NEUROSCIENCE

Isolated cortical computations during delta wavessupport memory consolidationRalitsa Todorova and Michaël Zugaro*

Delta waves have been described as periods of generalized silence across the cortex, and theiralternation with periods of endogenous activity results in the slow oscillation of slow-wave sleep. Despiteevidence that delta waves are instrumental for memory consolidation, their specific role in reshapingcortical functional circuits remains puzzling. In a rat model, we found that delta waves are not periodsof complete silence and that the residual activity is not mere neuronal noise. Instead, cortical cellsinvolved in learning a spatial memory task subsequently formed cell assemblies during delta waves inresponse to transient reactivation of hippocampal ensembles during ripples. This process occurredselectively during endogenous or induced memory consolidation. Thus, delta waves represent isolatedcortical computations tightly related to ongoing information processing underlying memoryconsolidation.

Most of our time spent asleep is dom-inated by slow oscillations (0.1 to 1Hz),when cortical neurons synchronouslyalternate between a depolarized (up)state associated with high levels of

endogenous activity and a hyperpolarized(down) state when neurons remain silent(1). Delta waves are large deflections of thelocal field potential (LFP) that correspondto the down states of the slow oscillation

and are thus considered periods of gener-alized cortical silence. The slow oscillationplays a causal role in memory consolidation(2–5), in particular by orchestrating an in-formation flow between the hippocampus andthe neocortex (6). Indeed, delta waves tend tooccur in close temporal proximity to hippo-campal ripples (7), which are instrumentalfor memory consolidation (8, 9). Hippocam-pal replay of awake activity (10), biased by

inputs from sensory cortices (11, 12), initiatesreactivation of prefrontal cortical cell assem-blies (13, 14) just before the occurrence of adelta wave (7). Cortical synaptic plasticitysubsequently takes place during networkreorganization early in the following up state(15, 16) and during the massive calcium entryaccompanying the ensuing sleep spindle(17–19). This hippocampo-cortical dialogue(20–22) is instrumental for memory consoli-dation (5). However, the incursion of gener-alized silence (delta wave) precisely betweenperiods of information exchange and periodsof network plasticity remains puzzling.We recorded prefrontal cortical activity in

nine rats during slow-wave sleep (5). Con-sistentwith previous reports,most deltawaveswere accompanied by neuronal silence. Yet,occasionally, spikes did occur during deltawaves (Fig. 1A), and when considering cumu-lative spiking activity over all recorded deltawaves, unexpected residual activity appearedat the peak of the waves (Fig. 1, B and C) (spikewaveforms recorded during delta waves werenot distinguishable from spike waveforms

RESEARCH

Todorova et al., Science 366, 377–381 (2019) 18 October 2019 1 of 5

Center for Interdisciplinary Research in Biology (CIRB),Collège de France, CNRS, INSERM, Université PSL,Paris, France.*Corresponding author. Email: michael.zugaro@college-de-france.fr

Fig. 1. Delta spikes.(A) Example of a nonsilentdelta wave. Colored curvesindicate LFPs recordedfrom the medial prefrontalcortex (color: recordingchannel). Colored verticalticks indicate spikes emittedby simultaneously recordedprefrontal units (color:channel from which theunit was recorded).Dashed lines indicate thebeginning and end ofdelta waves. A delta spike(black circle) occurs duringthe second delta wave,when the rest of thenetwork remains silent.Black calibration bars: 0.5 s(horizontal); 1 mV (vertical).mPFC, medial prefrontalcortex. (B) Mean perieventtime histogram of thenormalized firing rate ofprefrontal units centered on delta waves (top curve: mean field event). Thedashed white line indicates residual activity during delta waves. (C) Timedistribution of the spikes emitted by each prefrontal neuron closest to eachdelta wave. The large peak at ~100 ms corresponds with activity in the up state.The smaller peak consists of spikes occurring during delta waves. The dashedline indicates the 15-ms upper threshold used to define delta spikes insubsequent analyses (all results were confirmed by using ±30-ms time windows).

(D) (Left) Number of units that discharged in a given proportion of delta waves(gray curve: log-normal fit with the same mean and variance as the data;error bars: 95% confidence intervals from bootstrapped data). No unit firedin 0% of the delta waves. (Right) Number of delta waves containing agiven number of delta spikes. (E) No difference in average waveforms betweensilent (black: n = 101,161) and nonsilent (blue: n = 12,205) delta waves (MonteCarlo test, P > 0.05).

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recorded outside delta waves; fig. S1). Oncloser examination, neuronal activity occurredconsistently in a substantial fraction of deltawaves (12%), wherein one or a few neuronsremained active while the rest of the popu-lation became silent (Fig. 1D). We call thisunexpected persisting activity “delta spikes.”To investigate whether delta spikes were re-stricted to a particular subset of neurons, wecounted the number of delta waves in whicheach unit emitted one or more spikes. As ithappened, every single recorded unit firedduring delta waves, suggesting instead thatpersisting firing may actually constitute awidespread phenomenon (Fig. 1D and fig. S2).We then wondered whether delta spikes

tended to occur in specific delta waves with

distinctive characteristics. We thus compareddelta waves in which we did or did not detectcortical spikes and found no significant dif-ference between the two groups in terms ofwaveform (Fig. 1E), duration, timing (fig. S3),depth (fig. S4), decreased gamma power, orcoupling with hippocampal ripples and tha-lamocortical spindles (fig. S5). This suggeststhat spikes could take place during virtuallyall delta waves but may remain undetectedgiven the limited number of recorded neu-rons relative to the entire population (fig. S6).We thus hypothesize that firing during deltawaves might be an overlooked phenomenonmanifested in possibly all delta waves.These findings indicate that during any

given delta wave, the cortical network becomes

silent except for a small but ever-changingminority of cells. The most parsimoniousexplanationwould be that delta spikes consti-tute random activity reflecting imperfect co-ordination in the cortical alternation betweenthe up and down states. Yet, an alternativepossibility is that this activity serves a well-defined computational function. A hallmarkof cortical computation is the emergence of cellassemblies. We thus tested for the presenceof recurring coactive cell ensembles, usingtwo complementary approaches. As a firstapproach, we performed a standard indepen-dent component analysis (23), which identifiedmultiple significant components that wereactive during delta waves (fig. S7, A and B).However, these components were likely to

Todorova et al., Science 366, 377–381 (2019) 18 October 2019 2 of 5

Fig. 2. Hippocampal ripple activity predicts delta spikes. (A) Delta spikesand preceding hippocampal activity. Blue traces indicate LFPs from themedial prefrontal cortex. Colored ticks indicate simultaneously recordedprefrontal (blue) and hippocampal (red) spikes. Black circles indicatedelta spikes emitted within ±15 ms of the delta wave peak (shaded area).In the first two delta waves, delta spikes were recorded from the sameunit after similar hippocampal activity patterns. HPC, hippocampus.(B) Cross-correlations (curves and shaded areas, mean ± SEM; orange,data; gray, time-shifted control) between hippocampal ripple activity(sliding window) and delta spikes (fixed, 0 s). The horizontal orange lineindicates the Monte Carlo test: P < 0.05. corr., correlation. (C) Enrichmentin positive correlations [comparative distribution between data and control in(B)] when hippocampal activity was correlated with subsequent prefrontal

delta spikes. (D) Performance of a GLM trained to predict prefrontal activityduring delta waves on the basis of preceding hippocampal ripple activity(200-ms window). Delta spikes as well as delta components were significantlypredicted by multiple single-unit hippocampal activity (P = 0.0403 fordelta spikes, P = 0.0052 for delta components; Wilcoxon rank sum test)but not by global hippocampal drive ignoring cell identity (summedactivity, P = 0.2597 for delta spikes and P = 0.3258 for delta components;Wilcoxon rank sum test). **P < 0.01; ***P < 0.001, (Wilcoxon signed-ranktests). (E) Object responsivity index for partner (green) versus other(gray) prefrontal units (curves: cumulative distributions; inset: mean ± SEM).Only partner prefrontal units showed positive object responsivity (partnerunits, P = 0.0162; other units, P = 0.5967; Wilcoxon signed-rank test; partnerversus other units, P = 0.0465; Wilcoxon rank sum test). *P < 0.05.

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combinemultiple smaller but overlapping cellensembles, given the limited number of neu-rons active in any given delta wave. We thusperformed a second analysis to examine coop-erative activity (“peer prediction”) (24) amongdelta spikes, an idiosyncratic property of cellassemblies. This showed that the delta spikesof one neuron could be predicted from thedelta spikes of other neurons (fig. S7C).

We then asked whether delta spikes wereinvolved in the hippocampo-cortical dialogueunderlying memory consolidation. Becausedelta waves typically take place precisely be-tween hippocampal replay and cortical reor-ganization for memory consolidation, thishypothesis would be expected to have twoimplications: (i) Hippocampal activity duringripples should predictwhichneurons (orwhich

assemblies) are active during the followingdelta wave, and (ii) this predictive bias shouldemerge after behavior, and predictable corticalcells should be involved in the reactivation ofwaking experience.Rats were trained on a spatial memory task,

and hippocampal and cortical activity wasrecorded during both behavior and subsequentmemory consolidation during the first 2 hours

Todorova et al., Science 366, 377–381 (2019) 18 October 2019 3 of 5

Fig. 3. Delta waves isolate cortical computations. (A) Cross-correlations(curves and shaded areas, mean ± SEM) between hippocampal rippleactivity (fixed, 0 s) and prefrontal activity (sliding window). Observedcross-correlations (orange) were significantly different from a time-shiftedcontrol (gray) for cortical activity after ripples (horizontal orange line:Monte Carlo test, P < 0.05). Delta waves (dashed line; peak occurrence rate130 ms after ripples) tend to occur within the critical window when prefrontalactivity remains correlated with the preceding ripple activity. (B) Simulta-neous recording of prefrontal and hippocampal activity around a delta wave(gray-shaded rectangle). (Top) Proportion of prefrontal spikes predicted bythe firing of hippocampal cells (partner spikes). (Center) Raster plot of spikes

emitted by 68 simultaneously recorded prefrontal units (red ticks: partnerspikes; gray ticks: other spikes). (Bottom) Simultaneously recorded LFPs inthe mPFC (blue: delta wave) and hippocampus (broadband and ripple-bandfiltered signal; blue: ripples). During delta waves, partner spikes occurredin isolation (red ellipse). Partner spikes emitted by the same units outsidedelta waves (gray ellipses) formed a considerably smaller proportion of theongoing cortical activity. Black calibration bar: 0.5 s. Filt, filtered. (C) Signal-to-noise ratio (curves and shaded areas, mean ± SEM) of partner spikesrelative to other spikes around delta waves. Observed values (blue) weresignificantly different from a time-shifted control (gray) during delta waves(horizontal blue line: Monte Carlo test, P < 0.05).

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of sleep (5). Hippocampal spiking activityduring ripples was significantly correlatedwith cortical delta spikes that occurred im-mediately (50 to 200ms) afterward (the effectwas not due to data recorded from any single

rat) (Fig. 2, A and B, and fig. S8). This in-creased correlation was due to a large propor-tion of positively correlated interregional pairsof neurons (Fig. 2C). Furthermore, ripple spikeswere better correlated with delta spikes than

with spikes occurring at similar delays duringan up state (correlations were greater in thepresence of a delta wave) (fig. S9). A gen-eralized linear model (GLM) analysis showedthat ensemble activity in the hippocampus

Todorova et al., Science 366, 377–381 (2019) 18 October 2019 4 of 5

Fig. 4. Induction of memory consolidation by isolation of partner spikes.(A) (Left) Experimental protocol. Delta waves were induced by briefsingle-pulse electrical stimulation of deep cortical layers. Induced delta waveswere triggered to isolate either partner activity (coupled stimulation;green, 130 ms after ripples) or other cortical activity (delayed stimulation;purple, 290 to 370 ms after ripples) during sleep after limited trainingon a spatial object-recognition task. (Right) Object discrimination indexduring the recall phase. Only delta waves triggered to isolate partner activity(coupled stimulation) resulted in memory consolidation and enhanced taskperformance. (B) Performance of a GLM trained to predict delta spikes on thebasis of preceding hippocampal activity (200-ms window), measured as

percent improvement relative to a shuffled control (prediction gain). Onlydelta waves triggered to isolate partner activity resulted in a significantprediction of delta spikes (P = 0.0030 for isolation of partner spikes by coupledstimulation; P = 0.1301 for isolation of other spikes by delayed stimulation;Wilcoxon rank sum test). stim, stimulation. **P < 0.01. (C) Cross-correlation(curves and shaded areas, mean ± SEM) of hippocampal activity and deltaspikes (green: isolation of partner spikes by coupled stimulation; purple:isolation of other spikes by delayed stimulation; gray: time-shifted control;horizontal green line: Monte Carlo test, P < 0.05). (D) Enrichment in positivecorrelations upon isolation of partner spikes by coupled stimulation (top)but not of other spikes by delayed stimulation (bottom).

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could significantly predict which cortical cellswould emit delta spikes (Fig. 2D). In contrast,delta spikes could not be predicted from thecombined activity of all hippocampal unitsthat ignored cell identity (multiunit activity),ruling out the possibility that delta spikesmerely reflect the overall level of hippocam-pal excitatory drive during ripples. Finally,ripples facilitated (but did not entirely con-trol) the formation of delta assemblies (fig. S7).Furthermore, the same GLM analysis appliedto hippocampal and cortical ensembles showedthat hippocampal activity could even predictdelta components (Fig. 2D).Our second prediction concerned the rela-

tion of this predictive bias to behavior. In sleepsessions preceding the task, hippocampal spik-ing activity during ripples failed to predict sub-sequent delta spikes or assemblies (fig. S10),indicating that the predictive bias emergedafter task performance. We then investigatedthe behavioral correlates of the prefrontal unitswhose delta spikeswere significantly predictedby hippocampal ripple activity during sleepafter behavior (“partner cells”) (fig. S11 andtables S1 and S2). These cortical cells displayedhigher levels of task-relevant firing duringbehavior (Fig. 2E) (we failed to find a simi-lar effect for delta components, possibly be-cause of low statistical power due to theirlimited number: n = 14 components, n = 9predicted). We further investigated the be-havioral correlates of delta assemblies andfound that these assemblies were also ex-pressed during task performance but notoutside delta waves nor in sleep that precededbehavior (fig. S12).These observations suggest that in addition

to triggering the reorganization of corticalsubnetworks during the transition to theup state (5), an unsuspected role of the deltawave may be to isolate from interference spe-cific cortical computations taking place inresponse to hippocampal replay. Consistentwith this idea, delta waves typically occurredwithin a critical time window when corticalactivity remained correlated with hippocam-pal ripple activity (Fig. 3A). To test whetherdelta waves tended to preferentially silencecortical activity that was related to the on-going hippocampo-cortical dialogue, we clas-sified individual prefrontal spikes as “partnerspikes” if they followed spikes emitted bytheir significantly correlated hippocampalunits or “other spikes” if they were unrelatedto the preceding hippocampal activity (Fig.3B) (more examples are shown in fig. S13).The signal-to-noise ratio for partner spikespeaked during delta waves (Fig. 3C), and thiswas due to the selective silencing of non-partner activity during delta waves (fig. S14).

Does this isolation of cortical computationsplay a critical role in memory consolidation?A prediction of this hypothesis is that isolat-ing cortical assemblies by experimental induc-tion of delta waves should trigger memoryconsolidation, but only if the isolated activityis relevant to the hippocampo-cortical dialogue(partner spikes). We have already shown thattriggeringdeltawaveswhen endogenousmech-anisms fail to do so can boost memory con-solidation, provided that the delta waves areinduced in an appropriate timewindow (Fig.4A) (5). We thus sought to confirm the pre-diction that these delta waves actually isolatedpartner spikes (that delta spikes did occurduring induced delta waves and that theywere predicted by hippocampal activity). Sim-ilar to our observations in natural sleep (above),stimulation-induced delta waves did featurespiking activity (fig. S15), and these deltaspikes were predicted by preceding hippo-campal activity coinciding with the timingof ripples (Fig. 4, B to D). In contrast, slightlydelaying the induction of delta waves (by~200 ms) (Fig. 3A) to isolate nonpartnerdelta spikes (Fig. 4, B to D) failed to inducememory consolidation (5).Our results challenge the generally accepted

tenet that delta waves, reflecting the downstates of the sleep slow oscillation, are periodsof complete cortical silence (1, 6, 25), to thepoint that they have sometimes been definedas such (26, 27) and that occasional spikeshave been routinely ignored when detected(28, 29). We focused on delta spikes andfound that they are not neuronal noise dueto imperfect silencing of the cortical man-tle. On the contrary, they constitute a com-mon phenomenon potentially implicatingall neurons and all delta waves, and they re-flect genuine processing involved in memoryconsolidation.This observation also provides amechanism

for the documented but puzzling role of deltawaves in memory consolidation: Synchron-ized silence across most of the cortex isolatesthe network from competing inputs whilea select subpopulation of neurons maintainsrelevant spike patterns between epochs ofhippocampo-cortical information transfer(10, 12, 14) and epochs of cortical plasticity(15, 16) and network reorganization (5, 18, 19).Yet, in many cases, cortical activity duringdelta waves could not be reliably predictedfrom the preceding hippocampal ripple activ-ity. Such cortical activity could instead havebeen related to interactions with other brainnetworks. This suggests that delta spikes andassemblies might constitute a general mech-anism of isolated cortical computation beyondthe hippocampo-cortical dialogue.

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ACKNOWLEDGMENTS

We thank N. Maingret for collecting the data and R. Fayat forhelp with the delta wave detection algorithm. Funding: Thiswork was supported by the Agence Nationale de la Recherche(ANR-15-CE16-0001-02 and ANR-17-CE37-0016-01), Collège deFrance (R.T.), and a joint grant from École des Neurosciences deParis Île-de-France and LabEx MemoLife (ANR-10-LABX-54MEMO LIFE and ANR-10-IDEX-0001-02 PSL*) (R.T.). Authorcontributions: M.Z. designed the study. R.T. and M.Z. designedthe analyses and wrote the manuscript. R.T. performed theanalyses. Competing interests: The authors declare nocompeting interests. Data and materials availability: Data inthis study are available at CRCNS (30).

SUPPLEMENTARY MATERIALS

science.sciencemag.org/content/366/6463/377/suppl/DC1Materials and MethodsFigs. S1 to S15Tables S1 and S2References (31–34)

View/request a protocol for this paper from Bio-protocol.

16 May 2019; accepted 10 September 201910.1126/science.aay0616

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Isolated cortical computations during delta waves support memory consolidationRalitsa Todorova and Michaël Zugaro

DOI: 10.1126/science.aay0616 (6463), 377-381.366Science 

, this issue p. 377; see also p. 306Scienceconsolidation.

memorymay be to insulate specific cortical computations taking place in response to hippocampal replay and involved in widespread phenomenon, which could potentially involve all neurons and all delta waves. A critical role of the delta waveIkegaya and Matsumoto). They found that persisting action potential firing during delta waves is an overlooked but Zugaro sought to determine whether this neuronal noise could instead be an important signal (see the Perspective byHowever, upon closer examination, single neuronal action potentials can be detected during delta waves. Todorova and

Delta waves are moments of widespread cortical silence that alternate with active states during slow-wave sleep.Special moments at cortical quiet states

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