CELLULAR SUBSTRATES AND LAMINAR PROFILE OF
SLEEP K -COMPLEX
F. AMZICA and M. STERIADE*
Laboratoire de Neurophysiologie, Faculte ´de Me ´decine, Universite ´Laval, Quebec, Quebec,
Canada G1K 7P4
Abstract––We describe the cellular mechanisms that underlie the generation of the K -complex, a major
grapho-element of sleep electroencephalogram in humans. First we demonstrate the similarity between
K -complexes recorded during natural sleep and under ketamine-xylazine anaesthesia in cats. Thereafter,
we show by means of multi-site cellular and field potential recordings that K -complexes are rhythmic at
frequencies of less than 1Hz (mainly 0.5–0.9Hz) and that they are synchronously distributed over the
whole cortical surface as well as transferred to the thalamus. The surface K -complex reverses its polarity
at a cortical depth of about 0.3mm. At the cortical depth, the K -complex is made of a sharp and
high-amplitude negative deflection that reflects cellular depolarization, often preceded by a smaller-
amplitude, positive slow-wave reflecting cellular hyperpolarization. The sharp component of the
K -complex may lead to a spindle sequence and/or to fast (mainly 20–50Hz) oscillations. K -complexes
appear spontaneously or triggered by cortical or thalamic stimulation, and they arise within cortical
We suggest that K -complexes, either in isolation or followed by a brief sequence of spindle waves, are
the expression of the spontaneously occurring, cortically generated slow oscillation. ? 1997 IBRO.
Published by Elsevier Science Ltd.
Key words: slow oscillation, sleep, EEG, vertex potentials.
The K -complex (K C) is one of the major grapho-
elements of the electroencephalogram (EEG) and a
faithful landmark of sleep stage.26The K C was
originally described by Loomis and co-workers.21It
consists of a sharp biphasic, initially surface-positive
wave,27often followed by a spindle sequence.26The
K Cs may be elicited by sensory stimulation or may
The electrophysiological substrate of the K C
remains unknown. All studies dealing with the K C
have been limited to the description of this grapho-
element as recorded at the surface of the scalp.
Recent studies in our laboratory revealed the exist-
ence of a slow (<1Hz) cortically-generated oscilla-
tion,35described its relation with other sleep rhythms
within corticothalamic networks,6,32,36and demon-
through intracortical linkages.3,4
Thepresent work is thefirst to explorethecellular
substrates of the K C and to propose that it is
related to some components of the slow cortical
Recording and stimulation
The recordings were performed on acutely-prepared cats
and chronically-implanted cats.
(a) The acute experiments on cats were conducted under
ketamine and xylazine anaesthesia (10–15mg/kg; 2–3mg/
kg, i.m.). The tissues to be incised and pressure points were
infiltrated with lidocaine. The animals were paralysed with
gallamine triethiodide and artificially ventilated with con-
trol of end-tidal CO2at 3.5–3.8%. Body temperature was
maintained at 37–39?C and heartbeat was monitored. The
EEG was continuously recorded in order to maintain a
constant sleep-like state and additional doses of ketamine
and xylazinewereadministered at theslightest EEG change
indicating a tendency toward an activated pattern. The
EEG recordings were made through coaxial macroelec-
trodes with thering placed on thesurfaceof thecortex, and
the tip protruding at a depth of about 1mm. In order to
provide current–source–density (CSD) plots, in some ani-
mals (n=8) weused circular arrays of eight macroelectrodes
separated by 0.25mm at different depths, with the upper
electrode at the cortical surface. The diameter of each
electrode was 0.1mm and the maximum lateral distance
of the upper wire was 0.12mm. Filters were set between
0.1 and 300Hz. Intracellular recordings of cortical neurons
from areas 4, 5, 7 and 17 were performed with glass micro-
pipettes filled with a 3M solution of K acetate (impedance:
25–35M?). The reference electrode was placed in the neck
muscles. All recordings were monopolar. The stability of
intracellular recordings was improved by performing a
bilateral pneumothorax, drainage of cisterna magna, hip
suspension, and filling the hole made for recordings with a
solution of 4% agar. For extracellular unit or multi-unit
dischargesand field potentials, weused tungsten microwires
or coarser glass micropipettes (impedance: 1–5M?).
*To whom correspondence should be addressed.
Abbreviations: CL, centrolateral thalamic nucleus; CSD,
EMG, electromyogram; EOG, electrooculogram; EPSP,
excitatory postsynaptic potential; K C, K -complex; LED,
light-emitting diode; REM, rapid eye movement sleep;
SWS, slow wave sleep; VL, ventrolateral nucleus; W,
wakefulness; WT, wavelet transform.
Neuroscience Vol. 82, No. 3, pp. 671–686, 1998
Copyright ? 1997 IBRO. Published by Elsevier Science Ltd
Printed in Great Britain. All rights reserved
(b) Chronic implantation of EEG, electomyographic
(EMG) and electooculographic (EOG) electrodes, for
assessment of behavioural states in cats, was performed
under ketamine (15mg/kg, i.m.) followed by barbiturate
anaesthesia (somnotol, 35mg/kg, i.p.). Atropine sulphate
(0.05mg/kg, i.m.) was injected to prevent secretions. Two
doses of buprenorphine (0.03mg/kg, i.m.) were given
every 12h to prevent pain after surgery, and an antibiotic
(bicillin) was injected i.m.
operatively. Bipolar coaxial EEG electrodes were inserted
into neocortical areas4(motor), 3(sensorimotor), 17and 18
(visual), 5 and 7 (association), 22 (auditory) and in the
thalamic intralaminar centrolateral (CL) nucleus. Therefer-
encewasplaced in thenasiumbone. A holein thecalvarium
abovetheleft suprasylvian gyrus (areas 5 and 7), which was
sealed between recording sessions, allowed theplacement of
tungsten microelectrodes (impedance of 1–5M?) for unit
recordings. Recordings started after a one week recovery
period. The method used to keep the head rigid without
pain or pressure during the recording sessions was similar
to that previously described.34Animals were not sleep
deprived, and during recording sessions they could move
their limbs and often made postural adjustments.
All bipolar electrodes could be also used as stimulating
electrodes (electric pulses of 0.1–0.2ms and 0.05–0.8mA).
Visual stimulation was achieved through a flash (100ms,
20mcd) from a light-emitting diode (LED) placed at 20cm
in front of one of the cat’s eyes.
The signals were bandpass filtered (0–9kHz), digitized at
20kHz, and stored on tape for off-line computer analysis.
At the end of experiments, animals were given a lethal
dose of pentobarbital and perfused transcardially with
physiological saline followed by 10% formaldehyde. The
brain was removed and stored in formalin with 30%
sucrose. The locations of microelectrodes tracks and stimu-
lating electrodeswereverified on coronal or sagittal sections
stained with thionine.
during three days post-
CSD analyses were performed on averaged evoked or
spontaneous activities recorded with the array of eight
electrodes. The averaging of the spontaneous activity was
doneon 2ssweepssymmetrically extracted around thepeak
of K Cs detected in the deepest (1.75mm) lead. The current
flowing into or out of thecellular membraneisproportional
to the second spatial derivative of the potential.14The
calculation of this second derivative is made according to
the following formula:24
where ?(z) is the potential at location z, ?z is the distance
between adjacent recording sites (in our case, ?z=0.25mm,
the distance between two electrodes), and n·?z represents
the differentiation grid (in our case, n=1).
In order to eliminate all other signals contained in the
EEG that do not contribute to K Cs, field potentials under-
went digital filtering with a procedure that is based on the
wavelet transform (WT; F. Amzica, unpublished observa-
tions). For a given time series, the WT detects and locates
thepresenceof a given shape.2In our case, weobserved that
K Cs resemble the wavelet of Daubechies8and we based
our filtering on a direct WT that detects the presence of
Daubechieswavelets. Next, theensuing transformpassed an
amplitude gate and a frequency gate that left only those
components of higher amplitude (10 times the standard
deviation of the original signal) and of a given duration (a
K C usually lasts for 200–300ms27). Finally, this signal was
inversely wavelet transformed to provide the filtered EEG
where only K Cs appear.
Dynamic relations between K Cs occurring at different
sites were disclosed by sequential cross-correlations4calcu-
The analysis consists in extracting from a pair of digitally-
filtered leads sequential windows of 5s duration and
cross-correlating each of them. The resulting sequential
cross-correlations are represented as topograms that are
generated by uniting with a line all points with the same
height and by shading correspondingly theinner part of the
closed curve. The convention assigns white to high positive
values, while negative values are shaded with black.
Data presented in this paper contain 220 intra-
cellular recordings, from 50 acutely-prepared cats.
Three chronically-implanted animals provided extra-
cellular recordings of single-units (n=45) and field
potentials during various behavioural states.
Various shapes and the incidence of K Cs are
displayed in Fig. 1 during natural sleep and anaes-
thesia, in intracortical recordings from the same
chronically-implanted cat. These recordings were
performed in order to further validate our cellular
recordings, performed mostly under anaesthesia (see
below), and consisted in injecting i.m. the ketamine
and xylazine dose usually employed in acute exper-
iments, while the cat was under continuous record-
ing. Thefour insetsexpand a K C fromeach group of
recordings. In this and all other figures the polarity
of the signals is as in intracellular recordings, i.e.
with the positivity upwards. Comparing the electro-
graphical patterns of EEG during sleep and under
anaesthesia in cat, it was clear that they shared
common features: (i) light sleep was marked by less
regular spontaneous K Cs (Fig. 1 up), occasionally
triggering spindles (see insets at right); (ii) as sleep
deepened, the K Cs became more rhythmic, at a
frequency of lessthan 1Hz; (iii) thesamepattern and
similar values for rhythmicity were obtained in the
same animals after anaesthesia with ketamine and
xylazine. As expected, the anaesthetic state was
characterized by much more stable and rhythmic
patterns than thestateof natural sleep. Figure1 also
shows that K Cs are reflected in the thalamic record-
ing fromCL nucleus. This observation sheds light on
corticothalamic interactions in the generation of
sleep oscillations (see Discussion).
The slow rhythmicity of K Cs is demonstrated
by means of power spectra computed from periods
of 2min stable sleep patterns (Fig. 2). Both sleep
features, with a peak below 1Hz. Theaveragevalues
obtained from 20 such episodes were 0.8?0.14Hz
(mean?S.D., range 0.2–1Hz) for deep sleep, and
0.7?0.1Hz (range 0.5–0.9Hz) for deep anaesthesia.
Light anaesthesia and light sleep spectra weredevoid
672 F. Amzica and M. Steriade
of peaks in the 0–1Hz band, but expressed a broad
band component (Fig. 2, lower traces), probably due
to thearrhythmic, however slow, occurrenceof K Cs.
Theresemblancebetween theelectrographic patterns
during ketamine-xylazine anaesthesia and those in
natural sleepwasreportedincats30andasimilar slow
Synchronization of K-complexes
Similarly to the slow (<1Hz) oscillation, K Cs
appeared synchronously in all investigated areas of
the cortex. The topograms in Fig. 3 derive from
digitally filtered traces (seeExperimental Procedures)
and display the evolution of K Cs’ synchrony in a
Fig. 1. Rhythmic K Cs in a chronic cat and comparison of their features during natural sleep and under
ketamineand xylazineanaesthesia in thesameanimal. Depth monopolar recordings. Notesimilar features
during light sleep and light anaesthesia on one hand, and during deep sleep and deep anaesthesia on the
other. Cortical K Cs are also reflected in the CL nucleus of the thalamus. At the right of each group of
recordings, a K C (within squares) is expanded. Note the presence of spindles accompanying the K C
during light sleep or anaesthesia, and their diminished incidence in deep sleep or anaesthesia. In this and
following figures, the polarity of field potentials is as in intracellular recordings (negativity downwards).
Cellular substrates of the K -complex673
complete waking–slow wave sleep–rapid eye move-
ment (REM) cycle. The synchrony became stronger
with thedeepening of sleep, to attain its highest level
just prior to REM onset. This process also depended
on thedistancebetween therecorded sites: synchrony
was achieved earlier between sites located closely
both spatially (areas 5 and 7) and functionally (areas
7 and 18). Synchronization of K Cs was present but
less obvious in cortical areas that are connected by
long-range and indirect pathways (areas 18 and 4).
The slowly (<1Hz) oscillating K Cs were reflected at
the CL thalamic level (Figs 1, 3), a nucleus that has
widespread linkages with the cortex.17An average
over 20 sleep periods of the cross-correlation peak
was 0.92?0.15 for closely located and functionally
related sites(e.g., areas5and 7). It could reach values
as low as 0.54?0.21 for distant and unrelated areas
(e.g., areas 18 and 4). The mean thalamocortical
cross-correlation coefficient was 0.67?0.19.
Cellular correlates of spontaneous K-complexes
The transition from waking to sleep in a naturally
sleeping cat is shown in Fig. 4, with simultaneous
surface and depth field potential recordings together
with an extracellularly recorded neuron, all in corti-
cal area 5. The first 8–10s (left side of the upper
panel) depict a waking pattern, with activated EEG
and tonic firing of the neuron. The onset of sleep
coincided with the appearance of slower and ampler
waves that may represent vertex waves or biparietal
humps.12These waves were reversed between the
surface and the depth. At the same time the cellular
discharge diminished and tended to show a certain
slow rhythmicity. Looking at the cellular data,
we propose that vertex waves and K Cs represent
basically thesamephenomenon, at different stagesof
sleep development. At the cortical depth, the first
well-defined K C (a in Fig. 4) was a reversed wave,
starting, in thedepth, with a focal positivity, continu-
ing with a sharp focal negativity during which the
neuron displayed a high discharge rate (see detail
in panel a). As sleep developed, several such K Cs
appeared and some of them were followed by clear-
cut spindles (detail b in Fig. 4). Although the EEG
pattern showed occasionally compound waves that
rendered more difficult the recognition of K Cs, we
could identify them in relation to neuronal firing,
knowing that cells’ discharges generally occur during
the depth-negative (surface-positive) waves. It thus
became obvious that K Cs are rhythmic, at about
0.3Hz. Theaverageof 25 K Cs aligned on thedepth-
negativepeak (dotted lineinthelowest, right panel of
Fig. 4) provides the shape of a generic K C and
the comparison with the digitally-filtered K C (see
The study of cellular bases of the K C requires
intracellular recordings that, because of stability
problems, are performed on anaesthetized animals.
Since the mixture of ketamine and xylazine is one of
the agents that best mimic slow wave sleep (see Fig.
1), we used it as an anaesthetic (see Experimental
Procedures). Figure 5 presents two simultaneous
(intra- and extracellular) recordingsin cortical area 5,
together with field potentialsfromthesurfaceand the
depth of the same area. An initially activated period
(2–3s) developed into a slowly-oscillating (about
0.9Hz) pattern. Thisslow oscillation wasmadeup by
waves that resembled those of the K Cs, already
depicted in Fig. 4 (see also the averaged traces in the
lowest right panel). The K Cs recorded at the depth
were reversed in polarity and their sharp negative
deflection was associated with the onset of a mem-
brane depolarization and with increased cellular
firing. The first K C in the sequence (Fig. 5a) was
followed by two wavelets that may be considered as
Fig. 2. Slow rhythmicity of K Csasdisclosed by power spectrumof cortical field potential activity (area 4).
Both panels result from the same chronic animal, first during natural sleep (left), thereafter under
ketamineand xylazineanaesthesia (right) administered whilethecat was under continuous recording (see
Experimental Procedures). Each trace was computed from a 2-min recording divided in 10 consecutive
windows, by averaging the power spectrum of each window. The ordinates of the two graphs have the
same range. The upper traces display a peak at a frequency <1Hz, for deep sleep and deep anaesthesia,
674F. Amzica and M. Steriade
an abortive spindle. As anaesthesia deepened, the
incidence of spindles increased and their shape was
moreapparent (Fig. 5b, c). Another featurethat was
present during the depolarizing phase of the slow
oscillation, especially toward its end, werefast waves
recurring at around 30Hz. They were abolished
during the hyperpolarizing phase of the slow
The same cell-to-field relation was also recorded
in putative dendritic impalements (Fig. 6; n=5).
Dendritic recordings were considered when all of
the following criteria were met: i) upon impalement,
the membrane potential dropped suddenly below
?60mV; ii) the spikes were triggered at variable
thresholds and had various amplitudes as one
would expect if they would be generated at multiple
Fig. 3. Synchrony of K Cs during progression from waking to resting (light and deep) sleep and further to
REM sleep. Field potential recordings in a chronically-implanted cat. Each topogram depicts sequential
cross-correlations between digitally filtered (Wavelet Transform) waves from thesites indicated abovethe
respectivetopogram. Theabbreviationson theright sideof thetopogramsindicatewaking (W), light sleep
(light S), deep sleep (deep S) and REM sleep (REM). Central white areas denote good synchrony. Thus,
closely-situated (cortical areas 5 and 7) or functionally-related (cortical areas 7, 18 and thalamic CL
nucleus) foci tend to synchronizefaster and better with progression towards deep sleep. Cortical areas 18
and 4 show less synchronization and only during deep sleep.
Cellular substrates of the K -complex675
dendritic hot spots; iii) some spikes generated at
different sites would superimpose in time with delays
of less than 3ms (Fig. 6, lowest panels); otherwise,
the inactivation of Na–K pumps would prevent the
occurrence of such fast doublets; iv) the recording
remained stable for long periods of time (>30min),
ruling out signs of injury. Under such circum-
stances, the onset of a K C was associated with a
membrane depolarization of about 20mV (Fig. 6).
Sometimes, the end of the depolarization was
Fig. 4. Progressive appearance of K Cs with onset of sleep and their relation with cellular discharges in a
naturally-sleeping cat. Surface- and depth-EEG, and extracellular recordings from cortical area 5. The
upper three traces display the transition from waking to light sleep. The fast and low amplitude EEG
background is progressively superimposed by irregular humps (positivein surface, negativein depth) and
sleep spindles. The cellular discharge begins to show silent periods, as opposed to the tonic firing in
waking. As sleep deepens (second group of traces, below, continuing the upper one), the firing of the cell
becomes grouped at the rhythm of the slow oscillation (around 0.3Hz) and occurs in coincidence with
spiky EEG waves (negative in depth, reverted at the surface) that we regard as K Cs. The peak of these
complexes is preceded, similarly to those under anaesthesia, by a depth positivity during which there is
silenced cellular firing (detail a), and may be followed, as sleep deepens, by a spindle sequence (detail b).
The average of 25 K Cs (AVG), centred on the peak depth-negativity, shows potential reversal between
surfaceand depth. Thethickened lines represent theK Cs after digital filtering with thewavelet transform
(see Experimental Procedures).
676F. Amzica and M. Steriade
marked by a supplementary depolarization (Fig. 6,
short arrow in the right panel) followed by a long-
lasting hyperpolarization, probably a slow after
K Cs werenot confined to a particular cortical site.
Fig. 7 depicts slowly-oscillating cells and associated
K Cs in functionally distinct and spatially separated
areas, such as visual (area 17) and motor (area 4)
cortices. Both visual and motor cortical cells oscil-
lated slowly at a frequency of <1Hz. The cellular
oscillation was synchronous with depth field poten-
tials: wave negativities were present at the onset of
Fig. 5. Rhythmic K Cs (around 0.9Hz) under ketamine and xylazine anaesthesia. Recordings from
association suprasylvian cortex (area 5). The depicted period contains a short epoch of activated EEG
(left) followed by the recovery of the slow oscillation. The intra- and extracellular activities are
accompanied by the EEG recordings in the surface and in the depth of the cortex. The K Cs display a
potential reversal between the surface and the depth. The rhythmic negative peaks in the depth reflect
cellular excitation (see depolarization of the membrane potential in the intracellular recording, and tonic
firing in the extracellular recording) and are followed by spindles and/or by fast activities in the 40Hz
range. Thesenegativepeaks arepreceded by a slow, depth-positivewaveassociated with neuronal silence.
The evolution from the activated epoch (left) to the deep anaesthesia is paralleled by a progressive
propensity of the K Cs to drive spindles. The first K C (detail a) elicits an abortive spindle with only two
cycles. As anaesthesia recovers deeper states, spindles arebetter developed (details b and c), as onewould
expect from a process achieved under higher synchrony. The average of 25 K Cs centred on the depth
negative peak (AVG) further emphasizes the potential reversal of the K C occurring between the cortical
surface and depth, and the relation between cellular activities and field potentials. The thicker line (WT)
represents the depth averaged K C after digital filtering with the wavelet transform (see Experimental
Cellular substrates of the K -complex677
thedepolarizing phaseof theslow cellular oscillation,
whiledepth positivities occurred during theneuronal
silence. Stimulation of the ventrolateral nucleus
(VL) of the thalamus evoked K Cs in motor cortex
(bottom of Fig. 7B). The initial synaptic response
produced a depth-negative wave in the neighbouring
field potential recording, and was followed by an
inhibition and a rebound excitation at a latency of
about 200ms, that we regard as a K C. This is
in accordance with those authors who consider
the K Cs as secondary sensory-evoked potentials
The stimulation of the cat’s eye with a LED flash
elicited an ample response in the primary cortical
visual area, consisting of two early fast components
(Fig. 8). Part of these fast components could be
traced to thesomatosensory area 3 and auditory area
22 (although the LED flash was completely silent).
The fast responses were identical during wakefulness
(W) and slow wave sleep (SWS). The difference
between the photically evoked responses in W and
SWS states was marked by the presence of a late
biphasic, positive–negativewaveduring sleep (square
in Fig. 8). The latter represents the K C. Similar
waves, with diminished amplitude (arrows in Fig. 8),
can also be recognized in cortical leads that are
not directly related with the visual stimulus (areas 4
Under anaesthesia, K Cs were evoked by cortical
and thalamic stimulation. Virtually all cortical
neurons (95%) responded with K Cs to cortical or
Fig. 6. Rhythmic K Csin a presumed dendritic recording (seetext) froma cat under ketamineand xylazine
anaesthesia. The variations of the membrane potential are very similar to those of the somatic
impalements and have the same correspondence with neighbouring depth-field potentials (FP). The two
epochsin thesquaresareexpanded below to show a K C followed by a few wavesat delta frequency (left),
and a K C ending with a sustained excitation (right). Thelatter is expressed in theFP by a sharp negative
deflection (short arrow) and yields to an inhibition (long arrow). The periods underlined with an open
square are presented in further detail in the bottom panels. They show the variable amplitude of the
dendritic spikes and the presence of short-lasting inhibitory postsynaptic potentials.
678 F. Amzica and M. Steriade
thalamic stimulation. K Cswereampler with stronger
stimulation and if the stimulation site was closer
to the recorded site. Rhythmic K Cs, spontaneously
occurring during the slow oscillations (Fig. 9A,
upper traces), were mimicked by cortical stimulation
(Fig. 9A, lower traces) and by thalamic stimulation
(Fig. 9B, left panel). The cortical stimulation elicited
a monosynaptic excitatory postsynaptic potential
(EPSP; see detail at right in Fig. 9A) followed by a
long-lasting hyperpolarization. The rebound from
the latter corresponded, in the field potential trace,
to a K C.
It has already been demonstrated that
slow (<1Hz) oscillation is synchronized through
Fig. 7. K Cs are present, spontaneously as well as evoked, in visual and motor cortices. Intracellular and
field potential recordings. (A) Rhythmic K Cs in primary visual area 17 recurring every 3s. (B) Upper
panel: similar pattern in motor cortex. Note close relation between onset of cellular excitation and
depth-negative field potentials. Below: motor cortex responses evoked by stimulation of the thalamic VL
nucleus. The K C (K ) appears as a late component after the early synaptic excitation.
Cellular substrates of the K -complex679
intracortical linkage.4This property may thus be
extrapolated to the K Cs. In the present study we
indeed show that the thalamically-induced K C
spread on large areas of the cortex by means of
intracortical pathways (Fig. 9B). Stimulation of the
thalamic CL nucleus elicited an early excitation in
cortical area 5 that was reflected with some delay in
the posterior area 7 (see inset from the left panel of
Fig. 9B). This fast cortical excitation was followed,
similarly to the cortically induced K C, by a long-
lasting hyperpolarization (positive wave in the depth
field potential recording) and by the rebound K C.
The fact that the K Cs evoked at the posterior
location were also time-lagged with respect to the
anterior ones was taken as an indication that, in this
case, the K C was generated primarily in the anterior
site and then propagated to the posterior one. After
having recorded the control evoked K Cs, we separ-
ated, in five animals, the two cortical sites by a large
and deep transection. The lesion extended from the
marginal to the ectosylvian gyrus (black bar in the
figurine of the left panel from Fig. 9B), and for
10mm up to the white matter. This transection
produced a loss of evoked K Cs in the posterior
cortical area 7(Fig. 9B, right panel). Thebackground
activity of thissitewasnot affected by thetransection
and continued, in the absence of the stimulation, to
display spontaneous rhythmic K Cs. This activity was
however asynchronous to the one observed at the
anterior site (not shown).
Depth profile of the K-complex
The comparison of the thalamically-evoked K C
with the spontaneously generated one is made in
Figs 10, 11. Thesamenumber of sweeps (n=50) were
averaged to generatea spontaneous(Fig. 10, left) and
an evoked (Fig. 10, right) K C. Recordings were
performed simultaneously at eight depths of thearea
5 cortex. The shapes of the two K Cs were similar, as
shown by theexpanded windowsin thebottomof the
figure, and have an identical laminar distribution.
The potential reversed at a depth of about 0.3mm.
The CSD analysis (Fig. 11) for the two K Cs
displayed in Fig. 10 demonstrated similar patterns
(see especially the underlined sequences): a massive
sink between 0.3 and 0.6mm, i.e. in cortical layers
II–III, corresponding to the input of intracortical
linkages.5This sink was confined by a superficial and
a moreprofound source. Theresult was consistent in
all eight cats and it was checked by moving the CSD
electrodes up and down by 0.1mm (about half of the
interelectrode distance) and maintaining the source–
sink distribution at the same depth from the cortical
The main finding of this paper is that the slow
(<1Hz) cortical oscillation35underlies the genesis
of K Cs. This implies that K Cs are rhythmic and
that some properties already described for the slow
oscillation are also pertinent to the K C. With the
benefit of hindsight, one can detect rhythmic K Cs
in different figures of earlier investigators (see, e.g.,
Fig. 14 in Ref. 21 and Fig. 34 in Ref. 19).
Relevance of animal studies to humans
In this study we show that K Cs in cats are similar
in shape during natural sleep and under anaesthesia,
and that they occur with a similar incidence (Fig. 1).
Thefirst approach in detecting K Csin cat’sEEG was
made with intracortical recordings showing, at a
macroscale, that depth-recorded K Cs are reversed in
polarity compared to surface-recorded ones (Fig. 4).
To reveal the cellular substrate of K Cs, we used
anaesthetized preparations and showed that keta-
mine and xylazine anaesthesia is a faithful tool for
the study of sleep oscillations (Fig. 1). K etamine
has already been reported to effectively induce a
slow-wave sleep pattern.11X ylazine, an ?2receptor
agonist, may exert a doubleeffect: first, it increases a
Fig. 8. Averages (n=60) of visual evoked potentials in
cortical areas 17, 22, 3, and 4 during waking and sleep. The
stimulus consisted of a flash of 100ms delivered by a light-
emitting diode (LED). The visual cortex response consisted
of two successivesharp negativedeflections(latency: 50ms),
regardless of the vigilance state. These fast responses were
also reflected in area 22 during waking, and in other areas
during sleep. The state-dependent difference between the
evoked potentials consisted in the appearance of a K C
(square) during sleep in the visual cortex. The oblique
arrowsmark a similar latecomponent in thesomatosensory
and motor evoked responses. Theaveraged EOG and EMG
are added to demonstrate diminished amplitude of eye
movement and muscular tone during sleep.
680F. Amzica and M. Steriade
slow K+conductance25that might be involved in
the generation of the long-lasting hyperpolarizations
which shape the slow oscillation. Second, xylazine
blockstheactivity of locuscoeruleusneuronsprevent-
ing thus the release of norepinephrine.10It is known
that the blockade of the slow cortical oscillation by
stimulating brainstem-activating systems is achieved
through the suppression of these long-lasting hyper-
polarizations,31and that both acetylcholine and
norepinephrine block slow K+currents.28
In contrast to the stability of the EEG pattern
during anaesthesia, the natural sleep EEG almost
continuously shifts between different stages. This
suggests that the sleeping brain is much more
influenced by its environment
thought. There are, however, short periods of stable
oscillating EEG during natural sleep (see Fig. 1).
During transitional periods, neuronal populations
probably undergo competing influences that are
reflected in polymorphic waveforms.
Fig. 9. Comparison between spontaneous and evoked K Cs. (A) Intracellular (area 7) and field potential
(area 5) recording in a ketamineand xylazinepreparation. Stimulation of cortical area 5 (black rectangles
in the lower traces) elicited K Cs with shapes similar to the spontaneous ones (upper traces). The second
stimulus (square) is expanded at right to show the early synaptic response of the cell and its reflection in
thefield potential. (B) Similar K Cs could beelicited by thalamic (CL) stimulation. Thethick traces depict
averaged (n=50) evoked responses. Below each average, four individual sweeps illustrate the individual
variability. Theleft panel corresponds to thecontrol situation, with intact cortex. Therecording locations
are indicated in the figurine. Note the early responses in the detail (bottom). K marks the occurrence of
the K C. Right panel: after cortical transection, K Cs were elicited only at the anterior recording site.
Cellular substrates of the K -complex681
Cellular bases of the K-complex
The K Cs reflect, at the EEG level, a slow oscil-
lation generated in the cortex. During the slow oscil-
lation, the membrane of cortical neurons alternates
between a depolarized and a hyperpolarized potential
(Fig. 5; see also Ref. 35). The depolarized phase
expresses the synaptic bombardment of the cell and
contains both excitatory and inhibitory potentials
(Fig. 6; see also Ref. 35). The hyperpolarized phase
of the slowoscillationcontains short-lasting
inhibitory potentials,35but is mainly dueto a general
disfacilitation of the network.7
The frequency of the slow oscillation is state-
dependent. Various anaesthetics ‘‘freeze’’ the oscil-
lation at preferential values: urethane covers the
lowest range (0.3–0.4Hz, see Ref. 35), ketamine and
xylazine mostly produces a frequency of 0.5–0.9Hz
(mode at 0.7Hz; Fig. 2) that is overlapping with the
one recorded during natural sleep. The similarity
between natural sleep and anaesthesia (ketamineand
xylazine) patterns is reinforced by the fact that the
Fig. 10. Laminar distribution of spontaneous and thalamically-evoked K Cs. Simultaneous recording with
an array electrode at various depths of cortical area 4 in a cat under ketamine and xylazine anaesthesia.
Left column: average (n=50) of spontaneous and rhythmic (around 0.5Hz) K Cs centred on the peak
negativity of the deepest lead. Potential reversal occurred around the depth of 0.3mm. Right column:
evoked responses (n=50) at thesamerecording siteby stimulation of thethalamic CL nucleus. Theinitial
excitation-inhibition potential was followed by a wavethat was similar in shape, laminar distribution and
time-coursewith thespontaneousK C (left). To further emphasizetheir similarity, theboxed sequencesare
expanded below. Thecorrelation coefficientscalculated between spontaneousand evoked K Csrecorded at
the same depth, and within the depicted window, ranged from 0.9 to 0.95, with exception of the couple
situated at the isoelectric potential for whom the value is 0.85.
682 F. Amzica and M. Steriade
comparison was done in the same animal, within the
same recording session (Fig. 1). Although natural
sleep is marked by continuous shiftings and by
transients with arrhythmic K Cs, a general tendency
of acceleration from early stages of sleep (below and
around 0.5Hz) towards deep sleep (around 0.9Hz)
has been detected (Fig. 1). The periods with less
rhythmic K Cs or K C-like potentials (Figs 2, 6)
raise the issue of the limit between oscillatory and
non-oscillatory events. In a sense, an oscillation is
any variation of a phenomenon between two states.
A more restrictive definition also requires the vari-
ation to be regular. Regularity may become itself a
loose term and there are few, if any, absolute regu-
larly oscillating phenomena in biology. Therefore, in
accordancewith practical considerations that require
for spectral analysis time windows with durations of
at least 10 times the period of the oscillation under
Fig. 11. Current source density (CSD) of the spontaneous and CL elicited K C. These topograms
correspond to thewavespresented in Fig. 9and arepresented at thesametime-scaleasin that figure. Both
imagesshow, during thepeak of theK C (underlined epochs), a sink at a depth of 0.5mm, confined by two
sources, one superficial and the other in deeper layers.
Cellular substrates of the K -complex683
investigation, we think that any variation with at
least 10 cycles within a given frequency range could
be accepted under the term oscillation, and that
additional quantification of the regularity should
complement the oscillation. In this context, we think
that K Csreflect a trueoscillation asdemonstrated by
recordings in anaesthetized preparations, and that
the irregularities observed during natural sleep
should be regarded under the angle of disturbing
drives induced in a living, intact network. As to the
quantifications of the slow oscillation, the reader is
referred to previous papers.3,35,36
K Cs are synchronized in all recorded sites. This
feature is illustrated in Fig. 3 and comes as no
surprise since the slow oscillation is synchronized
in the corticothalamic network.3,6,32This further
implies that K Cs are transferred to the thalamus
(Fig. 1). In an intact brain, the thalamus may rein-
force the slow oscillation of the K Cs by feed-back
The slow oscillation is the outcome of the cortical
network and therefore we state that the K C is
generated in thecortex. Theslow oscillation survives
in the cortex of athalamic cats.36It has been shown
that thesynchrony of theslow oscillation isdisrupted
by interrupting intracortical linkages between the
recorded sites.4The disconnected sites continued
however to oscillate independently in the same slow
frequency range. In the same line of thinking, K Cs
that were evoked by cortical or thalamic stimulation
(Fig. 9) propagated through the cortex beyond the
area of their generation. This propagation was
impaired by cortical transections, thusreinforcing the
idea that K Cs are generated in the cortical network.
Further confirmation for the cortical origin of the
slow oscillation came from thalamic recordings of
decorticated cats where the slow oscillation was
absent.37The depth profile of the K C calculated in
this paper indicates the presence of a massive sink
in cortical layers II–III (Fig. 11), consistent with the
depth where intracortical projections contact the
apical dendrites of deeply-lying pyramids.5Long-
range projections, spanning over 2–8mm, have
been described in the visual,13,22somatosensory,18
auditory15and motor20cortices. They appear to exert
The IFSECN16suggests the use of the same term
for vertex potentials and K Cs. Both have, at the
EEG level, similar shapes but are expressed during
different sleep stages.26Our electrophysiological
description suggests in addition similar cellular
behaviour underlying vertex waves and K Cs (Fig. 4).
The isolated appearance of vertex potentials during
early sleep stages coincides with the onset of the
slow oscillation and with the relatively lower syn-
chronization of thecortical network. As thenetwork
becomes more and more synchronized and the slow
oscillation spreads coherently over larger territories,
vertex potentials become ampler (>250µV) and are
recognized as K Cs.
Human vertex potentials as well as K Cs havebeen
reported to attain their highest amplitude at the
vertex.26In thispaper weshow that K Csappear over
all recorded areas in cat, such as motor area 4 (the
equivalent of the human vertex), association areas 5
and 7, and visual areas 17 and 18. This finding is not
in contradiction to previous descriptions of the K C
because many of those studies, performed on human
EEG, were based on bipolar recordings. These
tend to obscure the equipotential events. Monopolar
recordings in humans have also shown the presence
of K Cs in parietal and occipital areas.4aOur
monopolar intracortical recordingswith electrodesof
higher impedance than the ones used in scalp EEG,
referenced to a paralysed muscle (in acute exper-
iments) or to nasium (in chronic animals), provide
potentials that express the activity of local neuronal
pools. Besides, cellular discharges reflect the global
coherence of K Cs (Figs 4–7).
K -complexes are also elicited by stimulating corti-
cal or subcortical structures. In agreement with
previous papers, our data point to the cortical origin
of the evoked K Cs. Davis and co-workers9consid-
ered thesecondary dischargeasa K C. Inour view, an
afterdischarge like the one in Fig. 8, present only
during sleep, represents a K C. We cannot expect for
absolute identity between the shapes of spontaneous
and evoked K Cs, simply becausethey vary within an
epoch and even more from one stage to the other.
However, during stable episodes, the similarities
plead rather for identity in the mechanisms generat-
ing the K C, and more so since their depth profile is
identical (Figs 10, 11). On the other hand, identity
does not mean that all spontaneous K Cs are in
fact triggered by sensory stimuli. The state of sleep
develops in rather sensory-free environments and it
would be hard to believe that this would generate
rhythmic stimuli to account for the slow oscillation
of the K Cs. Therefore, the evoked K Cs are the
exception rather than the rule. The wide majority of
K Cs that permeate our sleep stem from the slow
(<1Hz) cortical oscillation.
As already discussed for the slow oscillation, the
K C is transferred to thethalamus (Figs 1, 3) and has
an important rolein synchronizing thethalamocorti-
cal network during sleep and in triggering various
other sleep oscillations such as spindles and thalamic
intrinsic delta.6,32,36Delta wavesand delta oscillation
should not be used interchangeably. In the current
practice, delta waves are waves with a duration of
more than 1/4s,16while delta oscillation is made
of rhythmic events at a frequency of 1–4Hz. The
mechanisms providing cortical EEG with delta oscil-
lation remain unclear. Thalamocortical neurons are
able to generate an intrinsic clock-like oscillation in
thefrequency rangeof 1–4Hz.23,33However, thelack
of intranuclear collaterals in most dorsal thalamic
nuclei17diminishes the probability of synchroniz-
ationof theintrinsic delta oscillationat itsvery siteof
origin and its transfer to thecortex whereit could be
684 F. Amzica and M. Steriade
incorporated in the EEG. A replacing mechanism is
the synchronized drive to the thalamus from the
cortex,33that periodically resetsthethalamic intrinsic
delta. This role could be accomplished by rhythmic
K Cs that would set into action, every 1–2s, a
sequence of clock-like delta oscillations. Besides the
thalamically generated clock-like delta oscillation,
the existence of a cortically-generated delta oscil-
lation (1–4Hz) has been demonstrated in chronic
athalamic preparations.39The cellular correlates of
the latter oscillation remain still unexplored. Our
studies disclosing a slow (<1Hz) cortical oscil-
lation35have demonstrated that this is an oscillation
distinct from the delta one (see also Ref. 1). Indeed,
the slow oscillation groups the delta oscillation (see
Fig. 3 in Ref. 36). The present paper shows that K C
isanelectrographic expressionof theslow oscillation.
Through its shape, the K C contains delta waves (see
definition above) that have to be dissociated from
delta oscillation. Nevertheless, both delta waves
and delta oscillations contribute unspecifically to the
power spectrum of the delta (1–4Hz) band. The
mixture of K Cs with field potentials reflecting delta
oscillations may therefore be at the origin of the
difficulty in separating K Cs from the so-called delta
EEG during deep stages of sleep.
Recently, it has been demonstrated that synchro-
nized fast (30–40Hz) oscillations are present during
sleep, overriding the depolarizing phase of the slow
oscillation.30Due to the widespread synchronization
at its onset, the K C becomes a periodic promoting
factor for the synchronization of fast activities
during sleep. Previous experiments have indeed
shown that weakly-synchronized fast thalamocortical
oscillations at 30–40Hz become robustly coherent
over a time-window of 600ms after a synchronized
Acknowledgements—We are thankful to P. Gigue `re and D.
Drolet for technical assistance. Thisstudy wassupported by
the Medical Research Council of Canada and the Human
Frontier Science Program. F.A. is a postdoctoral fellow,
partially supported by the Fonds de la Recherche en Sante ´
du Que ´bec.
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(Accepted 29 May 1997)
686 F. Amzica and M. Steriade