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Electroencephalography and clinical Neurophysiology , 1988, 69:532-540 Elsevier Scientific Publishers Ireland, Ltd.
EEG 03335
Spontaneous EEG spikes in the normal hippocampus. II. Relations to synchronous burst discharges 1 Shinya S. Suzuki and Grant K. Smith Department of Psychology, McMaster University, Hamilton, Ont. L8S 4K1 (Canada) (Accepted for publication: 22 October 1987) Summary Spontaneous EEG spikes (SPKs) were recorded from the CA1 region of the dorsal hippocampus in normal rats during awake immobility and slow wave sleep. These SPKs were accompanied by synchronous burst discharges in the pyramidal cell layer. These discharges are called 'population bursts (PBs)' in that they seem to require a population of synchronously bursting neurons. PBs were classified into 2 forms on the basis of their morphologies. One form (mixed burst or MB) consisted of a mixture or superimposition of action potential bursts from a relatively small number of neurons. The other form (ripple) was a series of 3-13 (typically 5-8) high frequency (125-250 Hz) waves, usually waxing and waning. Unit action potentials were superimposed mainly on negative portions of these high frequency waves. The ripple was considered to represent summed activity of highly synchronized complex spike bursts from a relatively large number of pyramidal cells. The similarity in wave structure between these non-pathological ripples and multipeaked, epileptiforrn (interictal) field potentials recorded from the penicillin-treated hippocampus suggests that they may share some common underlying mechanisms.
Key words: Hippocampal EEG spike; Synchronous burst; Ripple; Fast EEG wave; Bilateral synchrony; (Rat)
In the preceding study (Suzuki and Smith 1987) we showed that the CA1 region of the dorsal hippocampus in normal rats generates EEG spikes (SPKs) during behavioral states not accompanied by rhythmic slow activity (RSA or 'theta rhythm'), such as awake immobility and slow wave sleep. These SPKs were positive in stratum oriens, negative in stratum radiatum, and accompanied by synchronous burst discharges in stratum pyramidale. We showed earlier (Suzuki and Smith 1985a) that synchronous bursts could be recorded from both CA1 and CA3 and that they were most frequent during slow wave sleep, slightly less frequent during awake immobility and virtually absent during movement and paradoxical sleep. Buzsaki et al. (1983) showed that, although CA1
1 This work was supported in part by Grant 7465 from the Natural Sciences and Engineering Research Council of Canada. Correspondence to: S.S. Suzuki, Department of Neuroscience, Mitsubishi-Kasei Institute of Life Sciences, 11 Minamiooya, Machida-shi, Tokyo 194 (Japan).
and CA3 bursts occurred nearly simultaneously, the latter were not accompanied by large local field potentials resembling CA1 SPKs. It has recently been reported that comparable bursts or burst-concurrent EEG spikes exist in other hippocampal regions such as dentate gyrus and subiculum (Buzsfiki 1986). Another form of synchronous bursting in the normal hippocampus, the so-called 'ripple,' was first described by O'Keefe and Nadel (1978, pp. 150-153). The ripple consists of a series of 4-10 waves with interwave intervals of 4-8 msec. Such ripples have been recorded near the pyramidal cell layer of the CA1 region during non-RSA states. The ripple usually takes a spindle shape because the amplitudes of individual waves wax and wane in an orderly way. This spindle-like shape as well as the relative invariability of its interwave intervals make the ripple appear stereotypical. Recently, Kanamori (1985, 1986) recorded ripples in the cat hippocampus during non-RSA states, though he called them 'minispindles.' It seems likely that ripples represent a form of synchronous
0013-4649/88/$03.50 © 1988 Elsevier Scientific Publishers Ireland, Ltd.
HIPPOCAMPAL EEG SPIKES A N D SYNCHRONOUS BURSTS
bursting similar to that described by Buzsfiki et al. (1983) and Suzuki and Smith (1985a). The present study was intended to provide further information about the basic characteristics of spontaneous burst discharges associated with hippocampal SPKs.
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Methods
Data were obtained from 16 adult male rats of the Long-Evans strain. Surgical, recording and histological procedures were the same as those described in the preceding paper (Suzuki and Smith 1987). Briefly, under pentobarbital anesthesia (40 mg/kg, i.p.) rats were implanted with a microdrive receptacle unilaterally or bilaterally on the skull over the dorsal hippocampus. After a recovery period of at least 3 days, microelectrode recordings were performed while the rat was placed without restraint on an elevated square (40 × 40 cm) platform with a 4 cm high frame. Synchronous burst discharges were obtained by positioning a movable microelectrode in the vicinity of the CA1 pyramidal cell layer. All microelectrode recordings were derived monopolarly with reference to a screw placed in the bone over the cerebellum. The spontaneous discharges were displayed on a digital oscilloscope and recorded on an X-Y plotter.
Results
Population bursts associated with SPKs As noted in our preceding paper (Suzuki and Smith 1987), the occurrence of each SPK coincided with that of a multiunit burst (or population burst, PB) in the pyramidal cell layer. Fig. 1B indicates the relationship between PBs and SPKs recorded at 4 depths depicted in Fig. 1A. PBs began to appear in stratum oriens where they coincided with or were superimposed on positive SPKs (Fig. 1B1). The amplitude of PBs became maximal in the vicinity of stratum pyramidale just below which SPKs reversed polarity (Fig. 1B2). As the microelectrode moved through stratum radiaturn, along the apical dendritic tree, the amplitude
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Fig. 1. Mixed bursts (MBs), a type of population burst (PB), and associated SPKs recorded at 4 depths in CA1. A: schematic parasagittal section of rat dorsal hippocampus. Numbers indicate recording sites and correspond to those in B. B: MBs (upper trace of each frame) and SPKs (lower trace) recorded at sites shown in A during awake immobility. The same signal was filtered differently for upper (300 Hz-10 kHz) and lower traces (0.15 Hz-80 kHz). Calibration in B1 applies to B2_ 4 (upper trace gain halved). Abbreviations: DG, dentate gyrus; Com, commissural fibers; Sch, Schaffer collateral fibers. Unless otherwise indicated, negativity is upward in this and subsequent figures.
of PBs decreased rapidly while that of now negative SPKs increased to reach a maximum at middle stratum radiatum (Fig. 1B3). With further electrode advancement PBs disappeared altogether and the size of negative SPKs began to decline (Fig. 1B4). Two forms of PBs could be distinguished on the basis of their morphologies, though they apparently represent basically the same phenomenon. One form (mixed burst, MB) consisted of a
i
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S.S. S U Z U K I , G.K. SMITH
mixture or superposition of action potential bursts as shown in Figs. 1B and 2A (see also Suzuki and Smith 1985a). Although complex spikes of individual complex spike cells (see Suzuki and Smith 1985b) were occasionally found in MBs, it was usually impossible to detect the type and number of bursting neurons in an MB. The peak-to-peak amplitude of MBs was less than 1 mV. The other form of PB ('ripple') is a series of 3-13 (typically 5-8) nearly sinusoidal waves with A
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4 - 8 msec periods (Figs. 2B, C, 3 and 5). Unit action potentials were usually superimposed primarily on negative portions of these highfrequency waves (Fig. 2B). Although most ripples appear very stereotypical due to the relative invariability of their interwave periods (Fig. 2C), some variant forms were also noted as shown in Fig. 3. Since the zone (150 250 btm in vertical length) in which PBs could be recorded was wider than the SPK reversal zone, a field potential associated with a PB could be positive, flat, or negative depending on the exact location of the microelectrode. However, the largest amplitude ripples (~< 1.5 mV) tended to be recorded in a positive to null zone, presumably corresponding to the pyramidal cell layer. The ripples presented in Fig. 3 were recorded from the positive SPK zone. Fig. 3] shows a small ripple almost hidden in a positive SPK. A ripple in Fig. 32 ended before an associated SPK reached a peak positivity. Ripples in F i g . 34 and 36 were followed by fast EEG waves with 10-15 msec periods. For the reasons described below these fast waves could be distinguished from ripples. A typical, well organized ripple is shown in Fig. 35.
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Fig. 2. Various forms of population bursts (PBs) in CA1. A1: a complex spike from a complex spike cell. A2_4: MBs with increasing numbers of bursting neurons. AI_ 4 were obtained from the same recording site. B: a stereotypical burst (ripple) superimposed on a positive SPK. Note that individual action potentials were superimposed mainly on negative wavelets. B2 is an expansion of B r Filter settings in A and B are the same as in Fig. lB. Calibration in A applies to B 1. C: stereotypical ripple wave forms can be seen most clearly after bandpass filtering (100 H z - 1 kHz). A, B, and C are from 3 different rats.
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Fig. 3. A variety of ripples and related potentials recorded at a single site in CA1. Ripples are indicated by R. Portions marked by broken lines indicate fast EEG waves. The same filter settings as in Fig. lB. Calibration: 0.2 mV (upper trace), 1 mV (lower trace), 50 msec. See text for further explanation.
HIPPOCAMPALEEG SPIKES AND SYNCHRONOUS BURSTS
A
B
Fig. 4. Polarity reversal of SPKs and phase reversal of fast EEG waves. A: both right (R) and left (L) hippocampal electrodes are in positive SPK zone. B: left electrode is moved to negative SPK zone, while right electrode remains as in A. 1: positive SPKs in A and positive/negative SPKs in B are bilaterally synchronous. 2: RSA and superimposed fast waves. Bilateral RSA waves in A are in phase while those in B are slightly out of phase. 3-4: fast waves on expanded sweep during RSA (3) and non-RSA (4). Note clear phase reversal of fast waves between A and B in both 3 and 4. Filter: 0.15 Hz-80 kHz for all traces. Calibration: 0.5 mV, 200 msec. Time scale in 4 applies to 3.
It is now well established that fast EEG waves (20-100 Hz) above and below the CA1 pyramidal cell layer are phase-reversed (Stumpf 1965; Boudreau 1966; Leung et al. 1982; Buzsfiki et al. 1983). Leung et al. (1982) also indicated that all E E G frequency components are generally in phase at the same depth in the two hippocampi. The data presented in Fig. 4 are consistent with these studies. This figure shows SPKs (1), RSA (2) and fast EEG during movement (3) or immobility (4) recorded from bilateral microelectrodes. In A both right and left microelectrodes were in positive SPK zones while in B the left microelectrode alone was moved down (176 ~m) to a negative SPK zone. Bilateral fast EEG waves appear to be in phase in A but approximately 180 ° out of phase
535 in B. This indicates that the polarity reversal point of SPKs and the phase reversal point of fast EEG waves were at about the same level in the vicinity of stratum pyramidale. On the other hand, in agreement with previous studies (Winson 1974; Leung 1984a, b; Buzs~ki et al. 1985, 1986), RSA phase shift did not occur abruptly but gradually along the whole length of stratum radiatum (compare A2 and B2 in Fig. 4). It should be also noted that the fast EEG was generally higher in frequency during RSA (3) than during non-RSA (4). Fig. 5 presents SPKs (1), ripples (unbroken lines in 2 and 3) and post-ripple fast EEG waves (broken lines in 2) recorded bilaterally from the two hippocampi (CA1). As in Fig. 4 the right microelectrode was stationary in a positive SPK zone while the left microelectrode was moved (176 /~m) from a positive SPK zone (A) to a negative SPK zone (B). Onsets and peaks of bilateral SPKs were almost always simultaneous with minimal latency variations (~< 10 msec) (Fig. 51). The individual wavelets of bilateral ripples did not seem phase-related in that they were sometimes in phase (Fig. 53) and sometimes out of phase (Fig. 52) irrespective of electrode locations. On the other hand, post-ripple fast EEG waves (Fig. 52) phasereversed across the SPK polarity reversal zone in a manner similar to the fast EEG waves superimposed on RSA or non-RSA (non-SPK) slow waves.
Dentate, CA3 and subicular activities The preceding section is concerned with the SPK-concurrent PBs recorded from the CA1 region. It is of interest to know if similar events occur in other hippocampal regions such as dentate gyrus, CA3 and subiculum. As described in the preceding paper (Suzuki and Smith 1987), SPKs and RSA in CA1 reached their amplitude maxima at middle stratum radiatum and hippocampal fissure, respectively. SPKs usually disappeared near the hippocampal fissure, while RSA was decreased in amplitude and increasingly mixed with fast EEG waves in the molecular and granular layers of dentate gyrus (dorsal blade). In dentate hilus RSA was no longer visible and the EEG during movement and immobility almost indis-
536
S.S. SUZUKI, G.K. SMITH
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Fig. 5. Phase relationships between bilaterally synchronous ripples. Electrode placements as in Fig. 4. Left hippocampal (L) electrode is moved from positive SPK point (A) to negative SPK point (B), while right hippocampal (R) electrode is stationary. 1:10 superimposed traces indicate bilateral synchrony of both positive and negative SPKs. Filter: 0.1 Hz-100 Hz. 2-3: bilateral ripples (unbroken lines) are sometimes in phase (2) and sometimes out of phase (3) in both A and B. On the other hand, post-ripple fast waves (broken lines) are phase-reversed between A and B. Filter: 0.1 Hz-10 kHz. Calibration: 1 mY, 50 msec.
Fig. 6. Dentate activities. AI: RSA (a) during movement and SPKs (b) during immobility recorded polygraphically in CA1 stratum radiatum (132 # m below SPK null point). A2: dentate EEGs during movement (a) and immobility (b) recorded in dentate hilus (1014 # m below SPK null point). B: RSA and superimposed fast waves (1), 2 pseudo-ripples (2), and unit discharges (dots in 3a) during a pseudo-ripple (3b), all recorded oscillographically near stratum granulosum. A and B are from 2 different rats. Filter settings: A, 1-35 Hz; B1, B2, B3b, 0.15 Hz-80 kHz; B3a , 300 Hz-10 kHz. Calibration: A, 1 mV, 0.5 sec; B, 0.2 mV (3a), 1 mV (1, 2, 3b) , 50 msec. Voltage calibration and polarity in 3 b applies to B 1 and B2.
3
tinguishable by visual inspection of EEG charts in most rats (see Fig. 6A2). A series of 2-10 ripple-like waves were occasionally recorded near the granule cell layer (Fig. 6B2). This activity, termed here a 'pseudo-ripple,' appears to be different from CA1 ripples for the following reasons: (1) The wave periods of these pseudo-ripples were about 10-20 msec and thus longer than those of CA1 ripples (4-8 msec). (2) Pseudo-ripples were usually superimposed on positive field potentials (30-100 msec) which were much less distinctive than CA1 SPKs. The laminar profile of these potentials or possible relationships between local cell discharges and pseudo-ripples have not been examined in detail. Some cells were observed to fire in phase with pseudo-ripple waves (Fig. 6B3), but others did not show this pattern
4
Fig. 7. Further characteristics of CA1 and dentate activities. 1-2: SPKs (1) and RSA (2) in CA1 stratum radiatum (176 # m below SPK null point). 3-4: pseudo-ripples (broken lines) superimposed on positive potentials (3), RSA and superimposed fast waves (4) in dentate molecular layer (792 /~m below SPK null). 5: pseudo-ripple and unit discharges (dots) in granule cell layer (882 # m below SPK null). 6: ripple-like waves in dentate hilus or CA3c (1176 # m below SPK null). All data are from the same rat. Calibration: 0.2 mV (upper trace), 1 mV (lower trace), 100 msec. Time scale in 4 applies to 1-4 and that in 6 to 5-6. Filter settings as in Fig. lB.
HIPPOCAMPAL EEG SPIKES A N D S Y N C H R O N O U S BURSTS
(Fig. 7B5). Although both CA1 ripples (or PBs) and dentate pseudo-tipples were observed to occur only during behaviors not accompanied by RSA, it is yet to be determined if they occur synchronously. PBs similar to those recorded from CA1 were also recorded from CA3 in 3 rats. Penetrations through the CA3 region did not give a definitive depth profile of either SPKs or RSA. In 5 rats, penetrations were made through the CAl-subiculum border in the posteromedial part of the dorsal hippocampus. These penetrations were characterized by long positive SPK zones with virtually no negative SPK zones. This pattern probably resulted from the fact that the microelectrode tracks were not perpendicular to the orientation of the pyramidal cells in this region. In summary, it appears that both PBs and SPKs with the characteristic depth profile were present in the entire CA1 region (i.e., CAla, CAlb, CAlc). Although the CA3 region was not studied extensively, PBs were clearly present there. However, it is not clear whether they are recordable from the entire extent of CA3. It is also yet to be clarified if PBs or SPKs exist in the subiculum proper or other retrohippocampal structures.
Discussion
The present study has shown that spontaneous SPKs in the hippocampal CA1 region are accompanied by PBs in the pyramidal cell layer. Our bilateral recordings as well as Buzsfiki et al.'s (1983) simultaneous recordings from stratum radiatum and stratum oriens/pyramidale clearlyindicate that both negative SPKs in stratum radiatum and positive SPKs in stratum oriens are concurrent with PBs in stratum pyramidale. We have already suggested that the CA1 SPK represents a massive excitation of middle apical dendrites (stratum radiatum) induced by synchronous discharges of CA3 pyramidal cells via the Schaffer collateral and commissural fibers (Suzuki and Smith 1987). The most convincing evidence for this hypothesis came from our recent experiment (Suzuki and Smith 1988a) indicating that brief high frequency stimuli (mimicking CA3 burst dis-
537
charges) applied to these fibers generate in CA1 population EPSPs and multiple population spikes very similar in wave shape and laminar profile to spontaneous SPKs and PBs (ripples), respectively. PBs could be classified into 2 types, MBs and ripples. The MB is basically a mixture of action potential bursts from a relatively small number of neurons. The ripple is a series of high frequency (125-250 Hz) waves, usually waxing and waning. The duration of both PB types is about 50 msec (20-80 msec). The existence of ripples in the normal hippocampus was briefly mentioned in O'Keefe(1976, p. 97). O'Keefe and Nadel (1978, p. 150) later presented an important figure containing ripples and associated SPKs. Recently, Kanamori (1985, 1986) recorded bilaterally synchronous ripples in the cat hippocampus which have intra-ripple wave frequencies (85-155 Hz) slightly lower than those in the rat. Furthermore, in agreement with our data, Eguchi and Satoh (1987) indicated that unit action potentials were often superimposed on negative portions of intraripple wavelets in the cat hippocampus. At a given electrode site only one type of PB activity could generally be recorded. It is not clear at present what factors contribute to the recording of one type rather than the other at a microelectrode tip. The characteristics (size, impedance, etc.) and precise location of a microelectrode may be among such factors. The number of bursting neurons and the degree of their synchronization may also determine the shape of a PB. An MB may be produced when the number of bursting neurons is small and the degree of synchronization relatively weak. On the other hand, a ripple may be formed when individual bursts from a large number of neurons are highly synchronized. It should be noted that the interwave period of a ripple (4-8 msec) is similar to the interspike interval of a typical complex spike burst from a complex spike (pyramidal) cell (Suzuki and Smith 1985b). Therefore, if many pyramidal cells generate complex spikes nearly simultaneously, the summed activity would look like a ripple. The waxing and waning form of the ripple may be explained in terms of gradually increasing and then decreasing numbers of participating neurons (for a model of synchronous bursting, see Traub and Wong 1983a, b). In
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conclusion, we propose that the ripple is a form of multiple population spikes based on the synchronous burst discharge of a pyramidal cell population. The ripple is somewhat similar in wave structure to the multipeaked field potential (burst) associated with a penicillin-induced interictal spike recorded from the hippocampus in vivo (Dichter and Spencer 1969a, b; Lebovitz 1979) or in vitro (Schwartzkroin and Prince 1978; Gjerstad et al. 1981; Hablitz and Lundervold 1981; Wong and Traub 1983). Inspection of the figures in these studies indicates that penicillin-induced bursts have (1) burst duration of 40-120 msec, (2) 5-15 intraburst waves, (3) interwave periods of about 2-10 msec, (4) waxing and waning wave amplitudes, and (5) peak wave amplitude of up to 10 mV. Except for its smaller amplitude (up to 1.5 mV) the ripple shares essentially all these burst characteristics. This suggests the interesting possibility that the ripple (or more generally PB) and the penicillin burst are based on common underlying mechanisms. Penicillin is known to induce interictal spikes by blocking GABA-mediated inhibition (e.g., Dingledine and Gjerstad 1979; Wong and Prince 1979). Thus it seems possible that PBs and associated SPKs observed in the normal hippocampus may similarly result from a decrease in GABA-mediated inhibition. This hypothesis was supported by our drug experiment (Suzuki and Smith 1988b) in which diazepam (facilitator of GABA-mediated inhibition) suppressed while bicuculline (GABA antagonist) enhanced hippocampal SPKs and associated PBs. In the in vitro hippocampal slice treated with penicillin a CA3 burst was observed to lead a CA1 burst with a latency of up to 20-25 msec (Schwartzkroin and Prince 1978; Gjerstad et al. 1981). Cutting the fibers between CA3 and CA1 resulted in abolition of CA1 bursts but not CA3 bursts. These results indicate that a CA1 burst is triggered by a CA3 burst via the connecting fibers (primarily the Schaffer collaterals). We have suggested earlier that this type of causation might be operative in the generation of the normal S P K / P B in CA1 (Suzuki and Smith 1987; see also Buzs~tki et al. 1983; Buzsfiki 1986). Although action potential bursts accompanied
S.S. SUZUKI, G.K. SMITH
by large depolarizing waves (depolarizing afterpotentials or DAPs) have been recorded intracellularly from pyramidal cells in the intact, anesthetized hippocampus (e.g., Kandel and Spencer 1961 ; Fujita 1975, 1979) as well as in the hippocampal slice bathed in physiological medium (e.g., Schwartzkroin 1975, 1977; Hoston and Prince 1980; Hablitz and Johnston 1981), synchronous bursting has not been reported in these studies. This may be due to the general reduction of neural excitability in these preparations caused by the use of anesthetics (in vivo) or the slicing procedure (in vitro). In agreement with previous studies (Stumpf 1965; Boudreau 1966; Leung et al. 1982; Buszfiki et al. 1983), fast EEG waves were observed to phase reverse across stratum pyramidale in CA1. This means that the phase reversal zone for fast waves and the polarity reversal zone for SPKs are similarly located near stratum pyramidale. Buzsfiki et al. (1983) presented data indicating that CA1 fast waves represent synaptic (IPSP) currents across pyramidal cell membranes induced by the discharge of inhibitory interneurons. In the present study, fast waves were occasionally observed at the end of a ripple. These fast waves may be a sign of recurrent inhibition on pyramidal cells by a ripple-triggered excitation of interneurons. If this is the case, then recurrent inhibition may be hypothesized to play a role in terminating a synchronous burst (ripple). However, the fact that not all ripples are followed by fast waves weakens this hypothesis. Furthermore, there is strong evidence that burst termination in hippocampal pyramidal cells involves self-generated repolarization and afterhyperpolarization (Wong and Prince 1979; Alger and Nicoll 1980; Hoston and Prince 1980; Schwartzkroin and Stafstrom 1980). Although PBs comparable to those in the pyramidal cell layer of Ammon's horn were not recorded from the dentate granule cell layer in the present study (cf., Buzs~tki 1986), ripple-like potentials (pseudo-ripples) were detected in this layer. Two hypotheses may be considered about the possible origin of dentate pseudo-ripples. One hypothesis states that the pseudo-ripple is a series of population spikes similar to the ripple in Ammon's horn. Available data do not support this
HIPPOCAMPAL EEG SPIKES AND SYNCHRONOUS BURSTS
hypothesis. Although single or double population spikes can be evoked from a population of granule cells by stimulation of the perforant path, the major excitatory input to the dentate area, multiple population spikes in the form of pseudo-ripples have never been reported to be evoked by perforant path or any other stimulation (e.g., Lomo 1971). Furthermore, it has been observed that dentate granule cells are much less prone to synchronous bursting than pyramidal cells under penicillin or other epileptogenic agents (e.g., Schwartzkroin and Prince 1978; Fricke and Prince 1984). The second hypothesis suggests that, like fast EEG waves, pseudo-ripples are based on IPSPs across granule cell membranes induced by interneuronal discharges. It should be remembered that the intra-ripple wave frequency of pseudo-ripples (50-100 Hz) is within the range of fast EEG frequencies (20-100 Hz). Although pseudo-ripples and fast EEG waves can be distinguished from each other (i.e., the former occur discretely only during non-RSA states, while the latter are present more or less continuously during most states and tend to be more pronounced during RSA states), the same neuronal mechanism may be utilized for the generation of these 2 types of electrical activity. One possibility is that, in addition to the well established recurrent inhibitory circuit, the direct associational/commissural projection from hilar neurons to inhibitory interneurons in the vicinity of granule cells (see Buzsfiki and Eidelberg, 1981; Laurberg and Sorensen 1981; Swanson et al. 1981; Seress and Ribak 1984) may be involved in the generation of pseudo-ripples (cf., Buzsfiki 1984). In any event, further research is needed to clarify the origin of dentate pseudo-ripples. The authors thank Dr. G. Buzs~ki and Dr. L.S. Leung for comments and discussions.
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