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Logo of nihpaAbout Author manuscriptsSubmit a manuscriptHHS Public Access; Author Manuscript; Accepted for publication in peer reviewed journal;
J Neurophysiol. Author manuscript; available in PMC 2010 September 20.
Published in final edited form as:
PMCID: PMC2941800

Propagating wave and irregular dynamics: Spatiotemporal patterns of cholinergic theta oscillations in neocortex, in vitro


Neocortical “theta” oscillation (5- 12 Hz) has been observed in animals and human subjects but little is known about how the oscillation is organized in the cortical intrinsic networks. Here we use voltage-sensitive dye and optical imaging to study a carbachol/bicuculline induced theta (~8 Hz) oscillation in rat neocortical slices. The imaging has large signal-to-noise ratio, allowing us to map the phase distribution over the neocortical tissue during the oscillation. The oscillation was organized as spontaneous epochs and each epoch was composed of a “first spike”, a “regular” period (with relatively stable frequency and amplitude) and an “irregular” period (with variable frequency and amplitude) of oscillations. During each cycle of the regular oscillation one wave of activation propagated horizontally (parallel to the cortical lamina) across the cortical section at a velocity of ~50 mm/sec. Vertically the activity was synchronized through all cortical layers. This pattern of one propagating wave associated with one oscillation cycle was seen during all the regular cycles. The oscillation frequency varied noticeably at two neighboring horizontal locations (330 μm apart), suggesting that the oscillation is locally organized and each local oscillator is about equal or less than 300 μm wide horizontally. During irregular oscillations the spatiotemporal patterns were complex and sometimes the vertical synchronization decomposed, suggesting a de-coupling among local oscillators. Our data suggested that neocortical theta oscillation is sustained by multiple local oscillators. The coupling regime among the oscillators may determine the spatiotemporal pattern and switching between propagating waves and irregular patterns.

Keywords: Voltage-sensitive dye, optical recordings, brain slice, acetyl choline, carbachol

Oscillation in theta band (5 to 12 Hz) is a well-characterized activity in the mammalian brain. Hippocampal theta occurs exclusively during exploratory behaviors (Vanderwolf 1969) and REM sleep (Vanderwolf 1969, Jovet 1969), suggesting that this activity may be related to spatial learning and memory deposition. Neocortical theta activity has been observed in animal and human subjects (Sarntheim, et al., 1998, Raghavachari et al. 2001) and may play a role in spatial learning and working memory (Lisman and Idiart 1995, Raghavachari et al. 2001). In vitro experiments indicates that at different phases of the oscillation, the same input to the local circuit may lead to different synaptic modifications (LTP or LTD, Huerta and Lisman 1995). Thus, the phase distribution of the oscillation in the horizontal directions (parallel to cortical lamina) must play a role in determining when, where and what synaptic modifications would occur in the cortical circuit.

The horizontal phase distribution over hippocampus was changing with behavior (O’Keef and Recce 1993, Skaggs et al. 1996), suggesting that cortical oscillators in CA3 and dentate gyrus may also contribute to the horizontal phase organization (Buzsaki 2002) in addition to the sub-cortical pacemaker neurons in the medial septum-diagonal band of Broca (Buzsaki et al. 1983, Leung 1984, Stewart and Fox 1990, Lee et al. 1994).

In neocortex, theta waves have been recorded during behavioral and mental tasks (Kahana et al., 1999; Raghavachari et al., 2001), however, almost nothing is known about the pace making and spatiotemporal organization of these waves.

An in vitro cholinergic oscillation (~7 Hz) can be generated in neocortical slices by bath applying of carbachol and bicuculline (Lukatch and MacIver 1997). This in vitro oscillation may share a common mechanism with the theta activity because applying these two agents together in vivo is sufficient to induce theta oscillations when the hippocampus is deafferented from the medial septum areas (Colom et al. 1991). These two agents may induce the oscillation by mimicking cholinergic depolarization (Benardo and Prince 1982, Cole and Nicoll 1984) and GABAergic disinhibition (Bilkey and Goddard 1985) of the assumed pacemakers. Under in vitro conditions neocortical neurons do not receive any innervation from subcortical pacemaker(s). Thus the pacemaking and phase distribution must be organized by intrinsic neocortical oscillators.

In this report we use voltage-sensitive dye (VSD) imaging to examine this in vitro neocortical oscillation. Pharmacologically generating the activity in brain slice allows us to exclude contributions from external (subcortical) pacemaker (s), allowing an analysis of how intracortical interactions organize the phase distribution.

In brain slices, the sensitivity of VSD imaging was high (Jin et al. 2002), allowing a simultaneously measurement from 50 to 100 locations over an area of ~4 mm in diameter. The advantage of optical recordings over an electrode array is that VSD imaging measures the transmembrane potentials of the neuronal population and thus the phase gradient caused by current source/sink pairs in the tissue is ignored, and only the phase in the membrane potential oscillation is measured. Our results show that the oscillation is organized as propagating waves. Local (~330 μm) phase variations suggest that the propagation wave may be composed of coupled local oscillators.


Cortical slice preparation

Sprague-Dawley rats (n= 20) of both sexes from P28 to P35 were used. The animals were deeply anesthetized with halothane and quickly decapitated. The whole brain was chilled in cold (0–4 °C) artificial CSF [ACSF, containing (in mM) NaCl, 132; KCl, 3; CaCl2, 2; MgSO4, 2; NaH2PO4, 1.25; NaHCO3, 26; dextrose 10; and saturated with 95% O2 , 5% CO2] and coronal slices (450 μm thick) including occipital areas (bregma -3 to -5 mm) were cut and transferred to a holding chamber for > 60 min (at 22 °C) before the next procedure.

VSD Imaging

The imaging apparatus and methods are described in detail by Wu and Cohen (1993) and Jin et al. (2002). Briefly, the slices were stained with ACSF containing 0.005 to 0.02 mg/ml of an oxonol dye, NK3630 [first synthesized by R. Hildesheim and A. Grinvald as RH482; available from Nippon Kankoh-Shikiso Kenkyusho Co., Ltd., Japan; See Momose-Sato et al. (1999) for molecular structure], for 30 to 60 minutes (22 °C). During staining the dye solution was gently bubbled with 95% O2 and 5% CO2. The stained slices were then perfused in dye-free ACSF in a submerge chamber at 28 to 32 °C during imaging experiments. A 124-element photodiode array system was used for the imaging. The preparation was trans-illuminated by 705 ± 20 nm light for the imaging. The illumination was only applied during recording trials (8 – 32 sec each trial, > 20 trials for each slice) and the exposure (light intensity and illumination time) did not cause detectable bleaching or phototoxicity (Jin et al. 2002). An objective of 5× (0.12 NA, Zeiss) was used to form the image on the diode array. Each photodetector received light from an area of 330 × 330 μm2 of the cortical tissue. With trans-illumination, neurons through the entire thickness of the slice (450 μm) contributed equally to the signal. The resting light intensity was about 109 photons/msec per detector and the VSD signal of the oscillation was about 10−4 (peak-to-peak) of the resting light intensity. The signal was AC coupled at 0.1 Hz, amplified 200 times, low-pass filtered at 333 Hz, and then digitized at 1,000 frames /sec with a 12 bit accuracy.

Local field potential recordings

Tungsten microelectrodes (epoxylite-coted, FHC, Bowdoinham, ME) with tip resistance of ~75 kΩ were used for sampling local field potentials. The electrode was carefully placed into the tissue so that the tissue surrounding the electrode produced normal VSD signals. The field potential signals were amplified 1000× and band-pass filtered at 0.1 to 400 Hz (by a Brownlee Precision 440 amplifier) and digitized at 1000 Hz simultaneously with the VSD signals.

Data analysis and display

The optical data were analyzed using the program NeuroPlex (RedShirtImaging, LLC, Fairfield, CT). Data were displayed in the form of traces for numerical analysis and pseudocolor images for visualizing the spatiotemporal patterns. To generate pseudocolor maps, we normalized the signals from each individual detector to their own maximum amplitude (peak =1 and baseline/negative peak =0). Then a scale of 16 colors was linearly assigned to the values between 0 and 1 (Variable scaling in NeuroPlex). The pseudocolor maps were displayed as “contour” maps using the CONTOUR function provided by IDL (Interactive Data Language, Research Systems Inc., Boulder, CO) and used by NeuroPlex.


Electrical and optical signals

When neocortical slices were perfused with 100 μM carbachol and 10 μM bicuculline at 28 to 32 °C, oscillations at theta frequencies (5 – 14 Hz) occurred in the occipital area of the slice (Figure 1), in agreement with the results obtained by Lukatch and MacIver (1997). These oscillations can be distinguished from epileptiform spikes in the same tissue: Epileptiform spikes had high amplitude (~1 mV) and low repetition frequency (0.5 – 1.5 Hz) whereas theta oscillations had a low amplitude (~ 0.5 mV) and high frequency (5–14 Hz) (Kowalczyk et al. 2001). Staining with the dye did not change the frequency, duration, or the amplitude of the theta oscillations recorded by the local field potential electrode (data not shown). During VSD imaging only a moderate illumination intensity was used so that bleaching and photodynamic damage (resulting from high illumination intensity, Jin et al. 2002) were not detectable.

Figure 1
left: Schematic diagram of the preparation and recording arrangement. Slices containing occipital cortex were sectioned from bregma -3 to -5 mm. A tungsten microelectrode was used to record local field potential (LFP) from cortical layer II-III. Voltage-sensitive ...

In cortical layer II-III, oscillations both in local field potential and optical signal were highly correlated in the same voxel (330 × 330 × 450 μm3, Figure 1, center, top two traces). However, in local field recordings there were harmonic frequency components (Figure 1, right). Local field potential signal has a continuous phase shift from Layers II-III to VI and opposite phases occurred in between superficial and deep layers (data not shown, but see Figure 7 of Lukatch and MacIver 1997). This phase reversal was not seen in the VSD recordings during most oscillation cycles (14 slices from 10 animals, one recording from layer V was shown in Figure 1 center, bottom trace, other examples are in Figure 3B, Figure 5C3, C5 and D3; an exception shown in Figure 6B). This difference between electrodes and optical recordings demonstrated that VSD and field potential recordings measured different aspects of the neuronal activity. VSD signal is a population sum of transmembrane potential; Local field potential represents the local current density; the phase shift and polarity reversal indicate a current sink/source pair located in the cortical column (Lukatch and MacIver 1997). This phase shift is not present in the membrane potential oscillations. The phase map of VSD imaging correlates with the phase distribution in the membrane potential over the neuronal population without the interference of current source/sink pairs resulting from the geometrical arrangement of the neurons.

Figure 3
A. Propagating wave during the oscillation. Top trace: Oscillation recorded from one optical detector in cortical layer V. The location of the detector is indicated by the small square in the images. Bottom: Pseudo-color images synthesized from recordings ...
Figure 5
Examples of irregular oscillations. Panels AD are from 4 different animals. In each panel all images were from the same epoch, however only part of regular and part of irregular cycles were shown. Images C3, C5, D3 and D5 were from 5 vertically ...
Figure 6
Vertical de-synchronization. A. Top trace: Local field potential recording of one epoch of oscillation. VSD imaging revealed periods of propagating waves (P) and Irregular oscillations (I). R: activation with reversed propagation direction (data not shown). ...

Oscillation epoch

This oscillation was organized in epochs. The epochs started spontaneously or could be triggered by an electrical stimulation (e.g., 0.5V × 0.1 ms). In local field recordings each epoch was composed of a large first spike (Figure 2B, i), a period of “regular” cycles (relatively stable frequency and amplitude) followed by a period of “irregular” cycles (with variable frequency and amplitude, Figure 2B). These three components were seen in all epochs, from five slices of five animals, with ~300 spontaneous epochs recorded from each slice by a local field potential electrode. When a large area of tissue was imaged optically, the three components could be more clearly characterized by their spatiotemporal patterns. When recorded with a single electrode from one point, there was no apparent activity before the first spike. With imaging we found that occasionally (2 out of 47 epochs recorded optically, from 14 slices of 10 animals) the first spike was preceded by a local oscillation (Figure 2C, 1, Figure 5C, 1). The first spike occurred as an excitation wave propagating across the tissue. After the first spike, the periodic activation spread to the whole field of view (Figure 2C, image 1) and the frequency and amplitude became relatively stable (Figure 2C, image 2–3). Each oscillation cycle was associated with one activation wave (comparing the traces and the image of Figure 2C, image 2; Figure 3A). This one-cycle one-wave pattern was seen during the entire course of the oscillation. The oscillation frequency decreased from cycle to cycle (Figure 2C, image 3; Figure 4D), and later the reoccurrence of the waves gradually became infrequent and “irregular”, as the initiation site and propagating velocity varied in different cycles (Figure 2C, image 5–7). The first cycle in Figure 2C, image 5 started simultaneously on several detectors and propagated in the two opposite directions with different velocity. The second cycle in Figure 2C, image 5 started from the bottom section and propagated up (a reversed direction as that in Figure 2C, image 2–4). Complex patterns, such as collision and reflection of the waves also occurred: The first cycle in Figure 2C, image 6 was initiated at the center of the tissue and propagates in both directions. Apparently the activity reflected at the edge of the field of view, and the reflected waves propagated back and collided in the center, forming an “O” pattern. Irregular periods were observed following regular cycles in all 47 epochs examined optically (14 slices from 10 animals). Other examples of irregular oscillations were documented in Figures 5 and and66 and discussed in the related sections.

Figure 2
Spatial-temporal patterns of a spontaneous oscillation epoch. A. Recording arrangement. Signals from eight optical detectors in deep cortical layers were used in (C). A local field potential microelectrode was placed in layers II-III and recorded simultaneously ...
Figure 4
Evidence of locally controlled frequency. A: Oscillation cycles recorded from two neighboring optical detectors (red and black traces) with a horizontal separation of 330 μm (Schematic diagram in B). The numbers on top of each cycle is the peak-time ...

Propagating waves

During the regular oscillation period, VSD imaging revealed a localized activation associated with each oscillation cycle (e. g., Figure 3A, pseudo color images). The activated area had a columnar shape, perpendicular to the cortical laminae. The width of the active area (the area with signal > 50% of the peak) was 400 ± 220 μm (n = 15). This activated area propagated continuously in the horizontal direction across the entire occipital cortex. “Propagating waves” were defined as one such activation wave correlated with one oscillation cycle (one-cycle one-wave). The mean propagation velocity was 55 ± 21 mm/sec (54 measurements from 54 waves in 3 slices). The horizontal propagation direction was the same (from medial to lateral, Figure 2, ,5)5) during regular cycles.

During propagating waves, the activation of the neuronal population was more synchronized in the vertical (columnar) direction. Figure 3B shows the time difference for the VSD signal to reach its maximum at two neighboring detectors (named “peak-time difference” in this report). In the horizontal direction the peak-time difference is centered around 6 ms, resulting from the propagation delay. In the vertical direction the peak-time difference is centered around 0 ms. The shape of the distribution histogram in the vertical direction (red envelope in Figure 3B) was also taller and thinner than that of the horizontal direction, indicating a better synchronization along the columnar direction than in the horizontal direction (also see Figure 5, C2, C3). Because of this vertical synchronization, the propagating wave had a columnar shape in the activity maps (Figure 3A bottom).

Local frequency

Local oscillation frequency was examined on a spatial scale of ~ 330 μm. In Figure 3B the peak time difference at two horizontal neighboring locations had variations as large as ±20 ms, suggesting a wide range of frequency variations within a 330 μm distance. Figure 4A shows the peak time difference of two neighboring detectors (330 μm apart, horizontally arranged in layer II-III, Figure 4B) in consecutive cycles of a regular period of oscillation. The overall propagation direction was the same for all the cycles. The peak-time difference changed from cycle to cycle, from positive to negative values. In 14 slices (47 epochs) imaged optically we found 11 detector pairs with continuous changing of local frequency (Figure 4C, blue and black) while others have apparent random fluctuations (Figure 4C, red). The continuous cycle-to-cycle change suggests that the local frequency variations were not randomly distributed nor caused by noises. Since the overall oscillation frequency declined with time (Figure 4D), if in one location the frequency declined faster than its neighbors, continues peak-time variations would occure. This suggests that the frequency at two neighboring locations were at least partially controlled by two local oscillators. The local oscillators would have a size similar to or smaller than 330 × 330 μm2 -- the area of tissue imaged onto one optical detector.

Much larger local frequency variations were seen during irregular cycles where the oscillation at two neighboring locations can switch from phase advance to phase delay in one cycle. The irregular patterns were analyzed below to demonstrate that the horizontal coupling regime could break and local oscillators could activate independently.

Irregular oscillations

Examples of irregular oscillations from four different slices where shown in Figure 5. In all the examples propagating wave occurred before the irregular patterns, indicating that a coupling regime for regular propagating waves existed in all preparations and this regime could degrade during the course of the epoch and dynamically change into other coupling patterns. The following irregular patterns were seen in the 14 slices we examined:

  1. Dynamic reversal of propagating direction: The waves changed from the “ \ “ to “ / “ shaped patterns in different cycles (Figure 5A, images 1 and 3). When propagation direction changed, the phase relationship reversed in all neighboring locations;
  2. Wave collision: Two waves propagated in opposite directions and collided in the middle, forming a “ > “ pattern (first 4 cycles in image 2 of Figure 5A);
  3. Wave initiated in the center and propagated in two directions, forming a “ < “pattern (first cycle in image 4 of Figure 5C);
  4. Possible reflection of the wave occurred outside the field of view, forming a “V” shaped pattern (image 4 of Figure 5B);
  5. Interruption of a propagating wave: In some cycles the wave did not propagated through the entire tissue (image 2 of Figure 5A and image 2 of Figure 5B);

More complex patterns may be explained by the combination of the above patterns, such as the “X” shaped pattern (image 4 of Figure 5D), which can be explained as a combination of a collision and then the collision point initiating a new wave. The “O” shaped pattern (image 6 of Figure 2C) can be explained as a combination of center initiation, reflections at both edges and then a collision at the center.

Vertical de-synchronization

As described before (Figure 3A and B), during propagating waves the synchronization along cortical columns was better than that of horizontal (along the cortical laminae). Vertical synchronization also persevered during most irregular cycles when regular waves were disrupted (Figure 5C-3; C-5; D-3). However, in the 14 slices we examined optically we found two irregular periods where superficial and deep layers did not activate together. In one example during some irregular cycles the activations in deep layers did not reach superficial layers (Figure 5D, 5). In another slice (Figure 6), the amplitude in layer II-III significantly reduced in some irregular cycles (Figure 6A). Before these irregular cycles there was a period (Figure 6A, X) in which superficial and deep layers showed an alternating activation. These examples suggest that superficial and deep layers of the same column may activate independently during the oscillation. However, vertical de-synchronization was much less frequently observed, suggesting that the coupling in the vertical direction is stronger that of the horizontal direction.


One-cycle one-wave

In this report we found that the in vitro cholinergic oscillation was organized as propagating waves. The oscillation has a one-cycle one-wave characteristic (Figure 3), that is, each oscillation cycle is associated with one propagating wave. This characteristic was seen in the NMDA 7–10 Hz oscillation (Wu et al. 1999). The NMDA waves can be blocked by AP5 (Wu et al. 1999) but the cholinergic waves in this report were not blocked by AP5 (data not shown, see also Lukatch and MacIver 1997), suggesting that these propagating waves can be generated by more than one polysynaptic mechanisms. The propagating waves during the two oscillations had a similar velocity of 20 to 60 mm/sec, slower than axonal conductance, suggesting both are mediated by polysynaptic local circuitry.

Propagating waves during oscillations were also observed in intact brains from turtle visual cortex (10–20Hz, Prechtl et al. 1997, Senseman and Robbins 1999,) and olfactory bulb (5–30 Hz, Lam et al. 2000) in response to natural sensory stimulation. In turtle visual cortex the propagation waves also had a one-cycle one-wave characteristic but their spatial pattern was much more complex (Prechtl et al. 1997). Oscillations of different frequencies happened at the same time and travel in different directions (Prechtl et al. 1997). In intact cortex there are two horizontal dimensions that allow variations in many directions. In brain slices there is only one horizontal dimension and therefore only two possible propagation directions. Reversal in the (e.g., Figure 2C, 5; Figure 5A, 3) and also in the NMDA oscillations (7–10 Hz) where the horizontal direction reversed dynamically in different cycles (Figure 7 of Wu et al. 1999). This dynamic change of propagation direction further suggests that the activation of the cortical neuron population is dynamically organized during the oscillation.

Coupled local oscillators and propagating waves

Our data suggests that the frequency of the oscillation may be determined by locally organized oscillators. Coupled local oscillators were also proposed during the evoked oscillations in turtle visual cortex (Prechtl et al. 2000). Mathematical models showed that propagating waves might emerge in a network of coupled oscillators with proper frequency gradient or coupling intensity (Ermentrout and Kopell, 1984, 1994; Kopell 1988). In our data the coupling intensity seemed to be variable in each epoch: During regular cycles the phase relationship is less variable, suggesting a stronger coupling; during the irregular cycles following the regular period, the phase relationship was more variable suggesting a weaker coupling. In all slices we found regular and irregular waves occurred in the same tissue, suggesting that the coupling intensity is controlled by dynamic factors of the local circuits, because the anatomical connectivity did not change within seconds. However, anatomical connectivity may still play a role: In an examination of the waveforms in different cortical areas, Lukatch and MacIver (1997) reported irregular waveforms were often seen in somatosensory areas while regular oscillations were mostly seen in occipital and entorhinal cortices, suggesting different cortical areas may have different background coupling strengths.

In thalamic slices the propagating patterns of spindle waves also have similar irregular patterns, such as collisions, multiple initiation points and local waves (Kim et al., 1995). Other kinds of one-dimensional propagating waves formed by coupled oscillators have been suggested in developing chicken spinal cord (O'Donovan et al. 1998) and in the lamprey spinal cord during fictive swimming (Rand et al. 1988, Mellen et al. 1995). Coupled local oscillations may have complex behaviors (e.g., Davidenko et al. 1992). However all the variety of propagating patterns observed (Figure 2, Figure 5 and and6)6) can be explained by the variations in the initiation site, collisions and phase advance/delay between two neighboring locations.

The size of local oscillators

The optical signal originates from the change in transmembrane potential of neurons (Ross et al. 1977). Our signal is the averaged transmembrane potentials of many neurons. The estimated neuronal density in neocortical tissue is about 100,000 neurons / mm3 (Douglas and Martin 1990). In the cortical tissue projected to one optical detector (330 × 330 × 450 μm3), there were about 5,000 neurons. In order to detect the oscillation optically, a fraction of these neurons must change their membrane potential synchronously. Frequency fluctuations (Figure 3) suggested that the size of the local oscillator is comparable to or less than the volume of the tissue (330 × 330 × 400 μm3) projected onto one optical detector. Thus we estimate that the local oscillator during this cholinergic oscillation is organized with thousands of at least partially synchronized neurons.

During an evoked 20 to 80 Hz oscillation in cortical slices (Figure 7 of Wu et al. 2001) the oscillation only appears on a field potential electrode but is not detectable optically from the same tissue, suggesting that the size of the local oscillator is substantially smaller than the volume of the tissue projected onto one optical detector. Another oscillation, a NMDA mediated 7 to 10 Hz oscillation (Figure 3 of Wu et al. 1999) can be detected optically, suggesting that it has larger local oscillators, similar to that of the cholinergic oscillation in this report.

Propagating velocity

The propagation velocity of excitation waves in neocortex has been measured during different population events (Chervin et al. 1988, Tanifuji et al. 1994, Bal et al. 1995, Golomb and Amitai 1997, Fleidervish et al. 1998, Tsau et al. 1998, Demir et al. 1999, Wu et al. 1999, Wu et al., 2001). GABAergic inhibition was proposed to be an important factor for controlling the propagating velocity of an excitation wave (Golomb and Ermentrout 2000). When the GABAergic network is intact, the propagation velocity of the evoked gamma oscillation is ~10 mm/sec (Wu et al. 2001). After blocking GABAa receptors with bicuculline, the propagation velocity increased to about 130 mm/sec (Wu et al. 2001). Here we show that in the presence of carbachol and bicuculline, the propagation velocity was much slower than that of adding bicuculline alone. We speculate that carbachol might modify the network to form localized oscillators and that the slow propagation wave may be due to network localization and the phase lags between neighboring oscillators.


Our results suggest that propagating waves during neocortical oscillations are organized by coupled local oscillators. Each oscillator is a population unit, composed of thousands of neurons. Variation in the coupling strength may contribute to the spatiotemporal dynamics of the waves. A number of questions remain. What defines a population oscillator? What determines the coupling strength? Finally, do similar oscillations also occur in vivo? The wavelengths of the propagating waves were small (~4 mm, Figures 3). It might be difficult for scalp EEG to reach such a high spatial resolution (Ferree and Clay, 2000) and detect waves with such small wavelengths. Additional experiments will be needed to address these questions.


We thank Drs LB Cohen, GB Ermentrout and JE Lisman for helpful comments. Supported by NIH NS36477 and a Whitehall Foundation grant.


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