{"paper_id":"611df19d-6426-471e-b526-4c6eff7e808a","body_text":"1 \n \nCircadian and Sleep-Wake Modulation of Functional Connectivity Across Brain \nOscillations and States Linked to Cognition in Humans \n \nAlpar S Lazar1,6*, Zsolt I Lazar2, Nayantara Santhi3,6, June C Lo4, 6, John A Groeger5, 6, Derk-Jan Dijk6,7 \n \n \n \n1. Faculty of Medicine and Health Sciences, University of East Anglia, UK \n2. Faculty of Physics, Babes-Bolyai University, Romania \n3. Department of Psychology, University of Northumbria, UK \n4. Centre for Sleep and Cognition, Human Potential Translational Research Programme, and \nDepartment of Medicine, Yong Loo Lin School of Medicine, National University of Singapore, \nSingapore \n5. Department of Psychology, Nottingham Trent University, Nottingham, United Kingdom \n6. Surrey Sleep Research Centre, Faculty of Health and Medical Sciences, University of Surrey, \nGuildford, UK. \n7. UK Dementia Research Institute, Care Research& Technology at Imperial College London and \nthe University of Surrey Guildford \n \nCorresponding author: *Alpar S Lazar \n \nEmail:  a.lazar@uea.ac.uk \n \nAuthor Contributions: D.-J.D. and J. A. G.  designed rese arch; D.-J .D. direc ted t he r esearch ; A.S .L., N .S., \nand J.C.L. p erformed resea rch; A .S.L. , an d Z.I.L. analyz ed dat a; and A .S.L. , Z.I.L. , N. S., J. A. G., J.C.L. , and \nD.-J.D. wrot e the pa per . \n \nCompeting Interest Statement: Derk-Jan Dijk is a consultant to Boehringer Ingelheim, Astronautx \nand Danisco Sweeteners, and collaborates and/or has received equipment from SomnoMed and \nVitalThings.  \n \n \nKeywords: EEG, Brain State, Homeostasis, Neural Networks, Phase Coupling  \n \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted October 21, 2025. ; https://doi.org/10.1101/2025.10.20.683464doi: bioRxiv preprint \n\n \n \n2 \n \n \n \n \n \n \n \n \n \nAbstract  \nSleep and circadian rhythms both contribute to cognitive performance, but the underlying neuronal \nnetwork-level changes remain unclear. We quantified the contribution of brain state, sleep-pressure \ndynamics across the sleep-wake cycle, and circadian rhythmicity to electroencephalographic (EEG) \nfunctional connectivity (FC) and examined how these network changes relate to cognition. Thirty-four \nhealthy adults completed a 10-day forced-desynchrony protocol to uncouple sleep-wake and \nendogenous circadian rhythms. From over 1,200 hours of artifact-free EEG, we derived phase-\ncoupling metrics to quantify FC across brain states, thirds-of-the-night (sleep pressure), and circadian \nphase, and related these network measures to a range of cognitive performance indices. FC differed \nmarkedly between brain states, especially in the alpha and sigma bands, and was modulated by sleep \nhistory and circadian phase. Principal component analysis revealed both a global and a \ntopographically distributed FC component which responded differentially to sleep pressure. Dissipation \nof sleep pressure was accompanied by increasing global FC in NREM sleep, and especially in the \ndelta, sigma and beta frequencies, and decreasing global FC in the alpha band.  During REM sleep, \nglobal FC decreased in nearly all frequency bands with dissipation of sleep pressure. The influence of \ncircadian phase on FC was smaller than that of sleep pressure and varied across brain states. Lower \nglobal theta-band FC in NREM and alpha-band FC during wake predicted better alertness and working \nmemory accuracy, an effect modulated by circadian phase. These results suggest that sleep \nhomeostasis and circadian timing interact to stabilize functional brain connectivity in wakefulness, \nthereby supporting optimal cognitive function. \n  \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted October 21, 2025. ; https://doi.org/10.1101/2025.10.20.683464doi: bioRxiv preprint \n\n \n \n3 \n \nSignificance Statement  \nIdentifying how sleep restores neural networks degraded during wakefulness is of significance for \nunderstanding sleep’s role in maintaining brain function. Here we used a protocol to isolate effects of \nsleep from effects of circadian rhythmicity on functional connectivity of neural networks and assessed \nassociations with cognitive performance. We found that circadian rhythmicity but in particular the \ndissipation of sleep pressure had profound effects on global connectivity which were different for \nNREM sleep, REM sleep and wakefulness and varied across frequency bands. Connectivity measures \nin the theta, alpha and sleep spindle frequency ranges were associated with cognitive performance. \nThese novel findings provide a new perspective on the nature of the sleep recovery process \ncontributing to the waking performance capability of human brains.  \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted October 21, 2025. ; https://doi.org/10.1101/2025.10.20.683464doi: bioRxiv preprint \n\n \n \n4 \n \nMain Text \n \nIntroduction \n \nSleep is widely conceptualized as a recovery process, which returns neural network function degraded \nby prior wakefulness toward a baseline state (1). Recovery may be understood mechanistically (e.g. \nsynaptic downscaling) or functionally (e.g. restoration of information transfer and integration capability); \nyet exactly how recovery unfolds across sleep and circadian cycles remains poorly defined.  \nOscillations in the electrical activity of the cortex are thought to reflect the fundamental \nneurophysiological mechanisms enabling the temporal organization, transfer, and integration of \ninformation in the brain which are essential for waking performance (2-5). Tracking how these rhythms \nare restored or reshaped during sleep may reveal the network mechanisms of recovery. \nIn humans, this oscillatory activity can be assessed by intracranial recordings of unit activity or field \npotentials and noninvasive techniques such as magnetoencephalography and electroencephalography \n(EEG) (6, 7). The power spectrum of the EEG signal derived from single electrode sensors provides \ninformation on the frequency composition of the oscillatory activity at the location of the sensors and \nthe underlying cortical neural firing rate and synchronicity (2). \nThe frequency composition and \namplitude of the EEG vary across and within brain states (wakefulness, NREM sleep, and \nREM sleep)(8). Furthermore, both the sleep-wake cycle and circadian rhythmicity have been shown \nto modulate brain oscillatory activity as quantified by power spectral analysis within each of the brain \nstates (9, 10). Among the most prominent modulations within vigilance states are the decline of slow \nwave activity within NREM sleep  from the beginning to the end of sleep episodes and an increase of \ntheta activity during wakefulness with elapsed time awake (11, 12). These dynamics of low-frequency \nEEG activity, which are observed in many mammalian species, have been used extensively as \nindicators of a recovery process during sleep and a buildup of sleep pressure/sleep debt  and \nassociated deterioration of brain function during prolonged wakefulness (13). However, it has been \nchallenging to establish how the dynamics of slow wave activity relates to a sleep dependent recovery \nprocess underpinning brain function during wakefulness.  \nBeyond the frequency distribution of the EEG signal measured by the power spectrum, the functional \nintegration of brain regions can also be characterised using connectivity metrics. A widely used \nmeasure is the phase\n‐ lag index (PLI) (14) which measures the consistency with which the phase of a \nsignal from one location leads or lags a signal from another location by ignoring phase differences \ncentred around zero. By taking the sign of the phase difference and averaging over time, PLI isolates \nstable, non-instantaneous phase relationships that reflect genuine synchrony. A commonly used \nextension of the PLI is the weighted phase\n‐ lag index (wPLI), which not only discards phase differences \naround zero but also weights each observation by the magnitude of the imaginary component of the \ncross\n‐ spectrum (Vinck et al., 2011). By emphasizing larger phase ‐ lag magnitudes, wPLI further \nsuppresses the influence of small, noise ‐ driven phase fluctuations and residual volume ‐ conduction \neffects that can still bias the unweighted PLI. In practice, wPLI therefore provides a more robust \nindicator of true, non\n‐ instantaneous synchrony, and hence potentially causal interactions, between \ncortical areas, strengthening our inferences about information transfer and integration across \ndistributed networks.  A further refinement of this connectivity metric is the debiased weighted phase \nlag index (dwPLI) which corrects for sample-size bias in wPLI and further reduces noise-driven inflation \nof connectivity estimates. This yields a more stable and interpretable measure of non-instantaneous \nfunctional connectivity (see Methods section). \nEEG connectivity measures are often used in cognitive neuroscience research to investigate \nassociations between functional connectivity (FC) and brain function at single time points. Several \nstudies have identified changes in FC in specific networks, such as the attentional or default mode \nnetworks, and their associations with performance on tasks that depend on these networks. Changes \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted October 21, 2025. ; https://doi.org/10.1101/2025.10.20.683464doi: bioRxiv preprint \n\n \n \n5 \n \nin FC are also associated with brain development and brain disorders, such as mild cognitive \nimpairment (MCI) and Alzheimer's disease (15-19). \nEEG connectivity measures also vary across brain states, indicating that they do not just reflect \nanatomical/structural connectivity but FC (15, 20, 21). One argument for the functional importance of \nconnectivity measures is the observation that the reduced responsiveness to external stimuli \nassociated with sleep is accompanied by decreased functional brain connectivity (22).  \nWhether FC measures of brain oscillatory activity in the various brain states are modulated by \ndissipation and increase of sleep pressure and circadian rhythmicity has not been established. Finally, \nit has not been established whether and how functional EEG connectivity measures relate to the well-\nestablished sleep-wake and circadian rhythmicity-dependent modulation of brain function as quantified \nby performance on a variety of cognitive tasks (23-25).  \nWe aimed to clarify these questions and hypothesized that the physiological effects of both sleep \npressure (its dissipation and accumulation) and circadian phase would influence functional connectivity \n(FC). We also hypothesize that FC will be linked to waking cognition. Given that brain oscillatory \nactivity exhibits brain-state (Wake, NREM, and REM) and frequency-specific patterns, we further \nhypothesized that these effects would be specific to particular brain states and frequency bands. \nThe separate contribution of the sleep-wake cycle and circadian rhythmicity-driven process to the \nrestoration and deterioration of brain function cannot be assessed by analysis of sleep and \nwakefulness under baseline conditions because under these conditions these processes are \nentangled.  Quantifying their separate contribution requires desynchronizing the sleep-wake cycle from \nendogenous circadian rhythmicity driven by the suprachiasmatic nuclei and indexed by melatonin, \ncortisol, and core body temperature rhythms (10, 11, 23, 26). \nHere, we quantified the independent contribution of circadian rhythmicity, and the dissipation and \naccumulation of sleep pressure (i.e., time elapsed in sleep and wake, respectively) to functional brain \nconnectivity (FC) as measured by an improved index of phase synchronization, i.e., debiased weighted \nphase leg index (dwPLI) (27) in both sleep and wake and its association with cognition.  \nFC was quantified across more than 1,200 hours of artifact-free NREM and REM sleep and nearly 90 \nhours of wake EEG, alongside performance on tests of vigilance and working memory, and processing \nspeed. The data were collected in a 10-day forced-desynchrony protocol in 34 healthy young adults \n(Fig. 1). \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted October 21, 2025. ; https://doi.org/10.1101/2025.10.20.683464doi: bioRxiv preprint \n\n \n \n \nFig 1. Research protocol and EEG data analysis. (A) Raster plot of the 28- h forced desynchrony (FD) protoco\nwith a representative example of sleep-wake schedule (habitual bedtime: 00:00). Following an 8- hour adaptatio\nnight (ADn) and adaption day (FdW1) participants were scheduled to a 28-h sleep- wake cycle, including 9 hour\nand 20 minutes of sleep (horizontal dark blue bars) and 18 hours and 40 minutes for wakefulness (horizontal ligh\nblue bars). The 24- h variation of plasma melatonin concentrati on was assessed on three occasions, at baselin\n(FdW1-FDn1), FdW4-FdN4, and FdW7- FdN7 to estimate the phase and period of the intrinsic circadian clock a\nindicated by the GREEN line, which repre sent the estimated onset of melatonin.  The red arrow pointing indicate\nthe start of each 24-hour-long melatonin sampling session. Vertical green bars indicate cognitive test session\nincluded in the current analysis. The gradient color on the wake period , ranging from green (habitual timing) to re\n(12 h out of phase), indicates circadian alignment of the wake periods with the FD protocol. The green and re\narrows to the right of the figure indicate the two wake periods (FdW2 and FdW5) included in the wak e EEG\nanalysis. During these two wake periods, each cognitive test session included two 2- minute Karolinsk\nDrowsiness Tests (KDTs) to measure resting wake EEG at the start and end of the assessments.  (B) Time cours\nof sleep stages (top panel), power spectral density (PSD) (middle panel), and debiased weighted phase lag inde\n(dwPLI) (bottom panel) measured during a baseline sleep episode in one participan\nWarmer colors represent higher spectral power  (logarithmic scale) and functional connectivity ( FC) as measure\nby dwPLI. Temporal resolution is 10 seconds/pix el, each representing the average of the short- time Fourie\ntransforms of four segments of 4- s long, Hanning tapered windows with 50% overlap. Power spectral densit\n(PSD) values were obtained by also averaging over the 12 channels (FP1, Fp2, F3, F4, C3, C4, T3, T4, P3, P4\nO1, and O2) whereas dwPLI values were averaged over all 66 electrode pairs. (C) The amount of artifact- fre\nWake, NREM, and REM sleep EEG data (in minutes) anal yzed for each sleep episode throughout the 10-day-lon\nforced desynchrony study. (D) The amount of artifact- free Wake EEG data (in minutes) analyzed for the baselin\n(FdW2) and the 12-h out-of-phase (FdW5) wake episodes.  \n \nWe conducted a comprehensive analysis involving principal component analysis (PCA) applied to th\nfunctional-connectivity (FC) matrices derived from 66 electrode pairs and 21 cognitive outcom\nmeasures. We found a global principal component (PC), reflecting widespread synchronization (globa\nFC). The second PC reflected a topographically distributed connectivity (distributed FC). To relat\nthese network patterns to cognitive function, we conducted a PCA on the cognitive measures an\nanalyzed the first two cognitive PCs representing cognitive alertness and working memor\nperformance (PC1) as well as processing speed and working memory performance (PC2).  \n \n6 \nocol \ntion \nours \nlight \nline \nk as \nates \nions \n red \n red \nEG \nska \nurse \ndex \nant. \nured \nurier \nsity \n P4, \nfree \nlong \nline \n the \nme \nbal \nlate \nand \nory \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted October 21, 2025. ; https://doi.org/10.1101/2025.10.20.683464doi: bioRxiv preprint \n\n \n \n7 \n \nWe found that recovery of brain function during sleep is associated with an increase in global FC \nduring NREM sleep and a decrease during REM and to some extent in wakefulness during \nspontaneous    interruptions of sleep.  The circadian day was associated with a reduction in global FC \nduring wakefulness in the alpha band, and this reduction associated with better cognitive performance.\n \nTogether, these data illuminate how sleep homeostasis and circadian timing orchestrate the recovery \nof large-scale network connectivity, enabling optimal brain function upon waking. \n \nResults \n \nEffect of brain states, homeostatic sleep pressure, and circadian phase on functional EEG \nconnectivity spectra  \nWe used linear mixed effects modelling to quantify the effects of the three consolidated brain states – \nNREM, REM sleep, and wake – during the sleep episodes as well as the effects of time elapsed in \nsleep (i.e., dissipation of sleep pressure) and circadian phase on power spectrum density (PSD) and \nEEG connectivity measures (Fig. 2). NREM included NREM2 and slow wave sleep (SWS) following \ncommon practice (Dijk at al. 1995, Lazar et al., 2015). Artifact-free EEGs recorded during 231 in bed \nperiods of 9h and 20 mins each, which were distributed across the circadian cycle, were analyzed for \n12 electrodes (Fp1,Fp2,F3,F4,C3,C4, P3,P4,T3,T4,O1,O2) and 66 electrode pairs (combinations of 12 \nelectrodes) and frequency bins between 0.5 and 32 Hz (Figs 1A -C). EEG connectivity was estimated \nusing the debiased weighted phase lag index (dwPLI), as well as additional PC metrics including \nweighted phase lag index, phase lag index, imaginary coherence, and phase coherence (Fig S1). In a \nfirst analysis step we averaged the absolute power spectrum density (PSD) across the 12 EEG \nchannels and connectivity metrics across all 66 individual intra and interhemispheric electrode pairs. \nPSD averaged across EEG channels showed the known characteristics of brain states (Fig 2 A and \nDataset S1.csv). Alpha (8-12 Hz) activity was higher in wakefulness than in NREM and REM sleep; \ndelta (0.5-4 Hz), theta (4 - 8 Hz), and sigma (12-16 Hz) activity in NREM exceeded the corresponding \nvalues in REM.  \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted October 21, 2025. ; https://doi.org/10.1101/2025.10.20.683464doi: bioRxiv preprint \n\n \n \nFig 2. Power spectral density and functional connectivity spectra across brain states and sleep episodes\nThe main effect of brain states on (A) power spec trum density (PSD) and (B) debiased weighted Phase Lag Inde\n(dwPLI) across all sleep episodes (231 nights) and averaged across EEG channels and cannels pairs\nrespectively. The upper panels represent least- square means (Lsmeans) and standard error of the mean (SEM\n(C and D) Effect size (Cohen’s f 2) of main effects of brain state on the PSD and dwPLI. (E and F) Effect size o\nmain effects of Elapsed time in sleep (red) and Circadian phase (blue) on PSD and dwPLI. (G and H) Effect size o\ninteractions between factors Elapsed time in sleep and Circadian phase on PSD and dwPLI. Colored triangles i\n(A) and (B) indicate significant (P<.01) effects. Detailed statistical results are in Dataset S1.xlsx. \n \nThe dwPLI also varied significantly across brain states and frequency (Fig. 2B , Dataset S1.xlsx ). It\nspectral profile was characterized by peaks in the alpha and sigma bands. Unlike PSD, dwPLI value\ndid not markedly decrease with increasing frequency. Brain state effects on dwPLI were mos\ndominant in the alpha-sigma range as well as in the delta frequencies (Fig 2C ). Within the alpha band\ndwPLI values were highest during wakefulness, lowest in REM sleep, and intermediate in NREM . I\nthe sigma range (12–16 /i1Hz), dwPLI peaked most strongly during NREM /i12 and SWS. Overall, brai\nstates were best distinguished by PSD in the delta and sigma bands (Fig. 2 A,C) and by dwPLI value\nin the alpha and sigma bands (Fig. 2B,D). In a confirmatory analysis, we repeated this procedure usin\nfour additional FC metrics (imaginary coherence, phase coherence, phase ‐ lag index, and standar\nweighted phase ‐ lag index and observed nearly identical brain state ‐ dependent spectral profiles\nconfirming that our findings are robust to the choice of FC measure (Fig S2A-E and Dataset S1.xlsx\nFor exploratory purposes, we also repeated the same analysis including all NREM substages in th\nmodel (NREM1, NREM2, SWS as well as REM and wake during sleep) (Fig S3 and Dataset S2.xlsx).\n \n8 \n \ndes. \ndex \nairs, \nM). \ne of \ne of \ns in \n. Its \nues \nost \nnd, \n. In \nrain \nues \ning \nard \niles, \nsx). \n the \n. \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted October 21, 2025. ; https://doi.org/10.1101/2025.10.20.683464doi: bioRxiv preprint \n\n \n \n9 \n \nMixed model analyses revealed significant (p<0.01) main effects of Time Elapsed in Sleep and \nCircadian Phase on PSD across all frequencies (Fig. 2E , Dataset S1.xlsx).  For dwPLI these effects \nwere much smaller and restricted to specific frequency bands (Fig. 2 F, Dataset S1.xlsx). The \nsleep‐ pressure and circadian effects on dwPLI were substantially smaller than the effects of Brain \nState (Fig. 2 D and F). For PSD, the strongest sleep ‐ pressure effects occurred in the delta and theta \nbands, reflecting the well ‐ known decline of low ‐ frequency power during sleep, while the largest \ncircadian modulations peaked in the alpha (8-12 Hz) and sigma bands (Fig. 2 E). Except near 10 Hz \nand 15 Hz, sleep ‐ pressure effects on PSD exceeded circadian effects. For dwPLI, sleep ‐ pressure \neffects on connectivity were largest in the  theta, and beta bands, with magnitudes similar to or larger \nthan circadian effects (Fig. 2 F and Dataset S1.xlsx). Circadian effects on dwPLI peaked in the low \ndelta (0.5–3 Hz) and a narrow sigma band (~13 Hz). Overall, dwPLI was less strongly influenced by \ncircadian phase than elapsed time in sleep. The interaction between brain state and both time elapsed \nin sleep and circadian phase showed more similar effect magnitudes across PSD and dwPLI (Fig. 2 G \nand H). This suggests that while sleep pressure and circadian phase may not independently affect FC, \ntheir influence is strongly modulated by brain state. \nA confirmatory analysis using four additional connectivity metrics, imaginary coherence, phase \ncoherence, wPLI, and PLI, produced effect-size profiles for elapsed time in sleep and circadian phase, \ncomparable to those observed with dwPLI (Fig S2 F and Dataset S1.xlsx). Some metrics, particularly \nimaginary coherence and phase coherence showed steeper sleep-dependent effect sizes and smaller \ncircadian effects (Fig S2).  \nBecause dwPLI provided a good balance between sensitivity to state-related changes and resistance \nto volume-conduction artifacts, we retained dwPLI and excluded the other connectivity measures from \nfurther analyses (see methods). We also did not pursue further analysis of power spectral density \n(PSD), as these effects have already been well-documented in the existing literature\n (9).  \nPrincipal components in the topographical distribution of functional connectivity \nIn the next step, we investigated the direction and topography of significant main effects of elapsed \ntime in sleep and circadian phase on functional connectivity (FC).  Given the large number of \ndependent variables (66 electrode pairs per brain state and frequency band), we first applied \ndimensionality reduction using principal component analysis (PCA) on FC as estimated by dwPLI from \nthe 231 sleep episodes scheduled across the circadian cycle.  \nWe conducted separate PCAs for each brain state NREM (Fig. 3), REM (Fig. 5), and wake during time \nin bed (Fig. 7) and each frequency band, resulting in a total of 18 analyses. Across all six frequency \nbands and three brain states, the PCA consistently identified one dominant component (PC1), which \nexplained between 30% and 64% of the variance (mean: 41%) (Table S1.xlsx). The second principal \ncomponent (PC2) accounted for 4% to 19% of the variance (mean: 9%). Overall, the combined \nvariance explained by the first two components was highest in NREM (mean: 55%), followed by REM \n(mean: 49%) and wake during the sleep episode (mean: 45%) (Table S1.xlsx). \nThe correlation patterns between the principal components (PCs) and dwPLI values across individual \nelectrode pairs indicated that higher loadings on PC1 reflected increased ‘global connectivity,’ \ncharacterized by overall elevated dwPLI across all electrode pairs (Figs. 3A , 5 A, 7 A and Dataset \nS3.xlsx). This pattern was consistent for PC1 across all frequency bands and brain states. In contrast, \nPC2 exhibited a more differentiated topography, and the interpretation of high loadings varied by \nfrequency band and brain state (Figs. 3D , 5 D, 7 D and Dataset S3.xlsx). Accordingly, PC2 was \ninterpreted as reflecting ‘topographically distributed connectivity.’ We limited our subsequent analyses \nto the first two principal components to optimize explained variance while controlling for Type\n/i1 I error. \nAlthough the second component explained a smaller proportion of variance, it was retained to mitigate \nthe risk of Type/i1 II error. \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted October 21, 2025. ; https://doi.org/10.1101/2025.10.20.683464doi: bioRxiv preprint \n\n \n1\n \n \nEffects of sleep-pressure dissipation on global and topographically distributed functional  \nWe conducted two mixed model analyses: a primary analysis focusing on the two principa\ncomponents (PCs) and an exploratory analysis examining connectivity in each electrode pa\nseparately.  \nThe number, magnitude, and direction of the significant ( P<0.01) effects of elapsed time in s leep an\ncircadian phase varied with brain state, frequency, and PC / topography (Figs. 3, 5, 7 and Datase\nS4.xlsx).  \n \nFig. 3.  Principal component analysis of functional connectivity (dwPLI) during NREM sleep: effects o\nsleep progression and circadian phase.  (A and D) Loading values of individual electrode pairs on PC1 an\nPC2, for delta, theta, alpha, sigma, beta and gamma frequencies. Values between brackets along the vertical axe\nrepresent the variance explained by the PC. (B and E) The modulation o f PC1 and PC2 by elapsed time in sleep\nLeast square means (LSMeans) and standard errors of  the mean (SEM) are presented for each 186.7- minut\ninterval (i.e., one-third of the sleep episode), averaged across all studied circadian phases. (C and F) the circadia\nmodulation of PC1 and PC2, with LSMeans and SEM shown for each 60° (~4-hour) circadian phase bin, average\nacross all sleep intervals. Data are double plotted to enh ance the visualization of circadian rhythms. The gree\nvertical line marks the dim-light melatonin onset (DLMO; 0° circadian phase), and the grey shaded are\nrepresents the average melatonin profile. Type III fixed effe cts are reported, with only statistically significant p\nvalues (α  = 0.01) indicated. Detailed statistical results are provided in Dataset S4.xlsx. \n \n1 0 \nipal \npair \nand \nset \ns of \nand \nxes \neep. \nnute \ndian \nged \nreen \narea \nt p -\n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted October 21, 2025. ; https://doi.org/10.1101/2025.10.20.683464doi: bioRxiv preprint \n\n \n1\n \n \nAs the sleep episode progressed and sleep pressure decreased, global FC (PC1) during NREM slee\nmarkedly increased in most frequency bands, except for alpha, where it slightly but significantl\ndecreased (Fig. 3 B). In contrast, topographically distributed connectivity (PC2) decreased across a\nfrequency bands except alpha, where it increased (Fig. 3 E). The exploratory analysis supported thes\nfindings, revealing that most electrode pairs showed a significant ( P<0.01) increase in coupling ove\nthe course of the sleep episode (Fig 4 A, B and Dataset S5.xlsx). T he widespread statistica\nsignificance of the effect across the studied EEG channel pairs is reflected in the small median p-valu\n(median p = 1.91 × 10 ⁻ ¹¹) calculated among all comparisons with p < 0.01.  In accordance with th\nresults for PC1 (Fig. 3B) the electrode pair-based analyses showed that the delta and in particular th\nsigma but also the beta band exhibited the strongest and most widespread increases in FC wit\ndecreasing sleep pressure (Fig. 4 A). Theta, alpha, and beta bands displayed a topographically spl\npattern, with some electrode pairs showing increases and others decreases in coupling (Fig. 4 A\nNotably, in the theta band, long-range fronto-centro-temporal connections exhibited an elapsed time i\nsleep-dependent increase in coupling, whereas long-range fronto-occipital and centro- occipita\nconnections showed a decrease over the course of the sleep episode. In the alpha band, elap sed\ntime-in-sleep-dependent increases were predominantly observed in interhemispheric connection\nbetween homologous regions. Decreases in connectivity over the course of the sleep episode in th\nalpha band were primarily found in fronto-occipital and long-range fronto-centro- parietal connection\n(Fig./i14A and Dataset S4.xlsx).  \n \nFig 4.  Topographical patterns of functional connectivity (dwPLI) in NREM sleep as a function of slee\nprogression and circadian phase.  (A)  Red lines represent the magnitude of effect sizes for elapsed time i\nsleep for electrode pairs, where a significant main effect of this predictor was observed (p < 0.01). Effect sizes fo\nelectrode pairs that showed a time-in-sleep–dependent increas e or decrease in functi onal connectivity are show\nseparately. The geometric mean and median p-value among all significant p- values are also indicated an\nhighlighted in red. (B) Representative examples of the effects of elapsed time in sleep on dwPLI. Lea st squar\nmean (LSmeans) and standard error of the mean (SEM) are presented indicating sleep- dependent estimates a\neach 186.7-minute interval (third of the sleep episode ) measured across all studied circadian phases. (C) Blu\nlines represent the magnitude of effect sizes for elapsed time in sleep for electrode pairs, where a significant mai\neffect of this predictor was observed (p < 0.01). The geometric mean and median p- value among all significant p\nvalues are also indicated and highlighted in blue. (D) Representative examples of the effects of circadian phase o\ndwPLI. LSmeans and SEM indicate circadian phase- dependent estimates at 60 degrees (~ 4 h) bins measure\nacross all studied sleep intervals and EEG derivations presenting a significant circadian modulation as shown in A\nData are double plotted to enhance the visualization of circadian rhythms. The green vertical line marks the dim\nlight melatonin onset (DLMO; 0° circadian phase), and the grey shaded area repres ents the average melatoni\n \n1 1 \neep \nntly \n all \nese \nver \ntical \nlue \n the \n the \nwith \nsplit \nA). \ne in \nital \ned-\nons \n the \nons \n \nleep \ne in \n for \nown \nand \nuare \ns at \nBlue \nain \nt p-\ne on \nured \nin A. \ndim-\nonin \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted October 21, 2025. ; https://doi.org/10.1101/2025.10.20.683464doi: bioRxiv preprint \n\n \n1\n \nprofile. Type III fixed effects are reported, with only statistically significant p- values (α  = 0.01) indicated. Detaile\nstatistical results are provided in Dataset S5.xlsx.  \nREM sleep (Fig. 5 B and Dataset S4.xlsx), unlike NREM, showed a significant decrease in global FC\n(PC1) with elapsed time in sleep across most frequency bands, except for alpha, where no significan\nchange was observed. In turn, topographical distributed FC (PC2) showed no significant effect of slee\npressure, except in the delta and beta frequency bands, where it increased with time elapsed in slee\n(Fig. 5E).  \nFig 5. Principal component analysis of functional connectivity (dwPLI) during REM sleep: effect s of slee\nprogression and circadian phase.  (A and D) Loading values of individual electrode pairs on PC1 and PC2, fo\ndelta, theta, alpha, sigma, beta and gamma frequencie s. Values between brackets along the vertical axe\nrepresent the variance explained by the PC. (B and E) The modulation of PC1 and PC2 by elapsed time in sleep\nLeast square means (LSMeans) and standard errors of  the mean (SEM) are presented for each 186.7- minut\ninterval (i.e., one-third of the sleep episode), averaged across all studied circadian phases. (C and F) the circadia\nmodulation of PC1 and PC2, with LSMeans and SEM shown for each 60° (~4-hour) circadian phase bin, average\nacross all sleep intervals. Data are double plotted to enhance the visualiza tion of circadian rhythms. The gree\nvertical line marks the dim- light melatonin onset (DLMO; 0° circadian phase), and the grey shaded are\nrepresents the average melatonin profile. Type III fixed effe cts are reported, with only statistically significant p\nvalues (α  = 0.01) indicated. Detailed statistical results are provided in Dataset S4.xlsx. \n \n \n1 2 \niled \nFC \nant \neep \neep \n \nleep \n, for \nxes \neep. \nnute \ndian \nged \nreen \narea \nt p -\n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted October 21, 2025. ; https://doi.org/10.1101/2025.10.20.683464doi: bioRxiv preprint \n\n \n1\n \nThe exploratory topographical analysis supported the PC1 findings showing that all electrode pairs tha\nexhibited a significant elapsed-time-in-sleep-dependent effect (median P = 5.91E-08) wer\ncharacterized by a decreasing coupling over the course of the sleep episode (Fig. 6 A, B and Datase\nS5.xlsx). The largest number of electrode pairs showing a significant decrease in connectivity wa\nobserved in the sigma band. \nFig 6.  Topographical patterns of functional connectivity (dwPLI) in REM sleep as a function of slee\nprogression and circadian phase.  (A)  Red lines represent the magnitude of effect sizes for elapsed time i\nsleep for electrode pairs, where a significant main effect of this predictor was observed (p < 0.01). Effect sizes fo\nelectrode pairs that showed a time-in-sleep–dependent increas e or decrease in functi onal connectivity are show\nseparately. The geometric mean and median p-value among all significant p- values are also indicated an\nhighlighted in red. (B) Representative examples of the effects of elapsed time in sleep on dwPLI. Lea st squar\nmean (LSmeans) and standard error of the mean (SEM) are presented indicating sleep- dependent estimates a\neach 186.7-minute interval (third of the sleep episode ) measured across all studied circadian phases. (C) Blu\nlines represent the magnitude of effect sizes for elapsed time in sleep for electrode pairs, where a significant mai\neffect of this predictor was observed (p < 0.01). The geometric mean and median p- value among all significant p\nvalues are also indicated and highlighted in blue. (D) Representative examples of the effects of circadian phase o\ndwPLI. LSmeans and SEM indicate circadian phase- dependent estimates at 60 degrees (~ 4 h) bins measure\nacross all studied sleep intervals and EEG derivations presenting a significant circadian modulation as shown in A\nData are double plotted to enhance the visualization of circadian rhythms. The green vertical line marks the dim\nlight melatonin onset (DLMO; 0° circadian phase), and the grey shaded area repres ents the average melatoni\nprofile. Type III fixed effects are reported, with only statistically significant p- values (α  = 0.01) indicated. Detaile\nstatistical results are provided in Dataset S5.xlsx. \nDuring the spontaneously occurring WAKE periods within the 9h20 min sleep episodes, the dissipatio\nof sleep pressure led to a significant decrease in global FC (PC1), particularly in the theta, sigma, an\nbeta frequency bands (Fig. 7B and Dataset S4.xlsx). In the delta and alpha bands, global FC initiall\ndeclined in the first half of the night but showed a subsequent increase during the final third of th\nsleep episode. The effects on PC2 were characterized by an increase in topographically distributed FC\nin the alpha band and a decrease in the beta band, with most other frequency bands showing a non\nmonotonic shift in FC across the sleep episode similar to PC1 (Fig. 7E and Dataset S4.xlsx).  \n \n \n \n \n1 3 \nthat \nere \nset \nwas \n \nleep \ne in \n for \nown \nand \nuare \ns at \nBlue \nain \nt p-\ne on \nured \nin A. \ndim-\nonin \niled \ntion \nand \nially \n the \nFC \non-\n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted October 21, 2025. ; https://doi.org/10.1101/2025.10.20.683464doi: bioRxiv preprint \n\n \n1\n \nFig 7.  Principal component analysis of dwPLI- based functional connectivity during wakefulness in th\ntime-in-bed period: effects of sleep progression and circadian phase.  (A and D) Loading values of individua\nelectrode pairs on PC1 and PC2, for delta, theta, alpha,  sigma, beta and gamma frequencies. Values betwee\nbrackets along the vertical axes represent the variance explained by the PC. (B and E) Th e modulation of PC\nand PC2 by elapsed time in sleep. Least square means (LSMeans) and standard errors of the mean (SEM) ar\npresented for each 186.7-minute interval  (i.e., one-third of the sleep episode ), averaged across all studie\ncircadian phases. (C a nd F) the circadian modulation of PC1 and PC2, with LSMeans and SEM shown for eac\n60° (~4- hour) circadian phase bin, averaged across all sleep intervals. Data are double plotted to enhance th\nvisualization of circadian rhythms. The green vertical line marks the dim- light melatonin onset (DLMO; 0° circadia\nphase), and the grey shaded area represents the average me latonin profile. Type III fixed effects are reported\nwith only statistically significant p-values ( α  = 0.01) indicated. Detailed statistical results are provided in Datase\nS4.xlsx. \n \n \nThe exploratory topographical analysis revealed that the number of electrode pairs showing \nsignificant elapsed-time-in-sleep-dependent effect during wake was relatively small compared to REM\nand NREM (Fig 8A and Dataset S5.xlsx). The electrode pairs which showed such a significant effect o\ntime in sleep were primarily characterized by a decline in connectivity over time, except for the alph\nband, which showed both decreases and increases in connectivity throughout the sleep episode (Fi\n \n1 4 \n \n the \ndual \neen \nPC1 \n are \ndied \nach \n the \ndian \nrted, \naset \ng a \nEM \nt of \npha \n(Fig \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted October 21, 2025. ; https://doi.org/10.1101/2025.10.20.683464doi: bioRxiv preprint \n\n \n1\n \n8A, B and Dataset S5.xlsx). T he only electrode pair showing a significant effect in the delta ban\nexhibited an initial decline, followed by a return to baseline connectivity levels (Fig 8B). \n \nFig 8.  Topographical patterns of functional connectivity (dwPLI) during wakefulness in the time-in- be\nperiod as a function of sleep progression and circadian phase.  (A)  Red lines represent the magnitude o\neffect sizes for elapsed time in sleep for electrode pairs, where a significant main effect of this predictor wa\nobserved (p < 0.01). Effect sizes for electrode pairs that showed a time-in-sleep–dependent increas e or decreas\nin functional connectivity are shown s eparately. The geometric mean and median p- value among all significant p\nvalues are also indicated and highlighted in red. (B) Repr esentative examples of the effects of elapsed time i\nsleep on dwPLI. Lea st square mean (LSmeans) and standard error of the mean (SEM) are presented indicatin\nsleep-dependent estimates at each 186.7-minute interval (third of the sleep episode ) measured across all studie\ncircadian phases. (C) Blue lines  represent the magnitude of effect sizes for elapsed time in sleep for electrod\npairs, where a significant main effect of this predict or was observed (p < 0.01). The geometric mean and media\np-value among all significant p-values are also indicated and highlighted in blue. (D) Representative examples o\nthe effects of circadian phase on dwPLI. LSmeans and SEM indicate circadian phase- dependent estimates at 6\ndegrees (~ 4 h) bins measured across all studied sleep intervals and EEG derivations presenting a significan\ncircadian modulation as shown in A. Data are double plotted to enhance the visualization of circadian rhythms\nThe green vertical line marks the dim-light melatonin onset (DLMO; 0° circadian phase), and the grey shaded are\nrepresents the average melatonin profile. T ype III fixed effects are reported, with only statistically significant p\nvalues (α  = 0.01) indicated. Detailed statistical results are provided in Dataset S5.xlsx. \n \nBoth global and distributed FC are modulated by circadian phase in a topographical, brain-stat\nand frequency-specific manner \nThe circadian modulation of FC was statistically significant across all brain states \nand frequency band\nwith fewer electrode pairs showing a significant modulation of FC compared to the effects of elapse\ntime in sleep (Fig 3C to Fig 8C and Dataset S4.xlsx).  \nIn NREM sleep, global FC (PC1) in the delta band (Fig. 3 C) and topographically distributed FC (PC2\nin the theta band (Fig. 3F ) showed significant circadian modulation, both peaking during the circadia\nday, i.e. when plasma melatonin levels are low (Table S5.csv) . Exploratory topographical analysi\nconfirmed these effects and further revealed significant circadian modulation for some electrode pair\nin all other frequency bands except in beta and gamma (Fig. 4 C and Dataset S5.xlsx). In the thet\nband, significant electrode pairs were primarily clustered over centro-posterior cortical regions\nwhereas in the sigma band, effects were more prominent over fronto-central areas. FC generall\n \n1 5 \nand \n \nbed \ne of \nwas \nase \nt p-\ne in \nting \ndied \nrode \ndian \ns of \nt 60 \ncant \nms. \narea \nt p -\ntate \nnds \nsed \nC2) \nian \nysis \nairs \neta \nns, \nally \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted October 21, 2025. ; https://doi.org/10.1101/2025.10.20.683464doi: bioRxiv preprint \n\n \n \n16 \n \npeaked during the circadian day, except in the sigma band, where FC was highest during the circadian \nnight, i.e. when plasma melatonin concentrations are high (Figs. 3C). \nIn REM sleep, only global FC (PC1) in the alpha and beta bands showed significant circadian \nmodulation, peaking at the end of the circadian day, i.e. near the onset of the nocturnal surge in \nmelatonin (Fig. 5 C and Table S5.csv). Exploratory analysis confirmed strong circadian modulation in \nthe alpha band across multiple electrode pairs, peaking in the second half of the circadian day (Figs. \n6C, D and Dataset S4.xlsx). In contrast, beta and gamma bands exhibited circadian modulation that \npeaked during the circadian night. \nDuring wakefulness within the sleep episode, circadian modulation of PC1 did not reach significance \n(P>0.01) (Fig. 7C ), while PC2 showed significant modulation primarily in the theta and alpha bands \n(Fig. 7F and Dataset S4.xlsx). Exploratory topographical analysis supported these findings, revealing a \nlimited number of electrode pairs, mostly in the alpha band, that exhibited significant circadian \nmodulation, all peaking during the circadian night (Figs. 8C, D and Dataset S5.xlsx). \nIn summary, FC during wakefulness tended to peak during the circadian night, whereas in NREM and \nREM sleep, the circadian phase of peak FC varied by frequency band and principal component / \ntopography. \nAlpha-band-specific global FC during wakefulness increases with time awake and is modulated \nby the circadian timing of the wake period. \nWe next investigated whether an increase in sleep pressure associated with time elapsed since waking \nup from a major sleep episode leads to changes in connectivity in wakefulness and whether these \nchanges are opposite to the changes observed when sleep debt dissipates. Wake EEG data collected \nduring 18h and 40 min wake periods starting either in the morning, i.e. at a circadian phase during \nwhich humans normally are awake (FdW2), or in the evening (FdW5), as would occur during night shift \nwork (Fig 1A), were analysed in a subgroup 12 participants. Wake EEG segments were collected while \nparticipants were resting with eyes open during the 2-min long Karolinska Drowsiness Tests (KDT) \nimmediately prior to and after each of six cognitive test sessions scheduled across the wake episode.  \nIn total, 365 mins of artifact-free wake EEG segments were analyzed for FC (i.e., \nwPLI) from 44 \nelectrode pairs (Fig 1D).  This includes 24 rest EEG wake periods (i.e., KDTs) per person (2 KDTs per \ncognitive test session per person). Given the limited statistical power inherent in our exploratory, \npilot-style analysis of wake-dependent functional connectivity, conducted to elucidate findings from our \nmore extensive sleep data, we took steps to balance Type\n/i1 I and Type/i1 II error risks. First, we limited \nthe number of statistical tests by a priori focusing exclusively on the theta and alpha frequency bands, \ngiven their well ‐ established associations with both sleep pressure (Finelli, Baumann et al. 2000) and \ncircadian phase (10) and we did not run secondary exploratory analysis. Second, we set our \nsignificance threshold at the conventional α/i1 =/i1 0.05 to balance sensitivity and reduce the risk of \noverlooking true effects (i.e., minimize Type/i1 II errors). \nDespite the smaller dataset, PCA applied to the 45 electrode pairs across the 24 rest EEG wake \nperiods (i.e., KDTs) per person revealed two primary principal components, with interpretations similar \nto those observed during NREM, REM, and wakefulness within the sleep episode (Figs. S3 A, C and \nTable S1). Based on the PC loadings PC1 reflected a global FC component (Fig S4 A), while PC2 \nrepresented a topographically more heterogeneous distribute FC component (Fig S4 C and Dataset \nS4.xlsx). A linear mixed-effects model including two within-subject factors, time elapsed in wake (thirds \nof the day: \n∼ 6-hour intervals) and wake period (FdW2 and FdW5), indexing sleep pressure \naccumulation and circadian phase, respectively, revealed a significant main effect of time elapsed in \nwake on PC1 in alpha and a significant interaction in both alpha and theta (Fig S4 B and Table S2). In \nAlpha global FC showed a steep increase during the 12-hour out-of-phase wake period and followed a \nnon-monotonic pattern during the baseline day. In the theta band, global FC decreased during the \nbaseline wake period, whereas during the 12-hour out-of-phase condition it did not decline and \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted October 21, 2025. ; https://doi.org/10.1101/2025.10.20.683464doi: bioRxiv preprint \n\n \n1\n \nremained overall higher than during baseline (Fig S4 B). No significant effects were observed on PC\n(Fig S4D and Table S2). \nAssociation of Sleep- and Wake-dependent Functional Connectivity with Cognition \nFinally, we examined whether EEG-based functional connectivity (FC) measured during sleep (NREM\nREM) and resting wake was associated with cognitive performance, measured in 1,421 cognitive tes\nsessions collected across the forced desynchrony protocol (Fig. 9) . To reduce dimensionality, 2\ncognitive outcomes were included in the analysis (Fig. 9B), spanning the Karolinska Sleepiness Scale\nthe Psychomotor Vigilance Test, and multiple N-back tasks (verbal, numerical, pictorial, and integrate\nat 1-, 2-, and 3- back levels). Two principal components emerged (PC1 = 29% variance; PC2 = 18%\nover an eigenvalue of 1, but only PC1 was retained for subsequent analyses due to its robust loading\nand interpretability with higher scores indicating higher alertness and working memory accuracy (Fig\n9A–B). Similarly, FC was represented by the PC1 for each brain state and frequency band extracte\nas described before, only to reduce multiplicity. \n \nFig 9. Principal component analysis of cognitive performance and its associations with NREM, REM, an\nwake functional connectivity. Cognitive performance was measured during the scheduled wake periods. In tota\nsix cognitive test batteries were conducted per wake period. The current PCA included the first cognitive tes\nsession following each sleep episode. (A) Explained variance ratio of principal components of cognitive tes\nperformance measured across 21 outcome measures cove ring multiple domains including sleepiness (Karolinsk\nSleepiness Scale, KSS), vigilance / sustained attention (Performance Vigilance Test, PVT), and working memor\n(N-back tests). (B) L oading values of individual cognitive outcome measures variables for the PC1’ (‘Highe\ncognitive alertness and working memory performance’ ) and PC2 (‘Slower processing but better working memor\nperformance’). Warmer colors indicate stronger positive colder colors stronger negative Pearson correlatio\ncoefficients. (C) Mean absolute SHAP values from random fo rest models assessing the association betwee\nfunctional connectivity (FC) in sleep and cognitive performance (PC1) the subsequent way period across th\ncircadian cycle (N=226). Predictors correspond to the first principal component (PC1) of dwPLI- based connectivit\nacross 66 channel pairs during NREM and REM sleep, calculated separately for each frequency band. Slee\n \n1 7 \nC2 \nEM, \ntest \n 21 \nale, \nted \n8%) \nngs \nFig. \nted \nand \notal, \ntest \ntest \nska \nory \nher \nory \ntion \neen \n the  \ntivity \nleep \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted October 21, 2025. ; https://doi.org/10.1101/2025.10.20.683464doi: bioRxiv preprint \n\n \n \n18 \n \nepisode (FdN1 to FdN7) was also included in the model . SHAP values represent feature relevance based on \ngame-theoretic Shapley values; their average absolute m agnitude reflects each predictor’s global importance in \ncognitive outcome prediction. (D) Spearman correlations between PC1 of FC in the NREM theta and sigma bands \nand PC1 of cognitive performance, computed for each sl eep episode (N = 34).  (E) Mean absolute SHAP values \nfrom random forest models assessing the association between functional connectivity (FC) measured in resting \nwakefulness (Karolinska Drowsiness Test) and cognitive performance (PC1) within the corresponding cognitive \ntest session (N=133). Predictors correspond to the firs t principal component (PC1) of dwPLI-based connectivity \nacross 45 channel pairs during wakefulness. Additional variables, such as wake period (FdW1 vs FdW5) and time \nspent awake (test sessions COG1 to COG6), were incl uded in the respective models. (F) Spearman correlations \nbetween PC1 of FC in the wake alpha band and PC1 of cognitive performance, computed separately for each \ncognitive test session and for both in-phase and out-of-phase wake periods (N = 12). Full statistical results are \nreported in Table S3 to S6. \nTo investigate the relationship between NREM- and REM-dependent FC (PC1 – ‘global connectivity’) \nand cognitive performance (PC1 – ‘alertness and working memory accuracy’) on the subsequent day, \nwe followed a two-step procedure. In the exploratory step, we applied both standard multivariate \nassociation testing using ordinary least squares (OLS) regression and machine learning-based \nprediction approaches, including linear regression as well as ridge, lasso, and random forest \nregressions to identify relevant features (see methods). Despite differences in methodology, both \napproaches highlighted similar predictors, suggesting convergence between statistical inference and \npredictive modelling. \nThe exploratory models included FC PC1 scores across six frequency bands in both NREM and REM \n(12 predictors), along with the sleep episode (FdN1 to FdN7) to account for repeated structure (N = 34; \n226 observations in total) (Fig. 1A). Predictive accuracy ranged from R² = 0.29 (OLS) to –0.17 (lasso), \nnonetheless, several converging associations appeared. In OLS, NREM-theta FC was negatively \nrelated to cognition (\nβ  = –0.97, p < 0.00001), while NREM-sigma (β  = 0.57, p = 0.001) and NREM-beta \n(β  > 0, p < 0.01) were positively related. These were also retained in the lasso model (Table S3). \nRandom forest models emphasized similar features, with SHAP rankings highlighting NREM-theta and \nNREM-sigma (Spearman ρ  = 0.69, p = 0.0095 vs linear rankings) (Fig. 9 C). Thus, across methods, \nglobal FC in NREM-theta emerged as the most consistent inverse correlate of cognition, although \ninterpretability is limited by the weak predictive fit.\n \nIn a confirmatory step, we ran Spearman correlations between the top two FC predictors (NREM-theta \nand NREM-sigma) and cognitive PC1, separately for each sleep–wake period. This analysis confirmed \nthat global FC in theta was negatively associated with cognitive PC1 while in sigma this association \nwas positive but considerably weaker and non-significant. The associations were further modulated by \nthe circadian timing of sleep–wake episodes (Fig. 9D and Table S4).\n \nWe next examined the relationship between wake-dependent FC PC1 scores measured during resting \nwakefulness in the Karolinska Drowsiness Test (KDT) across six test sessions and two wake periods, \nhabitual wake (FdW2) and 12-h out-of-phase wake episodes (FdW5), and the corresponding cognitive \nPC1 scores in a smaller pilot sample (N = 12; 133 observations in total). The initial exploratory \nmultivariate linear and non-linear regressions analyses included four predictors represented by wake-\ndependent FC PC1 (global connectivity) scores in the alpha and theta bands as well as test session \n(COG1–COG6) and wake period (FDW2, in-phase; FDW5, out-of-phase), given the repeated structure \nof the data. The dependent variable was represented by the PCA-derived cognitive scores for cognitive \nPC1 for each individual test session and studied wake period. Despite a poor predictive performance \n(linear: R² = –0.08; RF: R² = 0.06) both linear regression coefficients and rankings consistently \nidentified WAKE-alpha FC as the most relevant predictor (Fig 9 E) with higher alpha FC predicting \npoorer cognitive scores with strong significance (\nβ  = –0.67, p  < 0.00001, OLS), and was selected by \nthe lasso model (Table S5). Confirmatory Spearman correlation analyses between wake–alpha and \ncognitive PC1 showed that alpha-band global FC was negatively and significantly associated with \ncognitive performance, and this association was modulated by test session and the circadian timing of \nthe wake period (Fig 9F and Table S6).\n \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted October 21, 2025. ; https://doi.org/10.1101/2025.10.20.683464doi: bioRxiv preprint \n\n \n \n19 \n \nIn summary NREM-theta connectivity (negative association) and wake-alpha connectivity (negative \nassociation) emerged as the most consistent predictors of reduced alertness and working memory \nefficiency. These findings highlight potential frequency-specific links between FC and cognition. \n \n \nDiscussion \nSeparation of sleep-wake and circadian contributions to brain oscillations demonstrates that functional \nbrain connectivity differs across sleep–wake states, is modulated by circadian phase, and changes \nprofoundly with the dissipation of sleep pressure. As sleep progresses, functional connectivity \nincreases during NREM sleep and decreases during REM sleep. Functional connectivity in specific \nfrequency bands during NREM as well as during wakefulness associate with cognitive performance. \nThese novel findings imply that sleep-dependent changes in functional connectivity are related to the \nrecovery of brain function during sleep. \nFunctional EEG connectivity across brain states \nAlthough prior studies have reported sleep stage-dependent differences in EEG-measured functional \nconnectivity during nocturnal sleep, this is the first study to assess brain state (i.e. sleep stage) effects \nwhile simultaneously controlling for both elapsed time in sleep and circadian phase. In addition, we \nalso controlled for the confounding influence of including short EEG segments in the analyses.  As a \nresult, the brain state differences observed here may not align precisely with earlier findings, but it is \nour view that the current approach provides a more accurate assessment of state specific changes in \nfunctional connectivity.  \nThe current approach revealed that wake EEG is characterized by a dominant peak in connectivity \nwithin the broader alpha range and that connectivity in the alpha range is lower in NREM sleep and \nlowest in REM sleep. Wakefulness, however, does not consistently exhibit higher connectivity than \nother brain states across all frequency bands. For example, connectivity in the sigma band, which \nprimarily reflects sleep spindle activity, is highest in NREM2.  Our results support earlier findings \nindicating that alpha-band functional connectivity is a key feature distinguishing wakefulness from REM \nsleep and may reflect the degree of disconnection from the external environment (28). Notably, our \nresults, indicate that EEG connectivity in REM sleep is lower than in slow-wave sleep (SWS) across \nboth the broader alpha and sigma bands, with no frequency band showing higher FC in REM \ncompared to all other brain states. These findings were very similar across the five connectivity \nmeasures explored here.   \nOne conclusion of the current findings is that rather than considering REM sleep a paradoxical wake’ \nstate, it could be considered the least wake-like brain state and perhaps the deepest sleep stage.  \nChanges in functional EEG connectivity with time elapsed in sleep  \nThe sleep-dependent decline in the PSD in the low-frequency range and in particular slow-wave \nactivity (0.75-4.5 Hz) in NREM sleep has for many years been used as a canonical EEG biomarker for \nsleep homeostasis and the recovery processes occurring during sleep (12). Slow wave indices were \nsubsequently linked to electrophysiological and molecular markers of synaptic strength, which in turn \nwas linked to synaptic downscaling and the hypothesis that synaptic homeostasis is a core function of \nNREM sleep (1). The current data demonstrate that the dissipation of sleep debt also has large effects \non connectivity measures in NREM sleep and across a wide frequency range. Given that connectivity \nis also underpinned by functional and structural changes in cortical synapses, we expected some \nsimilarities between FC and spectral power dynamics. Contrary to our expectations, connectivity in \nNREM sleep increases with the dissipation of sleep debt, and in all frequency bands, except the alpha \nband.  This is in line with some reports showing an increase in connectivity from the first to the second \nsleep cycle in young participants. (15). However, other researchers reported that connectivity in \nNREM2 decreases as nocturnal sleep progresses (29). These previous studies, however, did not \ncontrol for circadian phase. Furthermore, focusing on NREM2 alone is insufficient to capture the full \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted October 21, 2025. ; https://doi.org/10.1101/2025.10.20.683464doi: bioRxiv preprint \n\n \n \n20 \n \ndynamics of functional connectivity modulation across all stages of NREM sleep. Topographical \ndistribution and differences across canonical frequency bands also need to be considered. Our data \nindicate that while NREM sleep is generally marked by a global increase in connectivity, particularly in \nthe sigma band, i.e. in the frequency range of sleep spindles, there is also notable topographical \nvariation. Specifically, certain clusters of electrode pairs show sleep-dependent increases or decreases \nin connectivity, which may represent region-specific specialized reorganization.  \nWhereas the increase in connectivity in delta and theta bands contrasts with the decreases in spectral \npower in these bands, the very widespread increase in connectivity in the sigma band parallels the \nsleep-dependent increase in sigma power (11). A possible explanation for the observed dissociation \nbetween the sleep-dependent changes in power spectral density (PSD) and functional connectivity \n(FC) in NREM lies in their distinct neurophysiological bases. PSD quantifies the local energy of \noscillations, though it can be inflated by volume conduction, whereas phase-based FC captures the \nsynchrony of activity across distributed regions within the same frequency band. \nThe observations that connectivity in REM decreased with the dissipation of sleep pressure while at \nthe same time NREM connectivity increased underlines the brain state specificity of the dissipation of \nsleep pressure dependent changes in connectivity. This also highlights an important distinction \nbetween functional connectivity and power spectral density measures, because for the latter measure \nthe direction of sleep pressure dependent changes in the lower frequency range are in general similar \nfor NREM and REM sleep (11).  \n \nCircadian modulation in connectivity  \nEEG connectivity in all brain states is influenced by circadian rhythmicity, but the magnitude and \ndirection of this circadian effect is dependent on brain state and brain topography. This is consistent \nwith previous findings showing circadian modulation of EEG measures, including slow-wave activity \nand sleep spindle activity in NREM sleep, alpha activity during REM and wakefulness, and markers of \nsynaptic strength such as the slope of slow waves in NREM sleep, particularly in similar forced-\ndesynchrony protocols (10, 11, 25, 30, 31). Although the extent and phase of circadian modulation of \nthese EEG measures depend on brain state, frequency, and topography, our results show that the \ndominant circadian rhythms of functional connectivity in wakefulness and NREM sleep are \napproximately 12 hours out of phase. Specifically, connectivity during wake peaks at the circadian \nnight, whereas connectivity during sleep peaks at the circadian day. \n \n \nFunctional connectivity and cognitive performance \nWhile the predictive power was weak and the findings should be interpreted with caution, FC during \nsleep—especially NREM—and during the major wake period showed frequency-specific associations \nwith cognition. This is not surprising as the human brain operates as a network of functionally \ninterconnected regions, the connectivity of which is believed to underpin behavior, cognition, and mood \nstates (32).  \nHowever, our findings suggest that the relationship between network synchrony, as measured by EEG, \nand cognitive performance is a non-trivial one. During NREM sleep, lower global connectivity in the \ntheta band and higher global connectivity in the sigma band (FC–PC1) were associated with better \nsubsequent alertness and working memory performance (cognitive PC1), independent of connectivity \nin other frequency bands during either NREM or REM sleep. While the increased sigma coupling may \nreflect more effective thalamocortical network interactions, the link between lower theta connectivity \nand waking cognitive performance remains unclear. \nNotably, previous work has shown that EEG-based functional connectivity in the theta and beta \nfrequency ranges increases with age, whereas connectivity in the sigma range decreases (Ujma et al., \n2019). Given that cognitive function normally declines with age, increased theta-band global \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted October 21, 2025. ; https://doi.org/10.1101/2025.10.20.683464doi: bioRxiv preprint \n\n \n \n21 \n \nconnectivity may be considered a negative predictor of waking cognitive function, potentially an even \nstronger one than sigma-based connectivity. This interpretation also aligns with findings in older \npatients with obstructive sleep apnea where, higher relative frontal theta power during NREM stage 2 \nwas negatively associated with Mini-Mental State Examination scores and was elevated in those with \nmild cognitive impairment (Chen et al., 2023). These findings suggest that the cognitive benefits of \nsleep arise from frequency-specific alterations in oscillatory coupling, with distinct roles for sigma- and \ntheta-band synchrony. \nIn contrast, during wakefulness, higher global alpha connectivity was associated with poorer \nperformance, consistent with previous reports linking excessive alpha synchrony to reduced neural \nefficiency and impaired cognitive flexibility in both healthy aging and clinical populations (Klimesch, \n2012; Babiloni et al., 2016). Resting-state alpha rhythms are generally slowed in mild cognitive \nimpairment, which has been associated with cognitive decline (33). Our observation that global alpha \nconnectivity decreases across sleep, but rebounds with extended wakefulness, may therefore reflect \nan oscillatory signature of sleep-dependent recovery versus wake-related deterioration of neural \nefficiency. Alternatively, some associations may reflect stable, trait-like relationships between the \nbrain’s functional neuroarchitecture and cognition (Touroutoglou, Andreano et al. 2015; Seitzman, \nGratton et al. 2019).  \n \nSpeculative interpretation of the results – Connectivity and Criticality of brain states  \nPrevious research (34, 35) suggests that optimal FC (and thus optimal brain performance) is achieved \nwhen the brain operates near a critical state. This critical state supports a balance between flexibility \nand stability, essential for cognitive processes and adaptability. Perturbations from this critical state, \nwhether due to anesthesia, sleep deprivation, or disorders of consciousness, result in less efficient \nconnectivity patterns. During wakefulness, connectivity levels may increase due to synaptic \npotentiation, leading to disrupted (super)critical dynamics and less efficient states, whereas sleep acts \nto restore critical dynamics(35). We demonstrate that the sleep-dependent recovery process is \ncharacterized by a pronounced reduction in waking-state connectivity, particularly in the alpha band, \nwhich has been linked to waking vigilance in both our and previous research\n (10) . And ind eed , alpha \nband emerges as a unique marker. Not only was alpha FC the only frequency to show a systematic \ndecrease over the course of both NREM and REM sleep, but daytime wake EEG also revealed that \nlower global alpha connectivity strongly predicted better subsequent cognitive performance. This \nrobust negative relationship suggests that efficient network desynchronization in the alpha band, both \nduring sleep and wake, may index a neural state optimized for vigilance and information processing. \nAlthough sleep recovery exerts broad, global effects on synaptic strengths, as described by the \nsynaptic homeostasis theory, the stage-specific patterns we observe (rising connectivity in NREM and \ndeclining connectivity in REM) suggest that the renormalization of large-scale network interactions and \ninformation-processing capacity depends on a coordinated, multi-phase recovery process rather than a \nuniform downscaling. That is the coordinated alternation between NREM- and REM-mediated network \nrecalibration with opposite directions may be critical for rebalancing neural integration and information-\nprocessing capacity. This aligns with theory suggesting that the inhibitory, collothalamic mechanisms \nof NREM sleep, in nightly tandem with the excitatory, lemnothalamic mechanisms of REM sleep, \nsupport the consolidation of new memories and their interleaved reconsolidation with existing memory \nrepresentations (36). \n \n \nLimitations and Strengths of the Current Study \nThe results presented here are based on a rigorous design and a large data set; nevertheless, the \nstudy has several limitations. High-density EEG and source analysis which would have allowed a more \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted October 21, 2025. ; https://doi.org/10.1101/2025.10.20.683464doi: bioRxiv preprint \n\n \n \n22 \n \ncomprehensive connectivity analysis was not implemented. As such, our EEG connectivity analyses \ncannot directly be linked to distinct functional brain connectivity networks. Our experimental \nmanipulation was limited to sleep-wake timing. We did not perturb physiological brain activity and \nconnectivity via electric or magnetic stimulation.  \n \nEven though our EEG methodology may be limited, the data reveal aspects of the sleep process which \nhave not previously been reported. The finding presents a unique demonstration of the separate \ncontribution of the sleep-wake cycle and circadian rhythmicity to FC in wake, NREM and REM sleep. \nPrevious reports were based on small sample sizes, did not separate circadian and sleep-wake \ndependent contributions and investigated effects of time awake by sleep deprivation which is a \nchallenge to the brain well beyond the challenges experienced during a normal sleep-wake cycle.  \nPrevious studies have generally emphasized differences between brain states (e.g., wake vs. \nNREM) or between sleep stages (e.g., NREM2 vs. SWS). In this large dataset, with repeated \nmeasures of both EEG and cognitive performance, we focus on changes in connectivity \nwithin brain states rather than differences between them.\n We have done so because, in our view, \nunderstanding how sleep contributes to recovery of brain function requires a description of the \ndynamics of FC during the sleep episode, i.e. analyse how it changes from the beginning to the end of \nsleep. Finally, our approach is unbiased because we considered many different frequency bands \nrather than focusing on only one or two frequency ranges.  \nConcluding Remarks \nTogether, these findings suggest that when the sleep–wake cycle is aligned with circadian rhythmicity, \nthe interaction between sleep homeostasis and circadian processes supports the maintenance of \noptimal brain connectivity. This balance may be disrupted during misalignment, which could contribute \nto cognitive performance deficits and neurological conditions associated with disturbances of sleep and \ncircadian rhythms.\n \nFor many decades, sleep-wake and circadian aspects of brain function were quantified by sleep \nstaging and simple EEG analysis methods that are dependent on amplitude characteristics of the EEG. \nMore recently amplitude independent measures, such as coherence, were introduced. However, these \nmeasures are confounded by volume conduction. These approaches revealed canonical aspects of the \nsleep process, although it remained to the larger extent unclear how these aspects of the EEG and \nsleep process associate with brain function. Novel approaches to EEG analysis, such as those used \nhere, combined with comprehensive assessment of brain function, implemented in protocols that \nseparate the contribution of sleep and circadian rhythmicity may provide new insights into the process \nby which sleep and circadian rhythmicity interact to maintain homeostasis of brain function.   \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted October 21, 2025. ; https://doi.org/10.1101/2025.10.20.683464doi: bioRxiv preprint \n\n \n \n23 \n \n \n \n \n \n \nMaterials and Methods \nThe study was approved by the University of Surrey Ethics Committee and conducted in accordance \nwith the Declaration of Helsinki. Written informed consent was obtained from all participants prior to \ntheir enrolment.  \n \nStudy protocol \nThe circadian and sleep-wake time-dependent modulation of EEG oscillatory was assessed using a \n10-day forced desynchrony (FD) protocol, conducted in the Surrey Sleep Research Centre at the \nUniversity of Surrey. The protocol and associated procedures have been described in detail elsewhere \n(25, 30, 31). Briefly, following a baseline day (FdW1) and night (FdN1), participants were scheduled to \na 28-h sleep-wake cycle comprising 18 h and 40 min of wakefulness in dim light (< 5 lx) and 9 and 20 \nmin of sleep opportunity in darkness (Fig 1a). Throughout the 10-day period, participants resided in the \nclinical research facility and followed a standardized routine including scheduled mealtimes and \ncognitive testing sessions without access to information about clock time. Participants were \ncontinuously monitored during wake periods by a member of staff to ensure wakefulness and followed \na strict schedule without physical exercise. During the scheduled wake periods, participants spent \nmost of their time in a lounge where they were allowed to chat with each other or with a member of \nstaff, listen to music, and watch movies and TV series from a pre-selected list. \nThe assessment of the circadian phase  \nBlood samples were collected hourly during the 1st, 4th, and 7th 28-h forced desynchrony sleep-wake \ncycles (FdW1, FdW4, and FdW7) for determination of melatonin concentrations and assessment of \ncircadian phase (25, 30, 31) (Fig 1a). Blood melatonin concentration was quantified using \nradioimmunoassay (Stockgrand Ltd, Guildford, UK). The time corresponding to the 25% of the daily \nmelatonin amplitude range [dim light melatonin onset (DLMO)] was assigned circadian phase zero (37, \n38). Circadian period was derived from the linear regression fitted to the 3 DLMOs measured at FD1, \nFD4, and FD7 for each participant (τ  = 24 h + slope) (39). \nAssignment of circadian phase and elapsed time in sleep and time in wake period to dependent \nvariables  \nTo estimate the independent contribution of circadian phase and time since the start of the sleep and \nwake episodes, to the outcome measures, we grouped the continuously recorded EEG data into time \nbins and assigned to each of those time bins a circadian phase and the sleep-wake dependent index \nas described earlier (25, 30). \nPSD and connectivity measures were computed for all consecutive 20-minute intervals from the start \nto the end of each sleep episode. We then assigned a circadian phase and a time since the start of the \nsleep episode to each of the 20-minute intervals. For this, we used the 9 h 20 min sleep episodes \nacross FdN1 to FdN7. In the next step, data from the sleep and wake epochs (e.g., wake, NREM, \nREM) and the consecutive 20-minute intervals (spectral data and connectivity measures) were \naveraged in 6 circadian phase bins, each of 60° (~ 4-hourly bins), and three sleep-dependent time bins \n(around 186.7 mins each) for each sleep episode. \nFor the wake-duration-dependent EEG analysis, we used the resting state wake EEG data collected \nduring the Karolinska Drowsiness Tests (KDT) with eyes open and fixating a point for two minutes. \nThese KDT sessions were scheduled immediately prior to and following each of the six cognitive test \nsessions during the 2\nnd and the 5 th wake period. The 2 nd wake period started at habitual wake time \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted October 21, 2025. ; https://doi.org/10.1101/2025.10.20.683464doi: bioRxiv preprint \n\n \n \n24 \n \n(e.g. approximately 8am) and the 5 th wake period started 12 hours later (Fig 1). Similar to the sleep-\nduration-dependent analyses, the wake data were averaged per third of the 18h-40 min wake periods.  \nAssessment of cognition \nParticipants completed approximately 40 /i1 minutes of computerized cognitive testing at three-hour \nintervals. For the present analyses, we examined subjective sleepiness using the Karolinska \nSleepiness Scale (KSS; administered at the beginning and/or end of each session), objective vigilance \nand sustained attention via the 10-minute Psychomotor Vigilance Test (PVT), and working memory \nand executive function using 1-, 2-, and 3-back tasks. A detailed description of these measures has \nbeen published elsewhere(25, 40). The KSS is a 9-point Likert scale ranging from 1 (extremely alert) to \n9 (very sleepy), with higher scores indicating higher levels of subjective sleepiness. From the PVT, we \nderived four outcome measures: mean reaction time (RT), number of lapses (RT\n/i1 >/i1 500/i1 ms), and \nthe inverse of the slowest and fastest 10 /i1 % of RTs. For the n-back tasks, performed in four variants \n(integrated, pictorial, spatial, and verbal), we extracted two main outcome measures for each variant: \nRT and A\n′  (A-prime). A ′  is a nonparametric sensitivity index that quantifies a participant’s ability to \ndiscriminate targets (hits) from non-targets (false alarms), ranging from 0.5 (chance performance) to \n1.0 (perfect discrimination).  \nPolysomnographic (PSG) and wake EEG assessment \nEEG was recorded throughout the forced desynchrony protocol during both sleep episodes and \nrepeated cognitive test sessions during the wake episodes. For the current analyses, we analyzed the \ncomplete EEG data acquired during 231 sleep episodes from 34 participants (18 females, age: 25.1 ± \n3.4). All participants presented a healthy sleep profile based on their baseline adaptation night which \nalso served as a clinical sleep screening with a full clinical EEG-PSG setup (12 EEG channels, EOG, \nEMG, thoracic belt, a nasal airflow sensor, a microphone, and leg electrodes). During the FD protocol, \nsleep and wakefulness were monitored by basic polygraphy (EMG, ECG, and EOG) with extended \nmonopolar EEG montage which covered the major brain areas (Fp1, Fp2, F3, F4, C3, C4, T3, T4, P3, \nP4, O1, and O2) following the international 10–20 system. The ground and common reference \nelectrodes were placed at FPz and Pz, respectively. Two referencing schemes were applied. For \npower spectral density (PSD) analysis, EEG derivations were re-referenced offline to the contralateral \nmastoid (A1 or A2). For connectivity analyses, a common reference was used across all connectivity \nmetrics. Polysomnographic (PSG) data were recorded using Siesta 802 amplifiers (Compumedics, \nAbbotsford, Victoria, Australia). \nDuring the scheduled wake periods, EEG data were collected using the TEMEC Vitaport 3 system \n(TEMEC Instruments B.V., Kerkrade, The Netherlands). The EEG montage was similar to the montage \nused for the sleep EEG recording except that Fp1 and Fp2 channels were not used due to eye blinking \nartifacts. For the current analysis, wake EEG from twelve participants out of 34 were included in the \nanalysis (nine men, and three women). This is because the paper focuses on the sleep data, while the \nwake EEG analyses represent a pilot investigation. The participants whose EEG data were analyzed \ndid not differ from the rest of the sample in terms of demographic characteristics or baseline sleep \nparameters. \nEEG data were stored at 256 Hz. The low-pass filter was set at 70 Hz and the high-pass filter was set \nat 0.3 Hz. Electrode impedance was kept below 5 k Ω . As reported earlier (30) sleep staging was \nperformed in 30 s epochs according to the Rechtschaffen and Kales criteria (41) by one experienced \nsleep researcher (ASL) whose scoring showed a concordance exceeding 90% when compared to a \nstandard scored data set.   \nEEG power spectrum and connectivity analyses  \nAll artifact-free EEG segments of the sleep stages of interest (WAKE, NREM1, NREM2, SWS, REM) \nwere concatenated within consecutive 20 min time intervals between lights out and lights on spanning \n9 hours and 20 minutes (28 intervals) sleep episode. In total, 76,264 min (1771 hrs) artifact-free EEG \nsections were analyzed for the sleep episodes including 58,155 min for NREM and 18,109 min for \nREM as well as 4865 min for WAKE in the sleep episode and 365 min in the KDTs during the wake \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted October 21, 2025. ; https://doi.org/10.1101/2025.10.20.683464doi: bioRxiv preprint \n\n \n \n25 \n \nepisodes with some modulations across the circadian cycle (Fig 1C and D). From the resting state \nwake EEG data, we processed a two-minute-long EEG segment recorded immediately before and a \nsimilar interval recorded immediately after each cognitive test battery. \nWe chose spectral methods to enable direct examination of frequency-specific effects, allowing us to \nassess how the circadian-homeostatic interaction modulates functional connectivity in each canonical \nEEG band. While non-spectral methods combined with bandpass filtering can also provide frequency-\ntargeted estimates, spectral methods offer native, direct frequency resolution, superior phase \naccuracy, and methodological clarity (42).  \nValues were either analyzed on a 0.5 Hz bin basis to investigate spectral profiles between 0.5 to 32 Hz \nor averaged over commonly used frequency bands: delta (0.5-4 Hz), theta (4-8 Hz), alpha (8-12 Hz), \nsigma (12-16Hz), beta (16-25), and gamma (25 - 32 Hz). All measures were computed across \nstandard EEG frequency bands (delta, theta, alpha, sigma, beta, gamma) and separately for each \nbrain state. Computations used Python’s NumPy and SciPy packages (43, 44).  \nDetailed descriptions of the Power Spectral Density and Local Connectivity measures are provided in \nthe Supplementary Appendix. \n      \nEvaluation and selection of functional EEG connectivity metrics \nWhile we ran the initial analysis characterizing the spectral profile of FC across different brain states \nusing five different connectivity measures, we chose to run the in-depth analysis using dwPLI. The \nchoice of dwPLI as the primary connectivity metric is well-supported by its correlation profile. It exhibits \na very high Pearson correlation with wPLI (0.95) and strong correlations with PLI (0.81) and ImCoh \n(0.66), suggesting that it effectively captures the core aspects of phase-based connectivity shared \nacross these widely used measures. At the same time, its low correlation with phase coherence (0.10) \nconfirms its resistance to volume conduction and common source artifacts, which often inflate \ncoherence-based estimates. This balance between specificity and robustness makes dwPLI a \nparticularly suitable choice as it summarizes the essential structure of inter-regional interactions \nwithout being compromised by methodological limitations inherent in simpler or more artifact-prone \nmetrics. \nThe selection of dwPLI was further supported by superior fit statistics for the mixed\n‐ effects model, \nspecifically lower Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) values, \ncompared to those obtained using ImCoh.   \nPrincipal component analysis of functional brain connectivity and cognition.  \nWe applied Principal Component Analysis (PCA) to the large, multivariate datasets related to FC and \ncognition including all electrode pairs and sleep/wake episodes to reduce dimensionality and \ninvestigate their underlying structure and relationships. For the FC data PCAs were run separately for \neach brain state and frequency band. The employed imputation strategy for handling missing values in \nthe datasets consisted of removing all rows containing missing data. All columns were standardized to \nensure that all variables contributed equally to the analysis. In this instance, standardization was \napplied by dividing each feature by its standard deviation. PCA was then conducted using a specified \nnumber of principal components; in this case, 10 components were chosen to represent the underlying \nstructure of the data. \nAfter fitting the PCA model, we extracted the component loadings and scores and calculated the \nexplained-variance ratio for each component to quantify the proportion of total variance accounted for. \nAcross all EEG connectivity matrices, PC\n/i1 1 captured the majority of meaningful variance and was \nmarked by a distinct elbow in the scree plot.  In a few frequency bands during NREM and wakefulness, \nPC2 also accounted for a relatively large share of variance (>10%). All remaining components each \nexplained less than 5\n/i1 % of the variance. In line with common PCA practices (e.g., Kaiser’s criterion \nand the scree test) and to maintain consistency across brain states and frequency bands, we therefore \nretained only the first two components for all subsequent analyses.  \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted October 21, 2025. ; https://doi.org/10.1101/2025.10.20.683464doi: bioRxiv preprint \n\n \n \n26 \n \nTo examine the association between FC and cognitive performance, a principal component analysis \n(PCA) was first conducted across all cognitive test sessions, in line with the approach used for FC. In \nthe first analysis, which focused on the association between sleep-dependent FC and cognitive PC1.  \nThe cognitive PC scores were analyzed as averaged for the entire wake episode (i.e., 6 test sessions) \nfollowing each sleep episode (see Fig. 1A). In contrast, the second pilot analysis, targeting the \nassociation between FC measured during habitual (FdW2) and out-of-phase (FdW5) wakefulness \nepisodes (Fig. 1A) and cognition, included both FC and cognitive PC scores from all six cognitive \nassessments conducted within each wake episode. Only the first principal component from the \ncognitive PCA was retained, reducing dimensionality while preserving the main axes of variance \nrelevant to our outcome. \n \nStatistical analysis  \nAll analyses were conducted in SAS 9.4 and visualized using GraphPad Prism 9.  \nPower and Connectivity spectrum analysis \nIn the first analysis, the dependent variables were spectral power and electrode-pair connectivity, \nmeasured with five metrics (coherence [COH], imaginary coherence [ImCOH], phase-lag index [PLI], \nweighted PLI [wPLI], and debiased wPLI [dwPLI]), computed at 1\n/i1 Hz resolution across each sleep \nstage (NREM1, NREM2, slow-wave sleep, REM, and wake) during the scheduled sleep episodes. The \nPSD and connectivity outcome measures were averaged across all EEG channels and channel pairs, \nrespectively, as topography was not evaluated at this stage. To examine the influence of circadian \nphase, elapsed time in sleep, and sleep stage on these dependent measures we conducted linear \nmixed-effects modelling for each log transformed PSD and connectivity outcome measure across the \nfrequency spectrum and across all 231 scheduled sleep episodes. The fixed effects included three \nwithin-subject factors: circadian phase (six levels, using 60° bins), elapsed time in sleep  (divided \ninto three approximately 3.1-hour intervals), and sleep stage (Wake, NREM1, NREM2, NREM3, and \nREM). To accommodate the repeated measures structure of the data, we created a composite factor \nrepresenting each unique combination of these three conditions and treated this as the unit of \nrepetition nested within each participant and session. Random intercepts were included to account for \ninter-individual differences, and a compound symmetry covariance structure was specified to model \nwithin-subject correlations across repeated measurement occasions. To improve the accuracy of \nstandard error estimates, we used the Kenward–Roger method for degrees of freedom estimation. The \nanalysis focused on estimating and testing the main effects of each factor on connectivity as well as \nthe two-way interactions of factors sleep stage with circadian phase  and elapsed time in sleep . To \ncontrol for Type\n/i1 I error, the significance threshold was adjusted to α/i1 =/i1 0.01 (see section on \nCorrection for Multiplicity). \nTopographical analysis of EEG connectivity  \nThe topographical analysis comprised two consecutive steps. In the primary analysis, the dependent \nvariables were the principal component (PC) scores derived from a PCA on dwPLI-based \nelectrode-pair connectivity. Connectivity was calculated within six canonical frequency bands (delta, \ntheta, alpha, sigma, beta, and gamma) across three consolidated brain states (NREM, REM, and \nWake) during 231 sleep episodes, and during baseline wakefulness (FdW2) and 12\n/i1 h out-of-phase \nwakefulness (FdW5) in a subset of participants. Although the PCA reduced the 66 individual \nelectrode-pair connectivity values to a smaller set of components, the original PC loadings enabled \ntopographical interpretation of each component.  \nFor the sleep episodes, we focused on the first two PCs, three brain states, and six frequency bands, \nyielding 2\n/i1 ×/i1 3/i1 ×/i1 6/i1 =/i1 36 unique models. Each model examined a single PC, brain state and \nfrequency-band combination. To control for Type /i1 I error, the significance threshold was adjusted to \nα/i1 =/i1 0.01. \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted October 21, 2025. ; https://doi.org/10.1101/2025.10.20.683464doi: bioRxiv preprint \n\n \n \n27 \n \nFor the wake EEG data (measured during the two wake episodes), we again used the first two PCs but \nrestricted our analysis to the theta and alpha bands, given their established roles in homeostatic and \ncircadian modulation, resulting in 2 /i1 ×/i1 2/i1 =/i1 4 models, each examining a single PC–frequency-band \ncombination. To balance statistical rigor with our small exploratory sample (N/i1 =/i1 12) due the intensive \nmanual artifact rejection required, we limited the number of tests and set the significance threshold at \nα/i1 =/i1 0.05. \nIn the second step, we conducted a more exploratory topographical analysis by examining \ndwPLI-measured connectivity for each electrode pair individually. In both the primary and the \nsecondary analyses, we applied the same linear mixed-effects modelling approach across brain states \nand canonical frequency bands. The fixed effects included two within-subject factors: circadian phase \n(six levels, using 60° bins) and time elapsed in sleep (divided into three approximately 3.1-hour \nintervals).  \nFor the sleep data, comprising 66 EEG channel pairs, three brain states (NREM, REM, and Wake), \nand six frequency bands, this resulted in 66\n/i1 ×/i1 3/i1 ×/i1 6/i1 =/i1 1/i1 188 unique models. For the wake EEG \ndata during the two wake episodes, comprising 45 channel pairs and two frequency bands, we tested \n45\n/i1 ×/i1 2/i1 =/i1 90 models. Each model analysed a single channel–state–band combination. \nSince each subject contributed up to seven sleep episodes (SEs), and within each SE up to three \nsleep intervals (i.e., thirds of the night), we specified a compound-symmetry (CS) covariance structure \non time elapsed in sleep nested within circadian phase (i.e., repeated ElapsedTimeInSleep \n(CircadianPhase) / subject = Subject*SE type = CS) to parsimoniously model within-episode \ncorrelations. \nFor the analysis of connectivity during the two wake episode, the two within-subject factors were \nelapsed time in wake (divided into thirds of each wake period) and wake episode (in-phase vs. \nout-of-phase), including their two-way interaction. Mixed models included a random intercept for each \nparticipant to account for between-subject variability. Model degrees of freedom were adjusted using \nthe Kenward–Roger method (ddfm = kr) to improve the accuracy of standard errors and test statistics. \n \nAssociation analysis between Connectivity and Cognition. \nAll multivariate analyses were conducted in Python (v3.8) (45) using standard scientific computing \nlibraries, including numpy, scipy, pandas, scikit-learn, statsmodels, and shap (46-48) . Functional \nconnectivity was calculated using the debiased weighted Phase Lag Index (dwPLI), separately for \nNREM, REM, and resting wakefulness. For each frequency band and sleep–wake stage, 66 (sleep) or \n45 (wake) channel-pair values were reduced via principal component analysis (PCA) to a single latent \nfeature: the first principal component (PC1), representing global connectivity for that condition. \nCognitive performance was likewise reduced through PCA across 21 behavioral outcomes spanning \nsleepiness ratings, vigilance, and working memory tasks. The first cognitive component (PC1), \ninterpreted as a general alertness and working memory factor, served as the target variable. For sleep \nanalyses, PC1 scores were averaged across the six behavioral sessions following each sleep episode. \nTo examine the relationship between functional connectivity and cognition, a two-step analysis was \napplied. In the exploratory phase, both association and prediction models were employed. Multivariate \nassociation was assessed using Ordinary Least Squares (OLS) regression via the statsmodels \npackage, yielding estimated regression coefficients, p-values, and 95% confidence intervals. In \nparallel, prediction was performed using linear regression, ridge regression with cross-validated \nregularization strength (49), lasso regression (also with CV-based regularization) (50), and random \nforest regression with 100 estimators (51). Feature values were standardized before modeling. The \noutcome variable was negated prior to training to align the direction of prediction across datasets. \nSubject identity was optionally included as a predictor to evaluate the extent to which individual \nbaselines influenced model performance. \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted October 21, 2025. ; https://doi.org/10.1101/2025.10.20.683464doi: bioRxiv preprint \n\n \n \n28 \n \nTo avoid data leakage, an 80/20 train/test split was used, ensuring that data from a given participant \nappeared only in one of the sets. Train/test splits were group-aware and stratified by subject identity. \nMissing values were handled via mean imputation. To interpret feature relevance in tree-based \nmodels, SHAP values were computed using the shap package. SHAP (SHapley Additive exPlanations) \nis a method for quantifying the contribution of each feature to model output, based on cooperative \ngame theory, and is conceptually related to feature importance measures but offers consistent, model-\nagnostic attributions (52-54). \nIn the confirmatory phase, the most relevant predictors identified during the exploratory phase were \ntested using univariate Spearman correlations with cognitive PC1 scores, calculated separately for \neach sleep–wake episode. Spearman correlations were performed in SAS 9.4. \nOutput and Diagnostic Tracking \nFor each model, we extracted key analytical outcomes, including the estimated least-squares means \nfor the levels of both predictors,  Type III tests of fixed effects (F -values and associated p-values), and \nstandard fit statistics such as AIC and BIC. We also recorded the residual skewness of the fitted model \nand documented whether the final model used a log-transformed or untransformed outcome variable. \nTo visualize statistical effect sizes, we calculated Cohen's f2 effect size (55): \nf2 = u/v/i1 ∗ /i1 F, \nwhere u and v are, respectively, the numerator and denominator degrees of freedom of the F statistic \nused to determine the corresponding main or interaction effect in the general linear mixed model \nanalysis.  \nIn the model ‐ selection process, we evaluated the residual ‐ distribution diagnostics, checked for \nconvergence issues (e.g., infinite likelihood), and compared fit statistics, namely the Akaike Information \nCriterion (AIC) and the Bayesian Information Criterion (BIC). The model exhibiting the lower AIC and \nBIC was retained as the final model. Correlational analysis was based on Spearman correlations.  \nCorrection for Multiplicity \nWe conducted a large number of statistical tests across several multivariate models. Although these \ntests were not entirely independent, we addressed the risk of Type /i1 I error through multiple strategies. \nFirst, we set a more stringent significance threshold at α/i1 =/i1 0.01. Second, in our primary \ntopographical analysis, we further limited the number of comparisons by reducing dimensionality via a \nPCA and only the PCs derived from the dwPLI connectivity data were tested. Third, we then carried \nout an exploratory channel-pair analysis to confirm the primary results, and throughout both stages we \nreported P\n/i1 values alongside standardized effect sizes, anchoring our main conclusions on the largest \nand most statistically robust effects. \nTo contextualize our chosen α/i1 =/i1 0.01 relative to a conventional multiplicity correction, we also \napplied the Benjamini–Hochberg procedure (FDR /i1 =/i1 5%). Across all 5100 individual p-values, the \nlargest p-value passing the Benjamini–Hochberg critical threshold was 0.021. Thus, under the \nBenjamini–Hochberg procedure, tests with p /i1 </i1 0.021 would be deemed significant. Our choice of \nα/i1 =/i1 0.01 is therefore more conservative than controlling the false discovery rate at 5%. \nFor the wake ‐ episode data, given the smaller sample size and the need to balance Type /i1 I and \nType/i1 II error risks, we reduced the number of analyses and set the significance threshold at the \nconventional α/i1 =/i1 0.05. \n \n \nAcknowledgments \n \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted October 21, 2025. ; https://doi.org/10.1101/2025.10.20.683464doi: bioRxiv preprint \n\n \n \n29 \n \nThis research was supported by a Biotechnology and Biological Sciences Research Council grant \n(BB/F022883; PI: DJD). DJD is supported by the UK Dementia Research Institute core awards UKDRI-\n7005 and CF2023\\7 and award UKDRI-7206 , through UK DRI Ltd, principally funded by the UK \nMedical Research Council; and by the National Institute for Health Research (NIHR) Oxford Health \nBiomedical Research Centre (BRC), (NIHR203316) . ASL received funding from the Wellcome trust \n(207799/Z/17/Z) and UKRI (ES/W006367/1) and NIHR (NIHR206949). We thank the staff of the Surrey \nClinical Research Center for their help with recruitment, screening and clinical conduct of the study. \nDrs Ana Slak, Sibah Hasan for their help with data acquisition.  \n \nReferences \n \n \n1. G. Tononi, C. Cirelli, Sleep and the price of plasticity: from synaptic and cellular homeostasis \nto memory consolidation and integration. Neuron 81, 12-34 (2014). \n2. P. L. Nunez, R. Srinivasan, Electric Fields of the Brain: The neurophysics of EEG (Oxford \nUniversity Press, 2006), 10.1093/acprof:oso/9780195050387.001.0001. \n3. P. 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