropped in all quintiles. However, lower firing cells rebounded strongly (Fig. 1E) whereas higher firing cells were suppressed across NREM. Consequently, the CV of firing rates decreased (Fig. 1E,G, ΔCV = −0.155 ± 0.014, p = 2.8 × 10 −21 , Wilcoxon signed-rank test), indicating a narrowed and more uniform distribution of neuronal firing rates. This rebalancing of excitability within NREM was accompanied by decreased firing in interneurons. In summary, we observed differential dynamics in lower and higher firing neurons, with transitions to REM widening the distribution of firing rates and both transitions to and continuation of NREM narrowing the distribution of firing rates.

Differential effects of REM and NREM on higher-and lower-firing rate neocortical neurons.
To examine whether similar state effects are also present in the neocortex, we extended these same analyses to neuronal spiking data recorded from frontal cortex of rats 10 and available on crcns.org (Fig. 2). Unlike in the hippocampus, firing rates increased at the transition from NREM to REM 12,27,28 (but also see refs 29,30 ). However, similar to the hippocampus, firing rate distributions widened upon this transition, with higher-firing neocortical cells showing relatively larger increases at the transition to REM (Δfiring rate = 24.9 ± 5.4%, 33.3 ± 5.7%, 34.0 ± 4.1%, 53.9 ± 6.7%, and 41.3 ± 3.8%, for each quintile from last 1/3 of NREM to first 1/3 of REM, F (4) = 4.3, p = 0.002, one-way ANOVA; Fig. 2B), increasing the CV of firing rates (ΔCV = 0.033 ± 0.021, p = 8.7 × 10 −5 , Wilcoxon signed-rank test; Fig. 2B,F) alongside increased firing in interneurons (Δfiring rate = 15.1 ± 48.7%, p = 7.8 × 10 −4 , Wilcoxon signed-rank test). Upon transitions from REM to NREM, firing rates decreased in the neocortex, and as in the hippocampus (Fig. 2E,G), the decrease was stronger in higher-firing than in lower-firing neurons. There was an accompanied decrease in interneuron firing and a significant decrease in the CV of firing rates across neurons (ΔCV = −0.034 ± 0.021, p = 5.9 × 10 −4 , Wilcoxon signed-rank test; Fig. 2E,G). The distribution of firing rates continued to narrow as NREM progressed (Fig. 2C). As the end of NREM approached, the firing rates began to increase, with further increases upon transition to REM. Overall, these results indicate that NREM and REM sleep states and the transitions between them have similar net effects on neurons with distributed firing rates in both the hippocampus and the neocortex. Regression-to-the-mean and sorting effects on firing rate changes. We wanted to better quantify these observations and to further evaluate how distributions of firing rates change within and across different sleep states. However, we first needed to better understand the relationship between variability and RTM in a population of neurons with log-normally distributed firing rates; ordering based on a part of analyzed data may bias the results due to RTM (Fig. 3A). We examined a simulated population of neurons where the source of variability is "multiplicative noise" proportional to each neuron's firing rate ( Fig. 3B; see also Methods). Despite the absence of any change in our model population, lower-firing neurons show an apparent increased firing, while higher-firing neurons show an apparent decreased firing (Fig. 3C) when the quintiles are based on rank-ordering during the first epoch (i) of a sequence i-j. This is RTM and it can confound evaluations of true effects (e.g. from sleep). To control for RTM, we need to either rank-order cells by their mean firing rates over the entire sequence, as we did for analyses in Figs. 1,2, or else instate an appropriate correction. We introduced a shuffle correction in which we randomly flipped indices for epochs of the same state (e.g. i and k for a NREM i /REM j /NREM k ) and repeated the analysis multiple times to obtain a surrogate distribution for the change index of quintiles 11 . This surrogate data provided us with valuable "control" shuffle means and confidence intervals for each quintile. We defined the "deflection index (DI)" as the difference between the observed change index (CI) and the surrogate mean within each quintile. These DIs were not significantly different from zero when changes were due only to noise (Fig. 3C).
We then examined DIs under two scenarios with a simulated change in addition to noise: when firing rates increase across the population, either additively by a fixed amount for all cells (Scenario 1; Fig. 3D) or multiplicatively, by an amount proportional to each cell's initial firing rate (Scenario 2; Fig. 3E). The shuffle-corrected DIs effectively described and differentiated the two scenarios. Under Scenario 1 the additive increase produced a larger relative effect on the DI in low-firing cells than in high-firing cells (Fig. 3D), while under Scenario 2, the evaluated DI's correctly depicted a uniform increase across the population (Fig. 3E).   Table 1 for details). Firing-rate spread in REM and homogenization in NREM. We next used the RTM correction methods described above to enable comparisons of firing rates in pairs of epochs. We did these analyses either within each state of sleep or across different stages of sleep. This approach is complementary to that shown in Figs. 1 and 2 and can serve as an independent verification of the observations shown there. During NREM sleep, the average firing rates of hippocampal pyramidal neurons increased (mean CI = 0.058 ± 0.005, p = 5.9 × 10 −27 , Wilcoxon signed-rank test). While the CI appeared to show the largest increase in low-firing cells, much of this apparent effect was due to RTM: in the shuffle corrected DIs, in fact the higher-firing quintiles showed the greatest relative increases (Fig. 4A, top row). In the frontal cortex the average CI decreased (mean CI = −0.023 ± 0.004, p = 3.2 × 10 −9 , Wilcoxon signed-rank test). When cells were separated into quintiles, the CI appeared to indicate increased firing in lower-firing cells and decreased firing in higher-firing cells (Fig. 4A, bottom row), but those changes were also largely explained by RTM. After correction for RTM in the DIs, some increase was evident in the second lowest quintiles, along with a decrease in the two highest quintiles. Changes in firing rate distributions showed a consistent picture to the DI analyses (Fig. 4A, bottom) with the distribution for the hippocampus narrowing slightly and shifting towards increased firing, while that in the frontal cortex narrowing and shifting left towards decreased firing.

NREM REM Awake
At the transitions from NREM to REM, hippocampal pyramidal cells decreased firing in all quintiles but the highest one, with the largest decrease in the lowest quintile (DI = −0.213 ± 0.019, −0.139 ± 0.016, −0076 ± 0.015, −0.038 ± 0.011, and 0.032 ± 0.010 for each quintile, all p values obtained by shuffling are <0.001; Fig. 4B, top row). Interneuron firing, on the other hand, increased (CI = 0.142 ± 0.013, p = 5.6 × 10 −22 , Wilcoxon signed-rank test), indicating a new steady state in the balance between network excitation and inhibition (but see 31 ). This increased inhibitory activity could potentially drive some of the decreased firing in pyramidal neurons 29 and allow for a winner-take-all mechanism whereby some high-firing cells dominate REM dynamics at the expense of lower-firing cells. These dynamics were somewhat different for the frontal cortex, however; at the onset of REM, principal neurons in the frontal cortex increased firing across quintiles, while interneurons showed little change (DI = 0.094 ± 0.029, 0.187 ± 0.023, 0.181 ± 0.019, 0.188 ± 0.020 and 0.162 ± 0.016 for each quintile of principal neurons, p values < 0.001 relative to shuffles, CI = 0.031 ± 0.033 for interneurons, p = 0.03, Wilcoxon signed-rank test). It is interesting to note however that the increased firing of hippocampal interneurons mirrored the overall increase in neocortical principal cell activity, consistent with neocortical control of hippocampal inhibition 32,33 . As a result of these changes, firing rate distributions became wider upon REM in both the hippocampus and the frontal cortex (Fig. 4B, right), consistent with our earlier analysis. Over the course of REM, we saw decreased firing across quintiles and interneurons in the hippocampus and in some quintiles of the neocortex (Fig. 4C). However, comparisons of the overall firing rate distributions did not reach statistical significance in the frontal cortex. The overall balance between excitation and inhibition therefore did not appear to change significantly within the course of REM states 34 .
In contrast, when REM transitioned to NREM sleep, lower-firing quintiles showed increased firing while higher-firing quintiles and interneurons showed a firing decrease both in the hippocampus and in the frontal cortex (Fig. 4D). Interestingly, among the various dynamics we investigated only this transition from REM to NREM was marked by a renormalizing effect on firing rates across quintiles even after correction for RTM, and it was the only one we investigated that was marked by decreased firing of inhibitory cells in the hippocampus. NREM  sleep therefore provided for the most uniform firing among the population of cells, potentially because of lower effective inhibition, whereas REM was marked by a widened distribution of firing activity.
Neuronal firing changes at transitions to and from wake. Our results thus far have outlined the effects of transitions and continuation of REM and NREM sleep states on neurons at different levels of excitability. We next applied these same methods to analyze the effects of transitions between sleep and waking on different quintiles and focused on our corrected DI analysis. Immediately upon transitions from waking to NREM sleep (direct transitions from wake to REM are rarely observed), the hippocampus showed increases in the middle of the distribution (Fig. 5A) whereas the frontal cortex showed a decrease in high-firing cells. Nevertheless, the wake-to-sleep transition was accompanied by decreased inhibition in the hippocampus (CI = −0.076 ± 0.016, p = 1.5 × 10 −6 , Wilcoxon signed-rank test) but not in the frontal cortex (−0.020 ± 0.032, p = 0.60, Wilcoxon signed-rank test) and a narrowing of the distribution of firing rates in both regions (ΔCV = −0.708 ± 0.076, p = 2.4 × 10 −11 , and ΔCV = −0.239 ± 0.035, p = 6.1 × 10 −7 for the hippocampus and the frontal cortex, respectively, Wilcoxon signed-rank test). The distribution narrowing in the hippocampus again indicates a new steady state in the balance between excitation and inhibition, with increased activity in the three middle quintiles (Fig. 5A), whereas the frontal cortex narrowing was a result of decreased firing in the highest-firing quintile and a trend towards more increase in progressively lower firing cells.
In contrast, the distribution of firing rates widened at the onset of wake. At transitions from NREM to wake (Fig. 5B), hippocampal firing decreased significantly, particularly among the lowest firing quintiles. These changes resulted in a leftward shift in the firing rate distribution (p = 2.9 × 10 −18 , Kolmogorov-Smirnov test) and an increase in the CV (ΔCV = 0.915 ± 0.137, p = 1.9 × 10 −7 , Wilcoxon signed-rank test). In the neocortex, on the other hand, higher-firing principle neurons increased firing at the transitions from NREM to wake, essentially reversing the change from wake to NREM (Fig. 5A) and producing a significant increase in the CV of the distributions (ΔCV = 0.243 ± 0.082, p = 0.019, Wilcoxon signed-rank test). The transitions from REM to wake showed slightly different effects across quintiles (Fig. 5C). In sum, wake and sleep have contrasting effects on the activity of neurons in different quintiles, with sleep states displaying a more homogeneous distribution of firing rates and greater variation among the population during wake.   10,11,16 . Time normalized firing rates and CVs in the triplets further illustrated and confirmed the distribution narrowing and widening effects of NREM and REM epochs, respectively (Fig. 6A,B), in both brain regions. However, based on these plots it appeared that these distribution changes largely offset and cancelled one another. To better quantify these impressions, we again calculated DIs for quintiles in both regions and compared firing rate distributions and CVs. All hippocampal quintiles showed decreased firing between consecutive NREMs interleaved by REM ( Fig. 6C; note also that these decreases were more uniform across quintiles than those reported in Miyawaki and Diba 11 because we have excluded epochs with >20% non-firing cells in the present analyses). Firing rate distributions were slightly but significantly shifted leftward (p = 2.7 × 10 −5 , Kolmogorov-Smirnov test), though CVs were not statistically significant (ΔCV = 0.024 ± 0.009, p = 0.066, Wilcoxon signed-rank test). In the frontal cortex, lasting effects of REM on NREM i+1 versus NREM i were more subtle and lower in magnitude. Only DI of the lowest firing quintile was significantly decreased, and we did not detect differences in the firing rate distributions (p = 0.99, Kolmogorov-Smirnov test), or CVs (ΔCV = 0.004 ± 0.011, p = 0.52, Wilcoxon signed-rank test). In the REM i -NREM-REM i+1 triplets, significant changes were not detected in DIs, distributions, or CVs from either region. Extending these analyses to the first and last NREM in continuous sleep (separated by longer sequences of alternating REM and NREM), we observed significant decreases across pyramidal cell quintiles in the hippocampus (Fig. 6E). In the frontal cortex, DIs were significantly negative only in the middle and highest firing quintiles. These indicate overall firing rate decreases resulting from sleep, consistent with previous reports 11,12,16 . Interestingly, the lowest firing quintile decreased most in the hippocampus while the highest firing quintiles decreased most in the frontal cortex. But while firing rate distributions were slightly shifted leftward in the hippocampus (p = 6.1 × 10 −6 , Kolmogorov-Smirnov test), the difference did not reach significance in the frontal cortex (p = 0.22, Kolmogorov-Smirnov test). Importantly, pairwise comparisons of the CVs did not detect significant changes in variability in either the hippocampus or the neocortex (ΔCV = 0.039 ± 0.018, p = 0.093 for hippocampus and −0.010 ± 0.019, p = 0.731 for frontal cortex, Wilcoxon signed-rank test). These results therefore indicate that distribution changes through multiple sequential REM and NREM states, alternately dispersing and homogenizing firing rates, were counter-balanced throughout sleep in both the hippocampus and the neocortex, despite excitability decreases in both regions in both the population as a whole and in specific quintiles.
Lastly, we compared the last minute of wake before sleep to the first minute of wake following sleep (Fig. 6F). In the hippocampus, DIs were significantly negative across quintiles, with those for lower firing quintiles more negative than those for higher firing quintiles, and firing rate distributions and CVs were significantly different In cases with non-zero changes in firing rate, DI is also significantly different from zero. Example of additive increase (D) and multiplicative increase (E). Gray bands indicate 95% confidence intervals obtained from shuffling (2000 times). Each example has 5000 cells whose firing rates are distributed log-normally.    Effects of OFF states, LOW states, and microarousals on sleep-dependent firing changes.
Throughout NREM sleep, neurons throughout the brain undergo periods of suppressed firing of varying durations, each likely a result of a different mechanism [35][36][37] . DOWN/OFF states are a characteristic of the slow oscillations of NREM sleep, featuring hyperpolarized neurons and suppressed firing for approximately 50-100 ms. Neuronal activity during UP/ON states, exclusive of DOWN/OFF states, has been reported to resemble that of the awake brain 38 . Moreover, DOWN/OFF and UP/ON states appear to have differential effects on low versus high firing neurons 10 . Relatedly, LOW states and MAs are longer lasting periods of suppressed neuronal firing, likely related to brain-wide infraslow oscillations during periods of light sleep and/or brief awakening 35,36 , which may also alter neuronal excitability in a subset of neurons 10,35,39 . We therefore examined the effects of removing these various substates of NREM sleep from the sleep/wake patterns we have so far examined. The most salient effect we observed was the obvious: that the exclusion of OFF states from NREM elevates firing rates, in both hippocampus and frontal cortex ( Supplementary Fig S1-S5). Interestingly, in contrast to during intact NREM (Fig. 2B,E and Fig. 4A), neocortical firing rates increased across quintiles within NREM exclusive of OFF states ( Supplementary  Fig S2A,B, Supplementary Fig S3A), similar to the hippocampus. Importantly, the homogenization of firing rates within NREM was still seen in both the hippocampus (Supplementary Fig S1) and the neocortex ( Supplementary  Fig S2A-B and Supplementary Fig S3A,E). The exclusion of LOW and MAs also did not result in any notable differences ( Supplementary Fig S1-S5), except that the effect of decreased firing over sleep was weaker, though still significant (Supplementary Fig S5D,F), as noted in a previous publication 35 .

Discussion
In this work, we aimed to provide a statistically controlled and analytically unified cross-regional examination of how the firing of populations of neurons is affected by sleep state cycling, to arrive at a better understanding of the function(s) of sleep states in mammals. Since many of our analyses depended on rank-ordering of firing rates and because low-firing and high-firing neurons regress to the mean by chance alone, in this study we designed our analyses to either prevent or correct for this effect. We used two methods; either we based the ordering on the mean firing rates over the entire period being considered, or else we measured all changes relative to a surrogate distribution obtained by random shuffles of the real data. These steps were necessary because ordering in any selected period produces illusionary normalization in a complementary period and any real changes must be evaluated in contrast to these non-negligible RTM effects. We found that, in general, sleep states and state transitions do not affect neurons uniformly, but that the changes depend on both the brain region and the relative activity of cells, which likely reflect a combination of neuromodulation of membrane excitability 40,41 and sleep-dependent network dynamics involving excitatory and inhibitory synaptic inputs to neurons 29,34,[42][43][44] .
Among the different state dynamics we investigated, NREM sleep was notable in homogenizing excitability across neurons. The transition from REM to NREM produced a greater relative decrease in high-firing cells in both hippocampus and neocortex, with an increase activity of low-firing cells in the hippocampus and a relatively smaller decrease in the neocortex. These changes at the onset of NREM serve to partially homogenize firing across both populations. In the frontal cortex, normalization continued during the NREM episode, and in both regions the coefficient of variation decreased at the onset and further throughout NREM. The onset of NREM was also marked by decreased firing in interneurons in the hippocampus, indicating a shift in the excitation/inhibition balance (see also 44 ). These dynamics across two states, characterized by a major shift in cholinergic tone, are consistent with the greater relative effect of muscarine on several classes of inhibitory cortical interneurons 45 . Interestingly, atropine, a muscarinic acetylcholine antagonist, also produces increased bursting in hippocampal CA1 pyramidal neurons of lower excitability ("regular spiking") but decreased bursting in higher excitability ("bursting") cells 41 . This suggests that the decreased levels of neuromodulators along with the release from active inhibition allow for a rebalancing of pyramidal cell excitability during NREM sleep.
In contrast, the NREM to REM transition led to greater interneuron spiking and a greater separation of firing between low-firing and high-firing cells, increasing the CV in both regions. These winner-take-all type changes may be implemented in a recurrently connected circuit endowed with inhibition [46][47][48] , such as region CA3, one synapse upstream from our CA1 recordings, or in layer 4 of the neocortex. The shift towards further competition may be supported by increased cholinergic levels during REM sleep that favor feedforward connections, such as from entorhinal cortex to region CA1 49,50 , while neuromodulatory tone in NREM instead favors recurrently-generated activity 51 . It is also worth noting that hippocampal interneuron firing patterns across different sleep states closely mirrored those of cortical principal neurons (e.g. see Fig. 6A,B), consistent with neocortical control of hippocampal inhibition 32 . We also noticed that principal neurons showed relatively dramatic changes (e.g. see Fig. 6A,B) at the transitions between NREM and REM. These transition points may have unique properties: the transitionary period from NREM to REM sleep may in fact be a unique period of "intermediate sleep" that is inundated with both thalamacortical sleep spindles and theta oscillations 10,52 , while the transitions from REM to NREM are often followed by LOW states and microarousals 35 .
The net effects of these state transitions, from the first to the last NREM epochs during extended sleep sequences were mostly consistent with our previous reports 10,11 , with some notable differences. Here, we find that distribution of the firing rates spread during REM and the homogenization during NREM largely cancel out in both hippocampus and neocortex, yielding a net effect of decreased firing rates in both regions over sleep 53 . These decreases were seen across all hippocampal quintiles over sleep, but preferentially in lower-firing neurons 11 . In the neocortex, decreases were less pronounced and were specific to high-firing cells, whereas Watson et al. 10 reported an additional parallel increase in firing of lower-firing neurons. This discrepancy between the present study and Watson et al. 10 may arise because of two factors: 1) Watson et al. 10 did not shuffle correct for RTM as in the current DI analysis and 2) Watson et al. 10 did not compare changes across entire episodes of NREM sleep, but rather across bouts or "packets" of NREM. The first and last packets of NREM fall onto the first and last thirds of NREM, and indeed, we observed a narrowing of frontal cortex firing rate distributions within each NREM episode over this period (see Scientific REpoRts | (2019) 9:689 | DOI:10.1038/s41598-018-36710-8 Fig. 4A). It should also be noted that the comparison of WAKE i versus WAKE i+1 (Fig. 6F) showed simultaneous firing increases in low-firing cells and firing decreases in high-firing cells, consistent with Watson et al. 10 .
We and others have conjectured that the slower firing rate decreases over sleep, on the other hand, are produced by the downscaling of synaptic connections 11,12,16,21 . Network modeling also supports the notion of a strong link between the strength a neuron's connectivity and its firing rate 2,54 . Hippocampal changes across sleep (Fig. 6E,F) are consistent with an additive change (e.g. Fig. 3C), which indicates hippocampal firing decreased by a similar amount across cells. If the conjecture between synaptic connection and firing rate is correct, the uniform decrease of firing rates could imply a uniform weakening of synaptic connections which effectively improves signal-to-noise in higher-firing cells 21 (see also 53 ). A recent study employing scanning electron microscopy of synaptic connections in the cortex supports this analysis; following sleep but not waking, smaller axonal-spine interfaces were observed in the four lower quintiles, with a lesser or no effect in the highest quintile 55 . Higher-firing neurons appear to show the least plasticity, perhaps as a consequence of rigidity or saturated synapses 24 . These distinctions may also reflect differences in neuronal subtypes within the CA1 pyramidal layer 50,56 that exist throughout the cortex 57 , though surprisingly in the frontal cortex we saw the greatest decrease in firing across sleep in the higher-firing quintile (but see discussion points below).
While these observations demonstrate a remarkable degree of agreement about the effects of wake and sleep states on neuronal firing in the hippocampus and the frontal neocortex, some inter-regional differences were also evident in the responses of quintiles. All quintiles in hippocampus showed a prominent firing rate decrease from the beginning of sleep to the end (measured either from first to last NREM or from prior WAKE to subsequent WAKE), while in frontal cortex the net effect of sleep was more differentiated, with firing-rate decreases specific to the highest-firing quintile. Other notable intra-sleep differences between hippocampus and frontal cortex were found during the course of NREM episodes and at the transition from NREM to REM. A possible source of differences in hippocampal versus cortical profiles is that the cortex has DOWN/OFF states-periods of temporary network silence during NREM-which are not as clearly defined in the hippocampus 37,58 . The predominance of DOWN/OFF states can potentially account for the relatively decreased firing activity in the neocortex during NREM (see also 12 ), particularly in the highest firing rate groups as slow waves in NREM develop, and the strong rebound in firing in these quintiles at the onset of REM sleep. Nevertheless, when we excluded OFF periods from our analysis, both hippocampal and frontal cortical neurons showed similar homogenization as before. On the other hand, LOW states and microarousals at the onset of NREM seem to have stronger suppressive effects on the firing of hippocampal neurons 35 . These apparent inter-regional differences may also arise because recordings and unit and state detection were performed by different experimenters in different labs. It is worth noting that overall firing rates were higher for the frontal cortex recordings than for the hippocampus recordings, so that lowest quintiles in the frontal cortex fire at similar rates to the middle quintiles in the hippocampus. Hence, sleep states may have effects that depend on absolute rather than relative firing rates and the normalizing and dispersing effects of NREM and REM sleep, respectively, represent broad effects of the neuromodulatory tones under different brain states.
In summary, our study provides a unified comparison of the effects of sleep and wake states on large populations of frontal cortical neurons and hippocampal neurons and highlights the importance of controlling for regression to the mean. Overall similarities and some specific differences were revealed -with commonalities including alternating patterns of firing rate homogenization and diversification in NREM and REM sleep, respectively, against a background of decreasing firing rates over the course of sleep. Progress in this line of inquiry will help us better understand the specific roles of different brain states in the function and homeostatic maintenance of neuronal circuits.

Methods
We re-analyzed data previously recorded from hippocampal CA1 region of four male Long Evans rats 11,35 and frontal cortex of 11 male Long Evans rats 10 . Units were separated into putative pyramidal and principal cells and putative neurons based on spike waveform, the histogram of inter-spike-interval distribution, and mean firing rate 10,59,60 . In total, we recorded and analyzed 1017 putative pyramidal cells and 116 putative interneurons from the hippocampus and 995 putative principal cells and 126 putative interneurons from the frontal cortex. We analyzed these cell groups separately and, unless otherwise specified, by high and low-firing neurons we refer strictly to those units from the putative pyramidal/principal cell population. Details of the experimental protocols, including animals, surgery, electrophysiological recording, spike detection and clustering, and sleep detection can be found in these refs 10,11,35 and are summarized below. EMG was obtained from either the nuchal muscles or from correlated high-frequency (300-600 Hz) signals from brain electrodes 10 Time normalized mean firing rates. In the series of analyses of sleep sequences (e.g. Fig. 1B,E and similar) NREM and REM epochs were divided into 30 bins and 10 bins, respectively, since NREM epochs are generally longer. Additionally, cells were sorted into quintiles within each epoch and firing rates of cells in each quintile were calculated in each bin. Importantly, sorting was based on their mean firing rates over the entirety of the windows of interests depicted in each panel, to avoid RTM effects which are particularly evident when tracking ranked groups of units such as quintiles. While ranking was based on the entire epoch in these analyses, to allow for comparisons across quintiles, firing rates were normalized by the mean firing rate in the last one-third of the first state. where FR i and FR j are mean firing rates of a neuron over time periods i and j (i < j), respectively, and FR x is the mean of the mean FR x over the neurons in the quintile. Neurons were first separated into quintiles based on FR i within each epoch, and quintile CI was then calculated across a given pair of epochs. If more than 20% of cells did not fire in epoch i or j, that sequence was excluded from the analyses since CI for the lowest quintile cannot be properly calculated in such a case. Note that this analysis still allows for changes in quintile membership between i and j. Because neuronal firing rates are log-normally distributed, the difference in logarithm of firing rates, ∆log(FR), had been previously used to assess firing rate changes 10 . Although CI and ∆log(FR) generally behave similarly, ∆log(FR) becomes singular when either FR i or FR j approach or equal zero. Therefore, in these analyses we opted to use CI.
Our null hypothesis was that changes across states are not different than changes within states, allowing for RTM. To evaluate the corresponding null distribution for this analysis, we generated 2000 shuffled surrogates by random flipping of FR i and FR k for each cell, where k is a control period of the same state as i. For analyses involving sleep, these control periods were taken from the corresponding periods (e.g. first/last one-third) in adjacent epochs of the same state (NREM or REM). Note that by chance these surrogate CIs therefore involve changes either forward or backward in time and always either ending or originating in epoch i. For transitions involving WAKE, control periods were randomly selected from 1-min periods of the same wake epoch (since wake periods separated by sleep display significantly different firing rates 11,12 ). Shuffled mean and 95% confidence intervals of CI were obtained from this surrogate data. The deflection index (DI) was defined as difference of CI from the surrogate mean.
Detection of OFF states, microarousals, and LOW states. We labeled periods with no spikes from any recorded units for >75 ms as OFF states 12,61 in both hippocampal and frontal cortical recordings. Following our previously published methods, transient (>0.1 s and <40 s) increase of EMG signal (>mean + 0.5 SD for hippocampal sessions and >local minima of EMG power for neocortical sessions) within NREM were marked as microarousals (MAs) 10,35 . LOW states were detected as periods with a transient drop of LFP power in the 0.625 to 50 Hz band, calculated in 0.1-s step sliding 1-s windows 35 . The threshold for each session were determined based on histogram of the power within NREM epochs (see ref. 35 for additional details).

Simulations.
To better understand the behavior of CI and DI we generated three random datasets involving noise combined with no-change, additive firing rate increase, and multiplicative firing rate increase. Each dataset has 5000 cells and 3 epochs, corresponding to epochs i, j, and k. To mimic the variability of real data, first we set a baseline firing rate for each cell based on a log-normal distribution obtained from hippocampal pyramidal cells during NREM (mean = 0.59 Hz, std = 0.84 Hz) and then added random ("multiplicative") noise proportional to each cell's firing rate in each epoch (std = 0.35 Hz). For the no-change simulation, each cell kept the same baseline firing rates across epochs with only random noise producing fluctuation across epochs. For additive and multiplicative increase simulations, baseline firing rates in epoch j were increased (by addition of 0.05 Hz or multiplication by 1.1 for additive and multiplicative increases, respectively).

Additional statistical analyses.
In this work we analyzed previously obtained data and no additional experiments were performed. Diversity of firing rates was evaluated by coefficient of variance (CV) and significance of difference was tested with Wilcoxon rank sum test. P-values of DIs were calculated relative to shuffled surrogates. Differences in DI and firing rate changes among quintiles were tested with one-way ANOVA. Firing rate distributions were compared by a Kolmogorov-Smirnov test. All analyses were performed with custom-written scripts running on MATLAB with statistics and machine learning tool boxes. Code is available upon request.

Data Availability
Frontal cortical data used in this study is available on CRCNS.org 62 . Hippocampal data will be made available upon reasonable request.