Intracortical connections are not required for oscillatory activity in the visual cortex

Geoffrey M. Ghose* and Ralph D. Freeman

Group in Vision Science, School of Optometry

University of California

Berkeley, CA 94720

Abbreviated Title: Oscillations in the Visual Cortex

Number of pages: 31Number of Figures:8

*Current address: Division of Neuroscience, Baylor College of Medicine, One Baylor Plaza S603,Houston, TX 77030. Internet: gghose@bcm.tmc.edu

Please send correspondence to:

Ralph D. FreemanSchool of Optometry360 Minor HallUniversity of CaliforniaBerkeley, CA 94720Phone: (510) 642-6341Fax: (510) 642-3323Internet: freeman@pinoko.berkeley.edu

Acknowledgments

We thank Greg DeAngelis and Ken Miller for their valuable comments on the manuscript. We alsothank Izumi Ohzawa and Akiyuki Anzai for their assistance in the collection of the data used here.This work was supported by grant EY01175 and CORE grant EY03176 from the National EyeInstitute and by a collaborative project of the Human Frontiers Science Program (HFSP).

1

Abstract

Synchronized oscillatory discharge in the visual cortex has been proposed to underlie the linking of

retinotopically disparate features into perceptually coherent objects. These proposals have largely

relied on the premise that the oscillations arise from intracortical circuitry. However, strong

oscillations within both the retina and the LGN have been reported recently. In order to evaluate the

possibility that cortical oscillations arise from peripheral pathways, we have developed two plausible

models of single cell oscillatory discharge that specifically exclude intracortical networks. In the first

model, cortical oscillatory discharge near 50 Hz in frequency arises from the integration of signals

from strongly oscillatory cells within the lateral geniculate nucleus (LGN). The model also predicts

the incidence of 50 Hz oscillatory cells within the cortex. Oscillatory discharge around 30 Hz is

explained in a second model by the presence of intrinsically oscillatory cells within cortical layer

5. Both models generate spike trains whose power spectra and mean firing rates are in close

agreement with experimental observations of simple and complex cells. Considered together, the

two models can largely account for the nature and incidence of oscillatory discharge in the cat's

visual cortex. The validity of these models is consistent with the possibility that oscillations are

generated independently of intracortical interactions. Because these models rely on intrinsic

stimulus-independent oscillators within the retina and cortex, the results further suggest that

oscillatory activity within the cortex is not necessarily associated with the processing of high-order

visual information.

Key Words: LGN, visual cortex, synchrony, oscillations, geniculocortical integration, dischargestatistics, coding

2

Introduction

Recent experiments have demonstrated the presence of synchronous oscillatory discharge

around 50 Hz in frequency among groups of neurons within the visual cortex of the cat (Gray and

Singer, 1987;Eckhorn et al., 1988;Engel et al., 1990;Engel et al., 1991a). The purported stimulus

dependence of these oscillations has been used as evidence to substantiate the proposal that

synchronous oscillatory activity encodes visual information (Eckhorn et al. 1988; Gray and Singer,

1989;Engel et al., 1990; von der Malsburg, 1992). A central issue that remains unresolved is the

mechanism by which such oscillations arise. A definitive knowledge of the mechanism might

provide insight into the functional role that such oscillations play. For example, if a subclass of

cortical cells exhibits strong oscillations or is particularly prone to oscillate, then these cells might

act as "pacemakers" and actively synchronize oscillatory discharge. If pacemaker cells display

oscillatory activity that is strongly stimulus dependent, then these cells might underlie the functional

role of oscillatory activity among groups of neurons. If, on the other hand, pacemaker cells exhibit

stimulus independent oscillations, then the only potential mechanism by which oscillations could

encode information would be in the phase relationships between different oscillatory cells (Engel

et al., 1992).

A critical issue, therefore, in elucidating the origin of oscillatory activity, is to determine if

particular cells are strong oscillators and potential pacemakers. If so, what are the properties of these

strong oscillations? The strongest oscillations in cortical discharge are found at around 30 and 50

Hz in frequency among both simple and complex cells (Gray et al. 1990;Ghose and Freeman, 1992).

Gray and Singer (1987) did not find oscillatory discharge at these frequencies among cells within

the lateral geniculate nucleus (LGN), the thalamic structure that provides the predominant input to

area 17 of the cat's visual cortex. Because of this they concluded that oscillations were generated

3

by intracortical mechanisms exclusively. Several models have been proposed based on the

assumption of an intracortical origin for oscillatory discharge. These models can be grouped into two

categories: those relying on intrinsic cellular properties (Llinás et al., 1991;McCormick et al., 1993)

and those relying on synaptic networks that are extrinsic to cells. In intrinsic models, the sequential

activation of membrane conductances results in oscillatory discharge. Such oscillations are seen in

the thalamus, and, as shown by local field potential recordings, are associated with the synchronous

discharge among groups of neurons (Steriade and Llinás, 1988). Intrinsic oscillations have been

observed in layer 4 neurons of the guinea pig frontal cortex at frequencies of up to 45 Hz (Llinás et

al., 1991). These neurons are likely to be inhibitory, however, and Jagadeesh et al. (1992) have

reported that oscillatory PSPs in visual cortex are solely excitatory. Intrinsically oscillatory cells

have also been found in layer 5 of a cortical slice preparation (Silva et al., 1991). These cells, under

certain conditions, can synchronize the discharge of neurons along distances of up to 2 mm.

(Chagnac-Amitai et al., 1990). However, the oscillation frequency of these cells (8-12 Hz) is lower

than the 30 to 60 Hz discharge seen in vivo from cells in the visual cortex.

Extrinsic models rely on the synaptic connections between neurons for the generation of

rhythmic activity. Because of the original finding that oscillations are absent within the LGN (Gray

and Singer, 1987), several investigators have proposed models that attribute cortical oscillations to

intracortical networks. These models have been associated with population-based encoding schemes

for visual information whereby synchronized oscillations underlie the linking of retinotopically

disparate features (Eckhorn et al., 1988;Singer, 1990;Engel et al., 1991; von der Malsburg, 1992).

It is also possible that oscillations originate from a combination of intrinsic and extrinsic properties

(Bush and Douglas, 1991), as seen in the hippocampus (Traub et al., 1989).

Experimental evidence, however, raises questions regarding the premise of a purely

4

intracortical origin. Oscillatory discharge in the 50 Hz range has been found in both the LGN

(Bishop et al., 1964;Arnett, 1975; Munemori et al., 1984; Ghose and Freeman, 1992; Ito et al., 1994;

Neuenschwander and Singer, 1996; Lehky and Maunsell, 1996) and the retina (Laufer and Verzeano,

1967;Robson and Troy, 1987; Neuenschwander and Singer, 1996). Strong oscillatory discharge in

the LGN is present both in spontaneous activity and during visual stimulation. Because certain LGN

cells exhibit stronger oscillations than any seen in the visual cortex (Ghose and Freeman, 1992),

these cells are likely candidates for acting as pacemakers and inducing synchronous oscillations in

other cells.

This paper verifies the feasibility of such a proposal by showing that oscillations

quantitatively consistent with those observed in the discharge of single cells of the cortex can be

generated without intracortical connections. Two models are used to explain all frequencies of

strong oscillatory discharge within the cortex. In these models, oscillations near 50 Hz arise

extrinsic to the cortex from pre-cortical spontaneous activity, while strong oscillations at around 30

Hz arise from the presence of intrinsically oscillatory cells within layer 5. Intracortical connections

are necessary to account for some multiunit observations, including that of trans-callosal oscillatory

synchronization (Engel et al., 1991a). However, our models demonstrate that intracortical

connections are not necessary to generate realistic cortical oscillations in single neurons.

Methods

Figure 1 depicts the basic principle of the first model: that the integration of strong oscillators

of variable phase and non-oscillatory cells results in relatively weak oscillations. This difference in

oscillatory strength between cells of the LGN and cortex is illustrated in the discharge records and

the interspike interval distributions in Figure 1. The strong oscillators are specific cells within the

LGN, and the weak oscillators are cells within the visual cortex that fire according to the integration

5

of a number of convergent LGN inputs (Salin et al., 1989). Because the input oscillations are not

phase locked and because the spike generation of each LGN oscillator is a random process, there are

only brief periods of time during which the input oscillators are discharging in phase (Gray et al.

1992). In order for a cortical cell to receive oscillatory input that is suprathreshold, these oscillatory

inputs must be discharging in-phase during certain periods of time. When oscillations are out-of-

phase, the combined effect of the inputs is that of an unmodulated source, and no oscillatory

discharge is exhibited by the cortical cell (Segundo et al., 1968;Crick and Koch, 1990). The result

is that cortical oscillations, when present, are far weaker in terms of signal-to-noise than those seen

among some cells in the LGN (Ghose and Freeman, 1992; Ito et al., 1994). This difference exists

even though cells within the two structures share a common oscillatory influence, namely, retinal

oscillations (Neuenschwander and Singer, 1996). In our model this difference is based on the

different degrees of input convergence onto single cells. Limited convergence onto LGN cells

results in neurons that are strongly oscillatory; more extensive convergence onto cortical cells results

in weak oscillatory discharge.

Discharge Statistics

A model of in vivo neuronal discharge must incorporate two features: an adequate description

of the synaptic inputs to the cell and a feasible scheme for the integration of such inputs and the

generation of action potentials. Within area 17 of the visual cortex synaptic inputs to single cells

reflect both intracortical connections and afferents from the LGN. Both excitatory and inhibitory

interactions are present within the cortex. However, the geniculocortical pathway is exclusively

excitatory (Colonnier, 1981; Ferster and Lindström, 1983; Tanaka, 1983). Since we seek to establish

the extent to which cortical oscillations can be explained solely by virtue of geniculate afferents, our

model ignores intracortical interactions in the generation of cortical action potentials. Simulated

(t;�,m) �(�t)m1e�t

(m1)!

6

cortical spike trains are generated according to the excitatory input from a group of LGN cells. Two

conditions of neural activity are simulated: spontaneous activity and visually evoked activity.

The occurrence of action potentials (spikes) can be modeled as a random point process that

is described by the distribution of interspike intervals (ISIs). For retinal ganglion cells (RGCs)

visual stimulation acts to alter the parameters of this distribution. For example, a spot of light that

evokes neural discharge lowers the mean of the ISI distribution thereby increasing the mean firing

rate. Although firing rate is the metric most commonly used to quantify extracellular activity, it is

relatively crude: many distinct ISI distributions can have the same mean. In particular, mean firing

rates (or mean ISIs) are especially inappropriate metrics for distinguishing oscillatory cells.

Gamma distributions have been shown to accurately fit the ISI distributions of several classes

of retinal ganglion cells (Kuffler, 1953 ;Robson and Troy, 1987). A gamma distribution is

formulated as,

(1)

where m is the order of the gamma function, l is the coefficient of variation, and t is the interspike

interval. When m=1 the intervals are independent and the distribution is Poisson. For X and Y cells,

m is typically 8, while for oscillatory Q cells, m is 80 during visual stimulation (Robson and Troy,

1987). In this model it is assumed that gamma functions can be used to simulate the discharge from

cells of the LGN. Although retinal discharge deviates from the gamma model because of serial

correlations (Troy and Robson, 1992) and LGN discharge is not exactly like that seen in the retina

(Bishop, 1964), these functions produce power spectra similar to those of real LGN cells (see

Results) and can therefore be used to mimic the oscillatory nature of LGN cells.

Geniculo-cortical connections

C(t) 1 if V(t)�� and C(t ) 0

0 otherwise

V(t) �N

i1wi ,

t

t�Li(-) ek(t-)d-

7

As stated above, LGN discharges are modeled as point processes with the appropriate gamma

statistics. Intracortical PSPs arising from LGN discharge are assumed to have an exponential decay

with a time constant of 3 ms. This is based on cross-correlation data that shows a decay time of

about 4 ms for monosynaptic peaks (Tanaka, 1983). The integration of PSPs is modeled as a linear

summation (Burke, 1967; Granit et al., 1966;Ferster, 1987; Heeger, 1993). Assuming uniform

geniculocortical latencies, the normalized post synaptic potential of a cortical cell V(t) is computed

by integrating over the recent history of activity among the N independent LGN inputs to the cell:

(2)

where L is the point process describing the firing of an LGN cell, k is the decay constant of PSPs ,�

is the interval over which PSPs can effectively sum (set equal to 3k), and w describes the synaptic

efficacy of each input. Note that V(t) is normalized according to EPSP amplitude from a single input

(i.e. the amplitude of the PSP associated with a single LGN action potential is assumed to be equal

to 1.0). Cortical discharge, C(t), is determined by comparing V(t) to a firing threshold q with the

assumption of equal weights among the inputs (w=1 for all I):i

(3)

where is the refractory period of the cell. In our simulations, is assumed to be 1 ms and V(t) is

8

not reset when C(t)=1. � is therefore the number of nearly simultaneous afferent action potentials

necessary to evoke discharge. This parameter is adjusted so that physiologically realistic firing rates

are obtained from the simulated cortical cells. All extracellular records are simulated as discrete

functions sampled at 1 ms.

Because of independence, each input can be described as a random process independent of

other inputs. Since all of the strong oscillations observed within the LGN are at frequencies between

50 and 60 Hz (Ghose and Freeman, 1992), the mean ISI (m/�) for oscillatory LGN cells is defined

to be 18 ms, corresponding to a frequency of 55.6 Hz. Although the oscillatory component of these

cells' firing is stimulus independent, the cells do discharge in a non-oscillatory manner in response

to visual stimulation. Because the visual response of these cells is an increase in non-oscillatory

discharge, the oscillatory strength, as measured by the proportion of spikes separated by regular

intervals, actually decreases during visual stimulation (Ghose and Freeman, 1992; Ito et al. 1994).

However, for the sake of simplicity, simulated oscillatory cells are defined to be completely stimulus

independent: their ISI distributions are independent of visual stimulation. By contrast, the firing rate

of non-oscillatory LGN cells is taken to be 10 spikes/sec (mean ISI = 100 ms) in the absence of

stimulation and an average of 30 spikes/sec during stimulation. These firing rates are consistent with

our observations of spontaneous activity in an anesthetized and paralyzed preparation. Using these

parameters, we simulate both spontaneous and visually driven discharge in the LGN and cortex.

Spontaneous discharge rates are computed in our simulation in order to ensure that simulated cortical

cells are consistent with experimental observations of low spontaneous firing rates. Because of the

low rates of spontaneous discharge for cortical cells, only the oscillatory discharge during visual

stimulation is analyzed. In our simulation, 2 Hz sinusoidal gratings produce modulations in the firing

rate of non-oscillatory LGN cells such that the cells' mean response rate, averaged over 4 second

9

trials, is 30 spikes/sec. The temporal response phases of the pool of non-oscillatory cells providing

input to cortical cells, are shifted from one another to ensure that the discharge of simulated complex

cells to drifting gratings is not strongly modulated.

The number of LGN cells (N) that provide input to a cortical cell is difficult to determine

experimentally. Measurements of the variability of cortical EPSPs with varying levels of LGN

stimulation suggest that at least 10 LGN cells provide input to each simple cell (Ferster, 1987).

Cross-correlation experiments between monosynaptically linked cells of the LGN and cortex also

suggest that at least 10 presynaptic cells contribute to each simple cell (Tanaka, 1983). These

experiments also suggest that each complex cell receives input from at least 30 cells. An anatomical

study, which showed that a single geniculate afferent is likely to make only one contact on a specific

post-synaptic cell, also supports the premise that single cortical cells are driven according to the

convergence of tens of geniculate cells (Martin, 1988). For the purposes of the simulations to

follow, simple cells and complex cells are defined as having 15 and 30 independent LGN inputs,

respectively. The exact numbers used are not critical to the results as long as complex cells have a

greater number of effective inputs than simple cells. Because we are only interested in temporal

response patterns, we do not make any assumptions concerning the spatial arrangement of the LGN

neurons providing input (Hubel and Wiesel, 1962; Ferster, 1987; Chapman et al., 1991, Ferster et

al., 1996).

The projection of oscillatory LGN cells to the cortex has been verified by the recording of

strongly oscillatory LGN fibers within the cortex (Ghose and Freeman, unpublished observations).

The fundamental free parameter of our model of LGN input is therefore the relative number of

oscillatory and non-oscillatory inputs converging upon single cells. If the total number of oscillatory

inputs is very large, then V(t) will not exhibit oscillations because the asynchronous oscillations in

10

intracellular potential associated with single LGN inputs will cancel each other (Segundo et al.,

1968;Crick and Koch 1990). If the number of oscillatory inputs is small, then they are unlikely to

exert a suprathreshold effect on the cortical cell. Thus, we would expect oscillatory discharge only

for cells in which the number of oscillatory LGN inputs is within a certain range. In the simulations,

cortical oscillatory behavior has been studied using different proportions of oscillatory input.

Oscillatory LGN cells have mean spike rates near 50 spikes/sec, which is larger than the firing rates

typically seen from non-oscillatory LGN cells (Ghose and Freeman, unpublished observations).

Because of this, as the proportion of oscillatory inputs increases, the firing threshold of the simulated

cortical cell has to be lowered in order to achieve realistic firing rates. For the case of simple cells,

the threshold is adjusted so that spontaneous activity never exceeds 4 spikes/sec and the maximal

discharge rate is no larger than 50 spikes/sec. For simulated complex cells, the threshold is adjusted

so that spontaneous activity never exceeds 10 spikes/sec and maximal discharge rates are no larger

than 75 spikes/sec. These firing rate limits are based on our laboratory’s measurement of thousands

of simple and complex cells and are consistent with published data on single cells in the cat’s visual

cortex. Simulations are therefore constrained so that mean firing rate statistics are consistent with

experimental observations. The range of thresholds that produces discharge rates within these limits,

yields the range of physiologically realistic oscillatory patterns that can be generated by the model,

given a certain proportion of oscillatory input.

Quantification of Oscillatory Discharge

Simulations are compared with data acquired from extracellular single-unit recordings within

area 17 and the LGN of the cat (Ghose and Freeman, 1992). Both simulated and actual spike trains

have been analyzed by computing autocorrelation histograms, in which the distribution of all spike

intervals is computed. Shuffle autocorrelograms are subtracted to eliminate stimulus-driven artifacts

11

in the correlogram (Perkel et al., 1967). Strong oscillatory discharge of neural origin is clearly visible

in the form of a regular rhythmic pattern within the shuffle-subtracted autocorrelogram. For both

simulated and actual cells, shuffle-corrected autocorrelograms are computed from intervals ranging

from -128 to 128 ms. Sinusoidal gratings of 2 Hz are used as visual stimuli in both the experimental

and simulated runs. For the simulations, power spectra are computed over 10 repetitions of 4 second

trials. For the experimental data, power spectra are computed over 4 to 20 repetitions of 4 second

trials.

Experimental data in this study were acquired from a previous study that used standard

electrophysiological methods for extracellular recording in the LGN and area 17 (Ghose and

Freeman, 1992). Oscillatory synchrony between cells recorded from the same electrode is evaluated

by constructing shuffle-corrected crosscorrelograms. Crosscorrelograms are normalized according

to the firing rates of the two cells, so that 1.0 corresponds to the correlation that would be predicted

if the two cells discharged independently according to Poisson statistics (Melssen and Epping, 1987).

Most of the experimental data and all of the simulated spike trains have a temporal resolution

of 1 ms, allowing the computation of power spectra up to 500 Hz (the Nyquist limit) in frequency.

The strength and frequency of oscillations are then assessed by taking the Fourier transform of the

autocorrelogram. This yields a power spectrum that describes the power present in the spike train

at different frequencies. Oscillation frequency is identified by finding the non-zero frequency at

which the power spectrum is maximal. The strength of the oscillation is then computed by averaging

the power over a frequency window of 9 Hz centered on this maximal value and comparing this

average with an estimate of the noise (Ghose and Freeman, 1992). Because no power spectra peaks

are observable beyond 70 Hz in any of the data, frequency-independent noise is estimated by

averaging the power present between 250 and 500 Hz in the power spectrum. For our data,

12

discharges are classified as oscillatory if the ratio of signal strength to noise exceeds an arbitrary

criterion of 1.5 (Ghose and Freeman, 1992). All power spectra shown in this paper are normalized

to their maximal amplitude.

Variable Phase in LGN Oscillations

A critical prerequisite for our model is that nearby oscillators within the LGN are not phase

locked (top, Figure 1). If nearby oscillators were phase locked with a small phase difference, then

the combined input that such cells would evoke within cortical cells would be strongly oscillatory.

Such strong oscillatory input would result in cortical cells whose oscillatory strength was equal to,

or greater than, that seen from some LGN cells. Yet an experimental survey of a large number of

cortical cells failed to find such strong oscillators (Ghose and Freeman, 1992). On the other hand,

if nearby LGN cells were 180 degrees out of phase, then their oscillations would cancel each other

and there would be no net oscillatory input to cortical cells receiving convergent input. Experimental

studies have demonstrated the LGN phase variability between nearby cells upon which our model

depends (Ito et al. ,1994; Arnett, 1986). Figure 2 shows further empirical evidence for the lack of

phase locking between nearby LGN oscillators. Here auto-correlograms and cross-correlograms are

based on the spontaneous discharge from an X and a Y cell that were recorded simultaneously from

a single extracellular electrode in the LGN. As evidenced by the rhythmic pattern of the two auto-

correlograms (Fig. 2 A and B), both cells are strong oscillators. Moreover, their oscillation

frequencies are identical, as evidenced by the alignment of correlogram and power spectra peaks

(Fig.2A and B). The cross-correlogram peak (Fig. 2C) occurs at + 4 ms, indicating that cell number

2 fired, on average, 4 ms after cell number 1. Given that the frequency of the oscillations is 59 Hz,

the peak interspike interval of 4 ms corresponds to an average temporal phase difference of about

90 deg between the two oscillatory cells. One way to evaluate the consistency of this phase

13

relationship is to calculate the signal-to-noise ratio of the correlated discharge. If the neurons were

completely phase-locked at 90 deg, then this correlated signal-to-noise ratio should be similar to, or

larger than, the ratio seen in individual discharges. As shown for our data in Fig. 2C, the signal-to-

noise ratio is 5.6, which is smaller than the signal-to-noise ratio seen for either of the individual cells

(8.5 and 13.5, respectively). The relative weakness of oscillations in correlated discharge

demonstrates that nearby oscillatory cells in the LGN are not phase-locked. Instead they exhibit

variable phase delays centered around non-zero values (Ito et al., 1994). The fact that the cross-

correlogram is less oscillatory than the auto-correlograms, implies that, if a cortical cell was

receiving equal input from these two cells, the net oscillatory input would be weaker than if that

cortical cell was receiving input from a single oscillator. If phase variability is a general phenomena,

it might explain the initial failure to find LGN oscillations in multi-unit recordings (Gray and Singer,

1989).

In our model, as more oscillatory cells are added, the oscillatory strength of the net input is

lowered. This requires that the phases of LGN oscillators are, on average, uncorrelated. It is not clear

if the experimental data are consistent with this condition. Although Neuenschwander and Singer

(1996) report an average phase difference of 49±40 deg between oscillatory multi-unit recording

sites in the LGN (n=36) there are some complicating factors in interpreting the data. First, it is not

certain how multi-unit correlations, which may reflect synaptic potentials and include an unknown

number of cells and synapses, compare with single unit correlations. Second, in their analysis,

temporal phase was measured by dividing the temporal offset of the central peak by the length of an

average cycle. An alternative analysis is to measure the phase over multiple cycles by looking at the

phase of the peak frequency in the cross-spectra. The two methods do not necessarily yield similar

results. Given these complications and the observations of phase variability in cross-correlograms

14

constructed from single unit activity (Ito et al. ,1994; Arnett, 1986), we believe that phase variability

is a reasonable assumption. In our model, phase variability is implemented by making simulated

LGN oscillators independent.

Results

Model 1: LGN Cells

Both cross correlation experiments and anatomical studies of retinal ganglion cells (RGCs)

and LGN cells have shown that LGN cells receive input from one to several RGCs (Cleland et al.,

1971;Hamos et al., 1987). It has also been shown that both oscillatory and non-oscillatory RGC

discharge can be well described by point processes with gamma distributions of interspike intervals

(Robson and Troy, 1987). To determine if the parameters of oscillatory retinal cells can be used to

replicate the oscillatory behavior of LGN cells, gamma distributions based on observations of

oscillatory RGCs were used to generate simulated spike trains. The auto-correlograms of these

simulated spike trains were then compared to autocorrelograms of experimentally observed discharge

in LGN. As seen in Figure 3, the experimentally observed LGN discharge is well represented by

gamma distributions whose parameters are the same as those seen with RGCs (Robson and Troy,

1987). Both sets of spike trains are well fit by simulated spike trains generated according to a

gamma ISI distribution (m=80) with a mean ISI of 18 ms. Power spectra of the simulated and

observed spike trains are very similar, showing that LGN oscillations accurately reflect both the

frequency and signal-to-noise ratio of oscillatory RGCs. Although the power spectra peak is sharper

in the simulated cells, the total area within the 9 Hz window around the peak is very similar.

Model 1: Simple Cells

Simple cells are modeled as receiving 15 independent LGN inputs. Figure 4 shows the

autocorrelogram and power spectrum of a simulated simple cell discharging at its maximal firing

15

rate. The spike train was generated by assuming that 5 inputs were oscillatory (m=80) and 10 were

non-oscillatory (m=8). In this example, firing threshold � was set at 4.1, resulting in a spontaneous

firing rate of 1.4 spikes/sec and a maximal firing rate of 25.1 spikes/sec. As predicted qualitatively

(Fig. 1), oscillations can be seen in the simple cell discharge, but at signal-to-noise ratios much lower

than those of single cells in the LGN. As illustrated in Figure 4, a quantitative comparison of

frequencies and signal-to-noise ratios shows that the simulated spike train accurately describes the

observed oscillatory behavior of simple cells within the visual cortex.

For simulated simple cells, oscillations with signal-to-noise ratios greater than 1.5 are

observed only when either 5 or 6 of the 15 inputs are oscillatory cells. The average signal-to- noise

ratio for simulated simple cells that oscillate is 2.8. This is roughly consistent with our experimental

data in which the average signal-to-noise ratio observed for oscillatory simple cells (N=27,f>40 Hz)

is 3.4.

Model 1: Complex Cells

Complex cells are modeled as receiving 30 independent LGN inputs. Optic radiation

stimulation and cross-correlation experiments between cells of the LGN and cortex have provided

evidence that complex cells can receive monosynaptic input from LGN cells (Bullier and Henry,

1979; Tanaka, 1983). The same PSP decay constant (3 ms) is used to simulate the activity of

complex cells. As with the simple cell, the proportion of oscillatory input is varied to study the range

of oscillatory behavior possible with this model.

Figure 5 shows an example of a simulation of visual evoked activity in which 14 out of the

30 LGN inputs are oscillatory. This simulated cell has a spontaneous activity rate of 6.8 spikes/sec

and an maximal response rate of 63 spikes/sec. As can be seen in the power spectra of Figure 5, both

the frequency and signal to noise ratio of this simulated spike train match those observed

16

experimentally.

For a complex cell, oscillations with a signal-to-noise ratio greater than 1.5 are observed only

if 9 to 15 inputs are oscillatory cells. The average signal-to-noise ratio for simulated oscillatory

complex cells is 4.1. This is consistent with our experimental data in which the average signal-to-

noise ratio observed for oscillatory complex cells (N=32,f>40 Hz) is 3.4.

This model differs from the strictly hierarchical model first proposed by Hubel and Wiesel

(1962) of complex cells receiving input solely from simple cells. In fact, cross-correlation studies

have failed to find direct excitatory connections from simple to complex cells (Toyama, 1981; Ghose

et al. 1994). Additionally, there is a report of direct LGN input to complex cells (Tanaka, 1983). In

view of these results, complex cells are simulated as if all their inputs are from LGN cells rather than

simple cells. In any case, a two-stage model, in which both simple cells and LGN cells are pooled

to elicit complex cell discharge, is unlikely to yield different results. This is because the fundamental

determinant of the strength of oscillatory discharge is the relative number of strongly oscillatory cells

providing input. This can be seen by the similarity in the proportions of oscillatory inputs necessary

to evoke oscillatory output for the two cases of 15 and 30 inputs (see above).

Model 1: Incidence of 50 Hz Oscillatory Cells

If we make the assumption that the distribution of strong oscillators is relatively uniform

within the LGN, and there is no particular biasing in the efferents of these oscillatory cells, then we

can use the number of inputs necessary to elicit oscillations in our simulated cells to predict the

overall incidence of oscillatory activity in the cortex. In the absence of such biasing, the question

is reduced to a statistics problem: given that a simple cell receives 15 inputs, for example, what is

the chance that 5 or 6 of them will be oscillators if 20% of the inputs are oscillators? For complex

cells (N = 30), we are interested in the probability that between 9 and 15 of their inputs are

poscill �6

i5

15

iP i (1P)15i

17

oscillatory. We can thus use a Bernoulli process to predict the incidence of oscillatory discharge

among both simple and complex cells given a certain incidence of oscillatory cells (P) within the

LGN. Given that the LGN model described above relies on strong oscillators (signal-to-noise ratio

= 12.8), P refers only to the population of strong oscillators within the LGN that exhibit signal-to-

noise ratios of 10 or greater. For a simple cell (N =15), the probability p that it will have a sufficient

number of oscillatory inputs is therefore given by

(4)

where i is the number of oscillatory inputs, and P is the incidence of strongly oscillatory cells in the

LGN. Figure 6 shows the relationship between oscillatory incidence in the visual cortex (p ) andoscill

LGN (P), and demonstrates that our model can accurately account for the incidence of oscillatory

activity from simple and complex cells. The arrows along the borders indicate the experimentally

observed incidence of oscillatory discharge near 50 Hz in both the visual cortex and LGN (18.6 ±

10% of LGN cells, 13.6 ± 5% of simple cells, and 15.6 ± 6% of complex cells) (Ghose and Freeman,

1992). The fact that the curves lie within the boxed regions indicating 95% confidence levels for

the actual incidences of oscillatory cells implies that both simple and complex cell oscillatory

incidence can be explained. The incidence of oscillatory LGN cells refers only to those LGN cells

that are very strong oscillators (S/N > 8).

Model 2: Intrinsic Oscillators

18

There is one striking pattern of cortical oscillatory discharge for which the LGN model

described above cannot account. There are a large number of cells oscillating at frequencies below

50 Hz (Ghose and Freeman, 1992). In fact, a large proportion of cells, especially complex cells,

oscillate near 30 Hz. Unless there are gross non-linearities in the integration of inputs, a model that

relies solely on LGN input cannot account for such low frequency oscillations because all strong

LGN oscillations are around 50 Hz in frequency. Yet, oscillations around 30 Hz are some of the

strongest that can be seen within the visual cortex (Ghose and Freeman, 1992). One possibility is that

30 Hz oscillations occur when subthreshold excitatory input from the LGN interacts with the

intrinsic tendency for some cortical cells to oscillate at around 10 Hz. On can model the membrane

potential of an intrinsic oscillator as regularly approaching a perfectly flat threshold (Fetz and

Gustafsson, 1983; Abeles, 1991). In vivo, we assume that synaptic noise components and sub-

threshold inputs effectively decrease (or increase in the case of inhibition) the potential necessary

to reach firing threshold (Bernander et al., 1991; Holt et al., 1996). This modulation results in

shorter ISIs than are present in the absence of LGN input. Thus, in vivo cortical discharge exhibits

oscillatory frequencies (30 Hz) higher than those expressed in the in vitro preparation (10 Hz).

Whole-field flashed stimulation evokes 10 Hz oscillations in extracellular discharge from

cells within areas 17, 18, 19 and PMLS of the cat (Dinse et al., 1991). These areas comprise about

80% of the cat’s visual cortex, and about 30% of the total cat neocortex. These oscillations occur

during periods of between 500 and 600 ms during which 7 to 8 peaks may occur. Although they are

apparently absent within the LGN, they are especially commonplace in areas 18 and 19. There is no

correlation between mean response rate and the strength of these 10 Hz oscillations (Dinse et al.,

1991).

Such low-frequency oscillatory discharge can be explained if certain cortical cells have an

VI(t) V(t) � I(t)

I(t) �8

i1E(tni1)

19

intrinsic tendency to oscillate. Silva et al. (1991) reported that layer 5 cells in a slice preparation of

somatosensory cortex can discharge with sustained bursts of 8-12 Hz after a brief pulse of

depolarizing current is injected intracellularly. With sufficient depolarization these bursts can last

up to 20 seconds. These cells are particularly relevant because we have found that the strongest 30

Hz oscillators are found in layer 5 (Ghose and Freeman, unpublished observations). We model the

intrinsic tendency to oscillate as an equivalent external input I(t) that repeatedly approaches firing

threshold (Fetz and Gustafsson, 1983;Abeles, 1991). The equivalent input is summed with the

geniculate inputs V(t) described in equation 2. The resultant sum V (t) produces action potentialsI

after reaching a threshold as described in equation 3.

(5)

We model intrinsic oscillators as producing a burst, with sufficient depolarization, of 8 action

potentials around 10 Hz. This pattern of discharge (between 8 and 12 Hz) was observed by Silva

et al. (1991) under voltage clamp conditions. In our formalism, I(t) is a sequence of 8 successive

exponentials E(t) which are "reset" by action potentials at intervals determined by a gamma ISI

distribution (order=80, mean ISI=100 ms). The process is initiated when the geniculate input V(t)

exceeds a certain threshold � The time at which this threshold is exceeded is defined as n . ThusI. 0

(6)

where the interval n -n is a random variable according to (�=0.8,m=80).i i-1

Because this equivalent external input E describes the membrane properties of the neuron,

20

the input must be negative at short interspike intervals to account for the refractory period. This

formalism is similar to the “neuromime” concept proposed by Perkel (1965) which has been applied

to a number of neural systems, including RGCs (Lankheet et al. 1989). There are therefore three

parameters that completely describe this equivalent external input: the threshold at which it is

activated (� ), its decay constant �, and the temporal interval at which it provides neither positiveI

nor negative input (t ).0

E(0) = �

(7) E(t>0) = (1 - e ) - C) � -�t

C can be expressed in terms of an x-intercept t0

(8) C = 1 - e -�t0

The input necessary to trigger this process (� ) must be larger than the firing threshold (�) to preventI

unlimited positive feedback. This activation threshold must also be sufficiently high so that

spontaneous LGN input is unlikely to trigger the oscillatory tendency. If � were such thatI

spontaneous LGN activity was sufficient to trigger oscillations, then cells that oscillated at 30 Hz

under visual stimulation would exhibit oscillations at around 10 Hz in their spontaneous activity.

Experimentally, however, we have not observed this (Ghose and Freeman, 1992). Unfortunately,

more specific quantitative data on these three parameters are not available. These parameters,

therefore, are varied to see whether suitable oscillatory activity with realistic firing rates can be

observed.

Because 30 Hz oscillations are seen predominantly in complex cells (Ghose and Freeman,

1992), the low frequency oscillations are studied by simulating cortical cells with 30 LGN inputs.

With different parameters of the intrinsic oscillatory tendency, low frequency oscillations can also

be seen in simulated simple cells receiving 15 inputs. Figure 7 compares a simulated 30 Hz

21

oscillation with observed data. For this simulated cell, �=0.03 ms , t = 22 ms, and � = 8.5, and 2-10 I

of the 30 inputs were LGN oscillators. The simulated complex cell has a firing threshold � of 4.5

(Equation 3) discharged at a rate of 82.5 spikes/sec when stimulated and 0.3 spikes/sec in the

absence of stimulation.

For cortical cells with an intrinsic tendency to oscillate, an increase in the proportion of

oscillatory LGN input decreases the strength of low-frequency oscillations. This is because an

increase in the proportion of oscillatory input increases the chance that shorter interspike intervals

will occur. In our simulations, when there are more than three 50-Hz-oscillatory inputs, 30 Hz

oscillations are not observed. When the number of oscillatory LGN inputs is three or below,

simulated discharge in terms of firing rate, optimal frequency, and signal-to-noise is constant.

Unfortunately we cannot use the Bernoulli model to estimate the incidence of low frequency

oscillators in our model, because extracellular recordings are unable to reveal which cells have an

intrinsic tendency to oscillate. Experimental data concerning the incidence of 30 Hz oscillations

among intrinsic oscillators is therefore unavailable.

Unlike the first model, this one has several free parameters in addition to the number of LGN

oscillators. Although we did not systematically test the model’s behavior over all combinations of

parameters, we did conduct simulations in which single parameters were varied around the values

used for Figure 7. As with the first model, varying the firing threshold, �, primarly affected firing

rate and had little effect on oscillation frequency or strength: at �=4 the firing rate was 104

spikes/sec, while at �=7,the firing rate was 19.2 spikes/sec. For q , low frequency oscillationsI

consistent with what is seen in Figure 7 were seen from 6 to 9. For q lower than 6, spontaneousI

oscillations around 10 Hz were seen; for � above 9 the oscillations were weak. Consistent behaviorI

was obtained when t was varied between 15 and 25 ms. Below 15 ms, oscillations were weak and0

22

had frequencies higher than 30 Hz. When t was above 25 ms, oscillations had similar frequencies0

but were considerably weaker than those shown in Figure 7. Oscillations consistent with those shown

in Figure 7 were observed when the decay constant � varied from 0.02 to 0.10. At g=0.01 low

frequency (20 Hz) oscillations were observed; at g=0.15, higher frequency (39 Hz) oscillations were

observed. Taken together, these ranges suggest that the model is robust for a variety of parameter

variations.

Thirty Hz oscillations have not been reported in local field potential recordings (Engel et al.,

1990). Local field potentials can reflect synaptic activity in addition to single unit discharge (Reinis

et al., 1988). Given the lack of low frequency oscillatory EPSPs (Jagadeesh et al. 1992), oscillatory

synaptic activity might predominantly reflect the higher frequency oscillations associated with the

LGN. Another possibility is that oscillations that originate from the cortex are less likely to invoke

synchronous discharge than those originating from the LGN because common input signals to nearby

cortical cells predominantly originate from the LGN. Experimental evidence consistent with this

hypothesis can be seen in Figure 8, in which the oscillatory correlated discharge between a pair of

nearby cortical cells has a non-zero phase difference. Both our data, and those of Engel et al. (1990),

demonstrate that oscillations between 40 and 50 Hz in frequency tend to be synchronized between

nearby cortical neurons. This synchrony, however, is not as common for lower frequency

oscillations. In 4 out of 9 cortical cell pairs whose crosscorrelograms show low frequency

oscillations (<35 Hz), the oscillations have asynchronies of 2 ms or greater, corresponding to

temporal phase differences larger than 20 degrees. This asynchrony might obscure the visibility of

low frequency oscillation properties in multi-unit and local field potential recording but is to be

expected if the oscillations originate intrinsically. It is also possible that low-frequency oscillators

represent a small proportion of the total input that cortical cells receive and are therefore less able

23

than LGN cells to serve as pacemaker cells. This is suggested in Figure 8 by the absence of

oscillatory single-unit discharge in both of the cells (A&B), despite the sharing of an oscillatory

common input. The relative weakness of 30 Hz, compared to 50 Hz input to cortical cells might

explain the lack of low frequency synchronization between nearby cells.

Discussion

We have developed two models to explain the origin of oscillatory discharge within the

visual cortex. In the first model, oscillations near 50 Hz in frequency are the direct result of

spontaneous 50 Hz activity within the LGN. In the second model, intrinsic membrane properties of

cortical cells are responsible for oscillatory discharge near 30 Hz in frequency. A simple pattern of

geniculocortical convergence, in conjunction with the first model, predicts the incidence of 50 Hz

oscillatory discharge from cells within the visual cortex. These models make use of physiologically

realistic parameters and are consistent with both intracellular and extracellular data concerning the

origin and nature of oscillatory discharge.

The models we describe here make several assumptions for the sake of simplicity. For LGN

oscillators we have assumed that their discharge can be modeled according to a set of statistics

observed for some cells in the retina. Bishop et al.'s (1964) demonstration of differences between

LGN and RGC interspike interval distributions suggests that LGN oscillatory activity cannot be

completely explained by RGC discharge. This difference may arise from the preponderance of

cortical feedback to the LGN (Sillito et al. 1994) or input from the perigeniculate nucleus (Levine

and Troy 1985). These differences might be responsible for slight difference in the bandwidth of the

power spectra peaks seen in Figure 3. However, recordings from pairs of cells located in different

laminae of the LGN indicate that oscillatory cross-correlograms are only seen in cases where both

24

cells are dominated by the same eye (Neuenschwander and Singer, 1996). These experiments

provide further evidence that retinal oscillations are an important contributor to LGN oscillations.

One characteristic of LGN discharge that we have not modeled here is the contribution of low

threshold bursts associated with the T-type Ca channel (Mukherjee and Kaplan 1995). These bursts2+

can be identified extracellularly by the presence of interspike intervals less than 4 ms (Lu et al.

1992). Using this criterion, some of our experimentally observed cells contain bursts (e.g., Fig. 2B

and Fig 3, center) while other cells do not (e.g., Fig. 2A and Fig. 3,top). A comparison of Fig. 2A

and Fig. 2B also shows, in confirmation of previous observations, that nearby cells do not necessarily

share a tendency to burst (Guido et al. 1992). Given the variability of bursting, both within a neuron

(Lu et al., 1992; Mukerhjee and Kaplan, 1995) and between neurons, and the small number of spikes

per burst, a model such as ours which integrates a number of LGN cells, would not be subject to

significant periods of synchronous bursty input. While bursts very likely affect the transmission of

visual stimuli at frequencies under 10 Hz (Mukherjee and Kaplan 1995), it is unlikely that bursts

affect frequencies in the 40-50 Hz range. First, interburst intervals are never of the order of 20 ms.

Instead, they are always larger than 100 ms. (Lu et al. 1992). Second, as can be seen in Figures 2 and

3, the overall power spectra, and in particular the shapes and bandwidths of the 50 Hz peaks, of

bursty and non-burst cells are indistinguishable. Of course, it is possible that certain cells within the

LGN have an intrinsic tendency to oscillate at higher frequencies (Pinault and Deschenes, 1992).

However, whatever the exact origins of oscillatory discharge in the LGN, the gamma distribution

clearly replicates observed frequency distributions of actual LGN discharge, and therefore can be

used to represent the 40-50 Hz discharge that is critical to our model.

There are clearly non-excitatory phenomena that influence cortical discharge and that are not

accounted for in the models presented here, including both inhibition and adaptation (Bishop et al.,

25

1973; Sillito, 1975; Morrone et al., 1982). For example, oscillatory inhibitory cells are responsible

for rhythmic field potentials seen in the olfactory bulb (Eeckman and Freeman 1990). However, in

the visual cortex, field potentials generated by excitatory pyramidal cells (Mitzdorf and Singer,

1978,Gray et al., 1989). Inhibition could affect oscillations by altering the integration of oscillatory

EPSPs. Inhibition might also interact with intrinsic bursting tendencies so as to produce oscillations

(Wilson and Bower, 1991). Unlike EPSPs, which primarily effect discharge in their rising phase,

IPSPs depress firing rates for their entire duration (Fetz and Gustafsson, 1983; Abeles, 1991).

Inhibition and adaptation are therefore likely to take place on time scales greater than that of the

excitatory integration period used in our models.

Tonic inhibition, if it was selective to particular inputs, could still affect input summation by

reducing the effective number of excitatory inputs. Although the orientation selectivity of

intracortical inhibition is still controversial, non-shunting inhibition should not selectively effect

specific geniculate inputs. Intracellular recordings using an in vivo whole-cell patch clamp of

cortical cells, suggest that inhibition is primarily linear rather than shunting (Ferster and Jagadeesh,

1992, Douglas et al. 1988, Douglas et al. 1991). If inhibition is linear and slow compared to

excitation, then it can be incorporated into our model by simply modifying the firing threshold.

Indeed, extracellular experiments suggest that intracortical inhibition effectively creates a floating

threshold, by which spontaneous activity is suppressed and responses saturate (Bonds, 1989;

DeAngelis et al., 1992). For a single cell, a dynamic firing threshold created by IPSPs is likely to

result in more variable discharge. In our model, changes in firing threshold are necessary to maintain

realistic discharge rates when the size or oscillatory nature of the LGN input pool is changed. It is

thus possible that inhibition is the mechanism responsible for the different firing thresholds of simple

and complex cells in our model.

26

A final possible role for inhibition is that inhibitory cells may be directly responsible for

oscillations (Crick and Koch, 1990;Llinás et al., 1991). However, Jagadeesh et al. (1992) report an

absence of oscillatory IPSPs in the cat’s visual cortex. Moreover, since all thalamic input is

excitatory (Tanaka, 1983; Ferster and Lindström, 1983), any inhibition must originate from the

cortex where strong oscillations (at least compared to those found in the LGN) are not observed.

Two further simplifications of the models used here are the uniformity of efficacies among

LGN inputs to a cell and the linearity of EPSP summation. It has been shown that the cumulative

receptive field area of LGN cells that provides convergent input to single cells in area 17,

corresponds to cortical receptive field sizes (Salin et al., 1989). This finding is consistent with the

assumption of relatively uniform efficacies among the LGN inputs within a convergent area.

Dendritic tree structure (Koch et al., 1983), the modulation of signals by synaptic spines, which are

the primary sites of geniculate axon termination (LeVay, 1986), and the effect of background

synaptic activity (Bernarder et al., 1991) all argue against strictly linear EPSP summation.

Phenomenologically, however, linear EPSP summation can produce both realistic receptive fields

(Ferster, 1987; Jagadeesh et al., 1993;Heeger 1993) and temporal responses and is consistent with

certain models of conductance non-linearities (Douglas et al. 1995). Moreover, several experimental

studies suggest that PSP summation can be linear (e.g. Burke, 1967; Granit et al., 1966). Unless

non-linearities or non-uniform efficacies specifically affect oscillatory inputs, the assumptions of

uniform efficacy and linear EPSP summation should not significantly affect the results of the model.

Finally, it is clear that a large proportion of a cortical neuron's input is intracortical. In layer

4, which is the primary site of geniculocortical afferents, less than 20% of the excitatory synapses

on cortical cells have a thalamic origin (Garey and Powell, 1971;LeVay and Gilbert, 1976; Peters

and Payne 1993). Cells in the cat’s primary visual cortex have around 10,000 synapses, and most of

27

these are from nearby cortical neurons (Beaulieu and Colonnier 1985; Cragg 1975). Indeed, several

investigators have proposed that local excitatory feedback is a major determinant of cortical response

properties (Douglas et al. 1995; Somers et al 1995). With the exception of supragranular layers,

however, direct LGN input is necessary for visual cortical response (Malpeli, 1983). Furthermore,

for layer 6 and many layer 5 cells, the inactivation of supragranular layers has little effect on

receptive field properties (cf. Schwark et al., 1986). These experiments suggest that cortical

response properties are largely determined by LGN input. Theoretical support for this premise was

provided by Ferster (1987), who showed that the spatial organization of LGN afferents is sufficient

to explain many simple cell receptive field properties. Physiological support for the spatial alignment

of LGN afferents along axes of orientation preference, which was first suggested by Hubel and

Wiesel (1962), has been found for cells in the ferret's visual cortex (Chapman et al., 1991).

Our models do not include excitatory feedback either within the cortex or from the cortex

to the LGN. However, our models are not necessarily inconsistent with intracortical feedback

models. For example, recurrent excitation might act to amplify relatively small LGN inputs to a level

consistent with cross-correlation data (Tanaka, 1983) and our model. Finally, although

geniculocortical feedback might explain the discrepancy between RGC and LGN firing statistics, it

is unlikely to strongly alter the oscillatory properties within the LGN, simply because of the

weakness and variability of cortical oscillatory firing (Gray et al. 1992).

Although not supported by experimental evidence (Toyama 1981; Ghose et al., 1984), Hubel

and Wiesel’s (1962) hierarchical model specifies that intracortical connections are solely responsible

for complex cell receptive field properties. If this model was accurate, it would have a large effect

on the estimate of the number of oscillatory complex cells. In our model incidence is determined by

a random selection of LGN inputs. If a strictly hierarchical model was applicable, one would expect

28

a very small incidence of oscillatory complex cells, since complex cells would have no access to the

strong oscillators of the LGN and would be completely dependent on simple cells, which exhibit

either weak oscillations or no oscillations at all. If complex cells receive input from both simple cells

and LGN cells, one would expect a smaller incidence of oscillators than our purely LGN model

predicts.

Varying the number of oscillatory inputs does not significantly affect cortical oscillation

frequency in any of our simulations. The number of oscillatory inputs only affects the signal-to-

noise ratio of oscillatory discharge in simulated cells. In the first model, both simple and complex

cells exhibit oscillatory discharge with similar ratios of oscillatory to non-oscillatory inputs. This

similarity provides additional support for the contention that the exact number of inputs from the

LGN is not critical to our models. In the awake monkey, oscillations are present in the LGN (Lehky

and Maunsell 1996), but largely absent in visual cortex (Young et al. 1992). Because the monkey

LGN oscillations appear to be purely stimulus driven, it is not clear if precortical oscillations are

analogous in the cat and the monkey. In any case, this discrepancy suggests that oscillatory activity

in species with geniculocortical and intracortical connectivity patterns that are very different from

those seen in cats (e.g. Peters et al. 1994), may not be well modeled by our approach.

The fact that many experimental observations concerning cortical oscillatory activity can be

explained despite these simplifications points to the robustness of the models. These models are the

first, to our knowledge, that quantitatively reproduce experimental observations regarding the

strength and frequency of oscillatory discharge in the cat. The data presented here show that simple

models whose parameters of spike generation and geniculocortical connections are derived from

experimental observations, are sufficient to largely explain oscillatory discharge within the visual

cortex.

29

Nature of Cortical Oscillations

Neuenschwander and Singer (1996) state that LGN oscillations cannot be responsible for

cortical oscillations for two reasons: 1) cortical oscillations are generally at lower frequencies than

retinal and geniculate oscillations, and 2) cortical oscillations are weaker and more variable than

LGN oscillations. As discussed below, our models only focus on frequencies for which oscillations

are the strongest. Although oscillations can be observed in the 30 to 70 Hz range in the visual

cortex, the strongest oscillations are around 30 Hz and around 50 Hz. Similarly, in the LGN,

oscillations can be observed at frequencies from 38 to 128 Hz (Neuenschwander and Singer, 1996).

However, the strongest LGN oscillations are around 50-60 Hz (Ghose and Freeman, 1992). Thus

for the strongest oscillations that are present in the visual system, the only cortical emergent

frequency is around 30 Hz. In our model, these low frequency oscillations are generated largely

according to the intrinsic oscillatory properties of cortical neurons. Taken together, our models are

able to explain the frequency range of the strongest cortical oscillations. In addition, as shown

above, our models quantitatively predict the strength of cortical oscillations. These models

demonstrate that LGN oscillations in combination with intrinsic cortical oscillators can indeed be

responsible for cortical oscillatory activity.

In contrast to experimental data that show a broad range of oscillatory discharge frequencies

(Ghose and Freeman, 1992), only two frequencies of oscillatory discharge are produced in our

simulations. For the intrinsic oscillators, all oscillations are at 31 Hz, and for non-intrinsic

oscillators, all oscillations are around the same frequency as the LGN oscillations (53 and 56 Hz).

Additionally, the power spectra of simulated cells tend to be slightly sharper than those of

experimentally observed cells. These differences are likely to be due to several simplifications

concerning the inputs to simulated cells. Only one frequency of LGN oscillatory input is used for

30

our models, when in actuality, strong LGN oscillations (S/N > 8) are observed at a range of

frequencies from 50 to 70 Hz (Ito et al., 1994). However, the majority are around the same

frequency of 53 Hz (Ghose and Freeman, 1992). Similarly, our models do not include relatively

weak oscillators within the LGN (1.5<S/N<8), which are commonplace (Ghose and Freeman, 1992).

Additionally, a single set of statistics is used to model non-oscillatory LGN cells when in fact

parameters such as the gamma order m and the mean firing rate vary from cell to cell (Robson and

Troy, 1983). Our models are primarily intended to provide an explanation of the strongest and most

robust oscillators within the cortex. We believe this focus on the strongest oscillators is appropriate,

because the oscillatory nature of these cells, unlike most cells in the cortex (Gray et al 1992), is the

most compelling and criterion independent. Since no strong oscillations (S/N > 8) are observed

between 40 and 50 Hz, or above 60 Hz, (Ghose and Freeman, 1992) our models do reflect the

frequency distribution of strong cortical oscillators. Weaker oscillations can be easily produced

within the framework of our model by either adding a range of frequencies to the input or adding

more oscillatory inputs. Intermediate frequencies might also arise due to variations in the intrinsic

oscillatory frequency of cortical cells (McCormick et al., 1993). It is also possible that intracortical

circuitry can modulate the frequency of pacemaker cells to create weaker mid-range (40-50 Hz)

oscillations.

Our models do not address the nature of discharge of very short epochs of time. This is

potentially a consideration because of the clearly non-stationary nature of oscillatory discharge in

the cortex (Gray et al., 1992;Ghose and Freeman, 1992). It is possible that individual oscillatory

bursts are of different lengths in our simulated and experimental records, even if the overall

oscillatory incidence within the spike trains is the same. Unfortunately, cortical oscillatory discharge

is so irregular that its overall incidence cannot be reliably measured without averaging discharge

31

records for multiple repetitions. To minimize this problem, we have compared the strongest, most

consistent oscillations present in the experimental data to our simulations. Given the simplifications

described above, even if there are differences in the microstructure of experimental and simulated

discharge records, it is significant that the maximal incidence of oscillatory discharge within a spike

train of substantial length can be replicated by our models. Previous models have not attempted to

replicate experimental observations of oscillatory incidence even though overall oscillatory incidence

is clearly relevant to the ability of oscillations to consistently encode visual parameters (Ghose and

Freeman, 1992). In addition, an explanation of average oscillatory discharge is a clear prerequisite

towards the construction of more elaborate models of the temporal microstructure.

Consistent with our experimental observations, oscillations are not visible in the spontaneous

activity of our simulated cells. One might interpret this as evidence for stimulus-dependent

oscillations. However, the oscillations themselves are stimulus-independent or, at most, luminance

dependent (Neuenschwander and Singer, 1996;Lehky and Maunsell, 1996). Our models predict that

oscillations are absent in the spontaneous activity of cortical cells simply because their high firing

threshold precludes discharge that is vigorous enough to exhibit consistent temporal patterns. This

would produce orientation “dependent” oscillations in cortical cells (Gray and Singer 1989) simply

because vigorous discharge is orientation dependent. An important test of this prediction would be

to conduct power spectra analysis, such as that done by Jagadeesh et al. (1992) during visual

stimulation, of the membrane potential of cortical cells in the absence of visual stimulation. Our

model predicts that the signal-to-noise ratio of 50 Hz membrane potential fluctuations should be

similar in the two cases. The power spectra of local field potential recordings are not sufficient to

resolve this issue since the local field potential reflects extracellular discharge as well as synaptic

potentials (Eeckman and Freeman 1990, Gray et al 1989, Langdon and Sur 1990).

32

It should be emphasized that our models address oscillatory discharge on the single cell level

only. It is possible that, even if single cell discharge is largely stimulus independent, the phase

relationships between oscillators are perceptually significant. For example, in somatosensory cortex

intrinsic oscillators, which are in themselves stimulus independent, have been proposed to underlie

the measurement of the temporal phases of periodic stimuli (Ahissar and Vaadia, 1990). However,

the visual system is not particularly sensitive to frequencies as high as 50 Hz. (If it was, television

broadcasts would appear to be constantly flickering). Alternatively, if one proposes that oscillations

in this frequency range play a role in perceptual grouping, then one might expect that flickering a

stimulus array at 50 Hz would affect perceptual judgments. However, no such effects are seen (Kiper

et al. 1996). Moreover, it is not clear on theoretical grounds how suitable oscillatory synchronization

is for the encoding of common visual features (Wilson and Bower, 1991). One simulation of

oscillatory patterns in the visual cortex indicates that coding visual features on the basis of oscillation

phase leads to many ambiguous classifications (Noest and Koenderink, 1991). In conjunction with

our models, these results suggest that oscillatory synchrony might be an epiphenomenon of

spontaneous oscillations and long-range horizontal connections within the cortex (Movshon 1993).

Laminar Distribution

Electrical stimulation of optic radiations suggests that the LGN provides monosynaptic input

to all layers of the visual cortex, particularly layers 4 and 6 (Bullier and Henry, 1979; Ferster and

Lindström, 1983) and to all physiological cell classes (Singer et al., 1975). These studies, in addition

to one in which cross-correlation analysis was performed on cells within the geniculate and cortex

(Tanaka, 1983), further suggest that complex cells, as well as simple cells, receive such input.

Therefore, cortical cells of all laminae and all physiological cell types should be susceptible to the

effects of oscillatory LGN activity. Thus the LGN model is consistent with experimental data

33

concerning the prevalence of both simple and complex cells in all laminae that exhibit oscillatory

behavior (Gray et al., 1990;Ghose and Freeman, 1992).

In our model, the nature of LGN input to intrinsically oscillatory complex cells of cortical

layer 5 determines their 30 Hz oscillation frequency. The model is supported by the fact that 5 out

of the 6 oscillatory cells with signal to noise ratios larger than 10 and oscillation frequencies of 30

Hz, are found in layer 5. Layers 5 and 6 are also the only sites where complex cells are more likely

than simple cells to be oscillatory (Ghose and Freeman, 1992). Geniculate input can affect layer 5

and 6 cells via their apical dendrites (Martin, 1984;Hornung and Garey, 1981). This interaction has

been demonstrated electrophysiologically through current source density analysis of cortical evoked

potentials (Mitzdorf and Singer, 1978) and through electrical stimulation of the LGN (Ferster and

Lindström, 1983). On the other hand, intrinsically oscillatory cells might receive primarily cortical

inputs: cells in the lower part of layer 5, for example, do not receive monosynaptic LGN input

(Ferster and Lindström, 1983). In fact, because a relatively smooth background of sub-threshold

input is necessary in order to obtain 30 Hz oscillations, our model predicts that intrinsic oscillators

that do not receive high frequency 50 Hz oscillatory input, are the most likely to oscillate at 30 Hz.

Oscillatory Synchrony

Gray and Singer (1987) postulated that the synchrony of local field potential and multi-unit

discharge reflects the synchronous 40-50 Hz oscillation of a local body of neurons, perhaps a cortical

column. This synchrony between potentials and discharge is not unusual and has been found in the

thalamus for 4 Hz oscillations (Steriade and Llinás, 1988), in cortical slice preparations (Silva et al.,

1991), and in the olfactory system (Eeckman and Freeman, 1990). Although cross-correlation

experiments suggest that nearby cells are likely to share inputs (Toyama et al. 1981), quantitative

measurements of the degree of geniculate afferent sharing between nearby cortical cells are not

34

available. If such numbers were available, we could use the Bernoulli process described above to

estimate the amount of correlation between nearby cortical oscillators with a random model of input

selection. If there is a large amount of sharing between nearby cortical cells, then nearby oscillators,

no matter what their relative orientation selectivities, would be likely to oscillate synchronously.

Moreover, the oscillations between nearby cells would tend to be stronger than those between distant

cells. These predictions are consistent with cross-correlation experiments which have demonstrated

that oscillations are the most synchronized for cells within 2 mm. of each other, and that this

synchrony is not dependent on the similarity of orientation preference (Engel et al., 1990). This

distance is suggestive of a geniculocortical model because it corresponds with anatomical

measurements of the divergence of LGN inputs onto the cortex (Salin et al., 1989).

Neuenschwander and Singer (1996) report stable phase relationships between oscillatory

neurons located in different hemispheres of the LGN. If this is generally true, it suggests that long-

range synchronization within the cortex could be largely due to long-range synchrony in the retina.

However, this observation is contrary to what we and others (Ito et al, 1994) have observed between

nearby cells in LGN. Moreover, we find it unlikely that phase synchrony is a general phenomena

within the LGN. If it was, one would expect very strong oscillations from monocular cells, since the

relatively strong oscillatory influences in the LGN would be providing synchronized input. Yet

oscillations in the visual cortex are an order of magnitude weaker than those seen in the LGN (Ghose

and Freeman, 1992; Gray et al. 1992). Similarly, one would expect that binocular cells would have

weaker oscillations than monocular cells since the two retinae are not synchronized. Yet this is not

the case either (Gray et al., 1990;Ghose and Freeman, 1992).

Cross-correlation studies have provided evidence of long-range synchronization between

regions as remote from each other as 7 mm., which is a greater distance than spanned by the afferent

35

divergence from the LGN (Engel et al., 1990; Engel et al. 1991b). Long-range horizontal

projections, as revealed anatomically and through cross-correlation, have been shown to link

columns of cells with similar orientation selectivities but disparate receptive field locations (Ts'o et

al., 1986). Such horizontal interactions are capable of propagating oscillatory activity and could

therefore serve to mediate long range oscillatory synchrony (Schwarz and Bolz, 1991). Both

anatomical and physiological studies suggest that these horizontal connections are relatively weak

and are much more likely to modulate rather than generate activity (McGuire et al., 1991;Hirsch and

Gilbert, 1991). Since Wilson and Bower (1991) found that synchronous oscillatory activity was only

observed in their simulations when horizontal excitation was weak, stable horizontal connections

might give rise to synchronous oscillations across large cortical distances (Engel et al., 1990;Engel

et al. 1991b).

More complicated cortical circuits might also contribute to long-range synchronization. For

example, inhibitory interneurons might be responsible for inter-hemispheric and long-range

synchronization (Crick and Koch, 1990; Engel et al., 1992; Bush and Douglas, 1991). Appropriate

combinations of short-range and long-range excitatory interactions (Sompolinsky et al., 1990; Traub

et al., 1996) or specific EPSP-IPSP interactions (Gerstner et al., 1993) can also synchronize

oscillatory cells. Our models suggest that although intracortical interactions could propagate and

even modulate oscillatory activity, they are not necessarily responsible for the generation of

oscillatory activity in the 40-50 Hz range.

Extracellular recordings of single unit activity demonstrate that specific cells within the LGN

exhibit strong oscillatory activity. Parsimonious models that employ physiologically realistic

interactions suggest that these cells could act as pacemakers and drive oscillations from cortical

neurons. These cells, as well as simulated intrinsic oscillators within the cortex, generate rhythmic

36

discharge quantitatively consistent with electrophysiological data without relying on intracortical

interactions. Because these oscillations are either intrinsic or dependent on luminance, cortical

oscillatory activity arising from the mechanisms proposed here can only play a sensory role if the

phase relationships between oscillators are stimulus specific. However, the models developed here

suggest that, to a large degree, the synchrony of cortical oscillations might be explained by the

presence of stable interactions (LGN divergence and horizontal interactions) without invoking

stimulus specific phase locking.

37

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Figure Legends

Figure 1:

In this model, discharge in the visual cortex is determined by the integration of the responses of a

pool of LGN cells. Certain LGN cells (black) are strong oscillators as indicated by the rhythmicity

of their discharge over time. However, their oscillations are independent; they are not explicitly

synchronized. Cortical cells integrate both asynchronous oscillators (black) and non- oscillatory

cells (white). This results in weak and irregular oscillations (gray) in cortical discharge. The

difference in the strength of oscillatory discharge between LGN cells and cortical cells can be seen

in different widths of their inter-spike interval distributions. LGN oscillators (black) exhibit a much

narrower range of inter-spike intervals than even the most oscillatory cortical cells (gray).

Oscillations can be synchronized among nearby cortical cells (gray) if the oscillatory input (black)

is common to the cells. Such a situation is expected given the divergence of LGN input onto the

cortex if there are relatively uniform conduction delays between the LGN and cortex.

Figure 2:

Oscillations in the spontaneous discharge from two nearby LGN cells are shown in A and B. The cell

shown is A is a Y cell; the cell shown in B is a X cell. The ordinate axes for these and all subsequent

correlograms represents spikes per bin. Bin width for A-C, and all subsequent correlograms is 1 ms.

Corresponding power spectra, plotted on a linear-linear scale normalized to the highest point of the

spectra, show the frequency distribution of the discharge (A and B, right). The crosscorrelogram for

these two cells, presented in C, also shows clear rhythmicity although the correlated oscillation is

weaker than either of the individual neuronal oscillations. The same cross-correlogram is shown in

D over a narrower range of interspike intervals with a bin-width of 0.1 ms. The asynchrony of the

49

oscillatory discharge is indicated in D by the location of the primary correlogram peak at +4 ms.

Thus, although the neurons are oscillating at the same frequency, there are not exactly synchronized.

Crosscorrelograms C and D are normalized according to the product of the cells' firing rates.

Figure 3:

Simulated oscillatory discharge is compared with experimentally observed responses from two LGN

cells. Shuffle corrected autocorrelograms showing spike intervals up to 256 ms are shown on the

left. Corresponding power spectra, plotted on a linear-linear scale on the right, show the frequency

distributions of the discharge. Vertical lines on the spectra indicate the location of peaks. Numbers

above the autocorrelograms indicate the vertical scales in spikes/bin. The data from extracellular

recordings of two LGN cells are shown in the first two rows. The final row shows the

autocorrelogram and power spectra associated with a simulated spike train generated according to

retinal ganglion cell spike statistics.

Figure 4:

Simulated oscillatory discharge is compared with experimentally observed responses from two

simple cells. Data are in the same format as Fig 3. The final row shows the autocorrelogram and

power spectra associated with a simulated cortical cell in which 5 of its 15 inputs are LGN

oscillators.

Figure 5:

Simulated oscillatory discharge is compared with experimentally observed responses from two

complex cells. Data are in the same format at Fig 3. The final row shows the autocorrelogram and

50

power spectra associated with a simulated cortical cell in which 14 of its 30 inputs are LGN

oscillators.

Figure 6:

We assume that a Bernoulli process determines which specific LGN inputs, within a range of visual

space, a cortical cell receives. From this assumption, the predicted incidence of oscillatory discharge

in the cortex is a function of its incidence among cells within the LGN. The filled points (dashed

line) are the predictions for complex cells with 30 inputs; the unfilled points (solid line), for simple

cells with 15 inputs. The arrows along the borders of the graph indicate experimentally observed

incidences of single-unit oscillatory discharge in the LGN and visual cortex (Ghose and Freeman

1992). The gray arrow along the LGN incidence axis refers the experimental observed incidence of

very strong (S/N > 8) oscillators in the LGN. The vertical and horizontal lines indicate the

incidences for the LGN and the cortex, respectively. The gray region bordered by a dashed line

delineates the 95% confidence level of incidences for both complex cells and LGN cells; the region

bounded by the solid line indicates the 95% confidence level of incidences for simple cells and LGN

cells. As indicated by the proximity of the simple and complex lines to the center of the respective

boxes, the model can account for both simple and complex cell incidences.

Figure 7:

Simulated low-frequency oscillatory discharge is compared with experimentally observed responses

from two complex cells. Format is the same as Fig 3. The simulated cell (bottom row) has an

intrinsic tendency to oscillate and two of its 30 inputs are LGN oscillators.

51

Figure 8:

Low frequency oscillations are seen in correlated discharge between two cortical cells. Format is

the same as that of Figure 3. Although the individual cells are not oscillatory (A and B have no

power spectra peaks), their correlated discharge does display strong oscillations (C). This oscillation

is asynchronous between the two cells: as shown in the expanded correlogram of D, the primary peak

is offset at -5 ms. Such asynchrony is common between nearby cortical cells whose correlated

discharge displays oscillations at low frequencies.

Fig 1

LGN

Cortex

Inter-Spike Interval Distributions

20 ms.

20 ms.

Time LGN

Cortex

Time

Time

Dis

char

ge

[spk

/sec

]

Time

Dis

char

ge

[spk

/sec

]

p149 3.32e+03

1.64e+03

25 5. e 0

+38 ms. -38 ms.

5.1

+256 ms. 0 ms.

0 ms.

A

B

C Cross

3.4

+128 ms. -128 ms. 0 ms.

D

+256 ms. 0 ms.

0 Hz 500 Hz

59 Hz S/N= 8.5

59 Hz S/N= 13.5

59 Hz S/N= 5.6 1.0

0.0

1.0

0.0

1.0

0.0

250 Hz

0 Hz 500 Hz 250 Hz

0 Hz 500 Hz 250 Hz

Fig 2

53 Hz S/N = 12.8

6.36e+03

53 Hz S/N = 15.6

53 Hz S/N = 14.5

Data

Model

256 ms.

326

1.61e+03p

86

504

500 Hz

0.0

1.0

250 Hz 0 Hz

Fig 3

49

Model

55 Hz S/N = 2.3

Data

p95

53 Hz S/N = 2.9

p2256

63 Hz S/N = 2.2

256 ms.

1.65e+04

7.12e+02

2.77e+02

500 Hz

0.0

1.0

250 Hz 0 Hz

Fig 4

56 Hz S/N = 3.5

Model

Data

256 ms.

1240

500 Hz

582

57 Hz S/N = 5.9

33

63 Hz S/N = 2.6

1.87e+02

1.2e+04

0.0

1.0

250 Hz 0 Hz

Fig 5

Proportion of LGN Oscillators

Pro

port

ion

of C

ortic

al O

scill

ator

s

Fig. 6

0.186

0.156 0.136

0.00 0.05 0.10 0.15 0.20 0.25 0.30

0.0

0.1

0.2

0.3

0.4

0.5

0.6

Model p642

31 Hz S/N = 6.4

73Data

31 Hz S/N = 5.0

p314

27 Hz S/N =3.8

256 ms.

1.99e+03

4.7e+03

9.58e+03

500 Hz

0.0

1.0

250 Hz 0 Hz

Fig 7

p1.51e+03

p6.64e+03

0.73

Cross2.1

A

B

C

D

+256 ms. 0 ms.

+256 ms. 0 ms.

+128 ms. -128 ms. 0 ms.

+12.8 ms. -12.8 ms. 0 ms.

31 Hz S/N = 7.12

1.0

0.0

1.0

0.0

1.0

0.0

1.08e+04

6.24e+04

9.79e+03

0 Hz 500 Hz 250 Hz

0 Hz 500 Hz 250 Hz

0 Hz 500 Hz 250 Hz

Fig 8