Division of Biology, California Institute of Technology, Pasadena, California 91125
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ABSTRACT |
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Protopapas, Alexander D. and James M. Bower. Spike Coding in Pyramidal Cells of the Piriform Cortex of Rat. J. Neurophysiol. 86: 1504-1510, 2001. The study of cortical oscillations has undergone a renaissance in recent years because of their presumed role in cognitive function. Of particular interest are frequencies in the gamma (30-100 Hz) and theta (3-12 Hz) ranges. In this paper, we use spike coding techniques and in vitro whole cell recording to assess the ability of individual pyramidal cells of the piriform cortex to code inputs occurring in these frequencies. The results suggest that the spike trains of individual neurons are much better at representing frequencies in the theta range than those in the gamma range.
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INTRODUCTION |
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It has been
known for many years that the olfactory system of mammals generates
field potential oscillations in the presence of odorants (Adrian
1942; Freeman 1960
; Freeman and Schneider 1982
; Macrides and Chorover 1972
;
Macrides et al. 1982
; Woolley and Timiras
1965
). The olfactory bulb of mammals receives direct projections from olfactory receptor neurons in the nasal epithelium and
produces oscillations in both gamma (30-100 Hz) and theta (3-12 Hz)
frequencies (Eekman and Freeman 1990
; Kay and
Freeman 1998
). Mitral cell axons from the olfactory bulb
project to piriform cortex, which is the primary olfactory cortex in
all mammals (Haberly 1998
). Electroencephalograms (EEGs)
recorded in piriform cortex also show oscillations in the 3- to 12- and
30- to 100-Hz frequency ranges (Kay et al. 1996
;
Woolley and Timiras 1965
). Other studies (Bressler 1984
, 1987
, 1988
; Kay and Freeman
1998
) have shown that oscillations in these two structures are correlated.
While the precise origin and function of these oscillations in piriform
cortex and other cortical structures remains to be understood
(Gray 1994, 1999
), their correlation to stimulus
presentation and behavior have given rise to numerous hypotheses
relating network oscillations to the representation of information or
the cognitive state of the animal (Crick and Koch 1990
;
Freeman and Schneider 1982
; Gray et al.
1989
; Murthy and Fetz 1996
). Modeling work in our laboratory (Wilson and Bower 1992
) and current
source density analysis by Ketchum and Haberly (1993)
suggest that oscillatory patterns in piriform cortex are the direct
result of synaptic currents produced in pyramidal neurons.
In this paper, we use electrophysiological techniques to determine how
well the output of individual pyramidal cells can represent inputs that
cover the frequency range of cortical oscillations. To quantify this
relationship, we have used an information-theoretic approach introduced
several years ago to study the spike coding of behavioral stimuli
(Bialek et al. 1991; Theunissen et al.
1996
; Wessel et al. 1996
). We use these methods
to measure the ability of the spike train of a piriform cortex
pyramidal cell to represent a fluctuating nonrepeating current stimulus
presented to the soma in vitro. This stimulus is meant to approximate
an input signal reaching the soma after it has first been transformed
by processes in the dendrite.
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METHODS |
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Experimental procedures
SLICE PREPARATION.
A total of 22 4- to 5-wk-old female Sprague-Dawley rats were used in
this study. Animals were decapitated under ether anesthesia following
procedures approved by the California Institute of Technology Animal
Care and Use Committee (protocol 1156). Brains were removed and bathed
in cooled medium previously bubbled with 95%
O2-5% CO2 during the
slicing procedure. A vibratome (WPI VSL) was used to cut five coronal
400-µm-thick slices starting at 0.4 mm caudal to the anterior
commissure. Slices were initially incubated at 35°C in medium bubbled
with the gas mixture described in the preceding text for 35 min before
transferal to medium at room temperature. The medium consisted of (in
mM): 26 NaHCO3, 124 NaCl, 5 KCl, 1.2 KH2PO4, 2.4 CaCl2, 1.3 MgSO4, and 10 dextrose (Barkai and Hasselmo 1994; Tseng and
Haberly 1989
). Kynurenic acid (660 µM) was added to the
medium during slicing and incubation to prevent excitotoxicity; however, kynurenic acid was absent during experiments (Hasselmo and Bower 1992
). During recording, a submersion-type slice
chamber was used (temperature: 30.1-34.7°C). Medium passed through
the chamber at a rate of approximately 3.5 ml/min.
RECORDING PROCEDURES.
As in other studies, piriform cortex pyramidal cells were identified by
their somatic position in layer II and their distinctive response to
current injection (Barkai and Hasselmo 1994;
Haberly 1998). A Zeiss Axioskop microscope (Carl Zeiss,
Thornwood, NY) was used to somatically position electrodes.
PHARMACOLOGY. Synaptic blockers were added to the bathing solution to isolate neurons from the effects of random synaptic input during stimulation. Specifically, 30 µM 6-cyano-7-nitroquinoxaline-2,3-dione (RBI, Natick MA), 100 µM DL-2-amino-5-phosphovaleric acid (Sigma), and 50 µM picrotoxin (RBI) were used to block AMPA/kainate, N-methyl-D-aspartate (NMDA), and GABAA receptors, respectively. Recording started at least 10 min following the application of these chemicals, which experiments indicated was the minimum time needed for cell properties to stabilize.
Data analysis
Data analysis was done using MATLAB (MathWorks, Natick, MA) and
EXCEL (Microsoft, Redmond, WA). Membrane time constants were calculated
by performing an exponential fit to the transient response of the
neuron when stimulated with a 0.1-nA current pulse.
Stimulus Reconstruction.
When the Kolmogorov-Wiener (KW) filter is convolved with a neuron's
spike train, an estimate of the stimulus is obtained (Riecke et
al. 1997). The KW filter guarantees the best linear estimation of the stimulus by minimizing the least-squares difference between the
stimulus estimate and the actual stimulus (Wiener 1949
).
Calculations used to derive the KW filter are described elsewhere
(Riecke et al. 1997
; Wessel et al. 1996
).
By comparing the reconstruction to the stimulus, we can quantify how
well a neuron's spike train represents the stimulus. We did this by
calculating the mutual information (between stimulus and estimate) and
the coding fraction using equations described in Wessel et al.
(1996)
. Coding fraction is a normalized measure of the quality
of the reconstruction (estimate). The coding fraction (
) equals one
when the reconstruction perfectly matches the stimulus. When
= 0, the reconstruction is no better than noise.
Calculation of sampling error.
The Jacknife method (Efron 1982; Theunissen et
al. 1996
) was used to calculate sampling error and bias in the
reconstruction. This method estimates the standard error by deleting
samples from the data set and recalculating KW filters, mutual
information, etc. Our methods were identical to those used in
Theunissen et al. (1996)
. We calculated sampling error
and bias by studying the effect of deleting half the data set from the
recordings used to calculate KW filters.
Stimulus characteristics.
All stimuli for the spike coding analysis consisted of continuous
nonrepeating current injections (sampled at 1 kHz) with a Gaussian
distribution of values (SD: 0.013-0.110 nA) and lasted from 10 to 60 min. These stimuli were able to induce membrane potential fluctuations
roughly similar in size to those found in in vivo intracellular
recordings from piriform cortex pyramidal cells (Nemitz and
Goldberg 1983). A range of mean spike rates (1-12 Hz) was
obtained by adding a DC offset (0.03-0.46 nA) to the stimulus waveform
during recording. This range of firing rates roughly matches those seen
in in vivo pyramidal cells responding to odorant stimulation (see Table
1). When we tried to force neurons to
fire at sustained rates above 12 Hz, the health of the cells rapidly
deteriorated.
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RESULTS |
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Requirements for linear reconstruction
The following experimentally determined requirements must be
satisfied for the application of the linear reconstruction techniques described in the METHODS (Riecke et al.
1997): stimulus values must have a Gaussian distribution; the
neuron must display stationarity over the period data are collected;
and spike coding must be largely linear. Figure
1, A and B, shows
that we meet the first two requirements.
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For the third requirement, we used two tests. The first is to plot
estimate versus stimulus values. If nonlinear terms contribute significantly to spike coding, then we would expect to see consistent deviations from linearity in the graph (e.g., saturation effects) (Riecke et al. 1997). The data set in Fig. 1C shows almost
no deviation from linearity, indicating that nonlinear terms are unlikely to contribute significantly. In some experiments there was a
very slight deviation from linearity at extreme data values; however,
points falling out of the linear range accounted for only a small
minority of waveform values.
A second type of linearity test (shown in Fig. 1D) was
used to examine the possibility that stimulus frequencies may interact nonlinearly to affect the accuracy of the reconstruction
(Theunissen et al. 1996). We divided the reconstruction
and corresponding stimulus into segments that were each 2.0 sec long.
The power spectrum of each segment was then divided into frequency bins that were 20 Hz wide. An arbitrary frequency (5 Hz, the most well represented frequency in this case) was selected, and its power in the
reconstruction was plotted against its power in the actual stimulus.
The slope of the regression line represents the gain at this selected
frequency. The shapes of the points in the scatter plot indicate the
dominant frequency (i.e., the 20-Hz frequency bin with the greatest
power) in the 2.0-s stimulus segments. If a dominant stimulus frequency
resulted in a better or worse than average reconstruction at the
plotting frequency, these points would cluster above or below the
regression line. Figure 1D shows that points representing
different dominant frequencies do not tend to cluster above or below
the regression line, indicating that nonlinear frequency interactions
are unlikely. In the case of Fig. 1D, we selected 5 Hz as
our plotted frequency; however, when we did the same analysis using
frequencies that covered the range of 1-100 Hz, we found similar
results for all neurons tested.
Stimulus reconstruction
Typical KW filters and reconstructions obtained with different stimulus frequencies are shown in Fig. 2. The 0- to 5- and 0- to 10-Hz stimuli are well represented by the reconstructions. This is partially due to the ability of a spike rate of <10 Hz to capture most of the low-frequency stimulus structure. A second factor is the ability of KW filters generated from these stimuli to represent negative peaks in the stimulus. In contrast, results generated with high-frequency stimuli (0-50 and 0-100 Hz) show a much poorer match between stimuli and reconstructions, especially for negative peaks.
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The dependence of various information measures on spike rate is shown
in Fig. 3. Figure 3A shows
that for each stimulus type, the relationship between spike rate and
coding fraction () is linear. In these plots, the slopes of the
regression lines used to fit data from different stimuli are inversely
related to the highest frequency in each stimulus. Therefore the
improvement in stimulus representation for a unit increase in spiking
frequency is much greater for 0- to 5-Hz stimuli than those in the 0- to 100-Hz range.
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When mutual information is plotted against spike rate (Fig.
3B), the relationship is again linear; however, in contrast
to , mutual information measures are greater for higher bandwidth stimuli. This is because mutual information is an absolute measure of
the number of bits in the reconstruction, while
quantifies the
match of the reconstruction to the stimulus. Reconstructions of high
bandwidth stimuli include frequency components that are absent in the
reconstructions of low bandwidth stimuli and hence contain additional information.
Figure 3C shows a trend of decreasing mutual information per spike with increasing mean spike rates. In this case, data were better fit to decaying exponential curves.
To examine how well individual pyramidal cells code different stimulus frequencies during the course of a single 0- to 100-Hz stimulus, we measured the gain (or coherence) between the stimulus and reconstruction. Figure 3D shows that frequencies in the 0.5- to 30-Hz range are much better represented than those that exceed 30-Hz, regardless of whether a pyramidal cell is spiking at low or high rates (in the 1- to 12-Hz range). Since mean firing rate was controlled primarily through the amplitude of the DC current offset, a comparison of gain functions for low and high firing rates should approximate the effects of stimulus magnitude on the spike coding of pyramidal cells. If this is the case, we find that stimulus amplitude does not qualitatively change the spike coding properties of these neurons.
Ideally one would want to test the effects of stimulus amplitude on spike coding using a single neuron to control for differences in physiology between individual cells. A single pyramidal cell would be stimulated at multiple levels of DC current, and a KW filter would be calculated for each level of stimulation. Unfortunately this approach turned out to be technically problematic because of the prolonged periods of stimulation and steady spike rates required for the proper calculation of KW kernels. We tried this multiple times and were able to achieve acceptable results for a single neuron using a 0- to 100-Hz stimulus. In this case, we kept the stimulus SD constant and brought down the DC current offset so that the cell would decrease its mean spike rate from 9.9 to 4.4 Hz. We then calculated KW filters for each level of stimulation. The gain functions were qualitatively similar, showing peaks at 6.4 Hz (high spike rate) and 2.0 Hz (low spike rate) and then monotonically decreasing. One difference was that the gain function associated with the higher spike rate showed better representation of higher frequencies. These results are similar to those shown in Fig. 3D, where averaged gain functions for cells with higher spike rates showed better coding for higher frequency components in the stimulus.
Similarly, for the SD range we used, we could not find any significant differences in frequency coding between cells.
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DISCUSSION |
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In this study, we sought to determine how well a spike train generated by a piriform cortex pyramidal cell can represent a time varying current change in the soma. Somatic current injection can be thought to approximate the input that would reach the spike initiation zone after it was first filtered through the actions of synaptic receptors, voltage-gated channels, and the passive properties of the dendrite.
Ability of pyramidal neurons to represent stimulus
The gain function in Fig. 3D shows that coding is best
at 2.5 Hz, then drops off monotonically at higher stimulus frequencies. To some extent, the behavior of this curve can be explained by the
physiology of the neuron. A membrane time constant of 9.9 ± 2.4 ms (n = 39) suggests that stimulus frequencies above
100 Hz will be filtered out. Similarly, the inability of pyramidal cells to sustain prolonged mean spike rates above 12.2 Hz, might partially explain the lack of coding fidelity at stimulus frequencies above 30 Hz; however, this does not imply that a neuron's gain function can somehow be intuitively derived from its physiology. Mean
spike rates do not yield insight into the precise temporal structure of
a spike train. Before analyzing data from our experiments, we
anticipated that pyramidal cell gain functions might have two peaks, a
large one in the theta range and a smaller one in the gamma. A previous
spike coding study in the cricket cercal sensory system had shown peaks
in a neuron's gain function at multiple stimulus frequencies
(Theunissen et al. 1996), so our hypothesis seemed
plausible. Here, we find a single peak followed by a monotonic decrease. This was surprising given the presumed frequency
characteristics of inputs to piriform cortex pyramidal cells (see later text).
It is important to note that previous physiological studies
demonstrated considerable accommodation in the spike trains of piriform
cortex pyramidal cells (Barkai and Hasselmo 1994;
Protopapas et al. 1998
). In our experiments, the
portions of the spike train used in calculating KW filters were
recorded after accommodation had taken place, to fulfill the
stationarity requirements necessary for calculating KW filters (Riecke
et al. 1997
). While it is possible that unaccommodated pyramidal cells
may better represent frequencies above 30 Hz, such high-frequency
coding would only be present for the short time following the initial
presentation of the stimulus prior to the onset of accommodation.
Functional significance
The table shows the frequencies of various physiological phenomena
associated with olfaction in the rat olfactory system. Data presented
in this paper suggest that individual pyramidal cell spike trains
could represent input associated with the theta rhythm (3-12 Hz),
respiration (0.8-2.0 Hz), exploratory sniffing (4-11 Hz), and the
mean spike rates of olfactory bulb mitral cells (3-20 Hz).
Interestingly, fMRI experiments show that activity in human olfactory
cortex correlates with the sniff cycle rather than the presence or
absence of odors (Sobel et al. 1998).
Although our data suggest that the spike trains of individual pyramidal
cells poorly represent frequencies above 30 Hz, experimental and
modeling work has shown that the gamma frequency is likely to be a
direct outcome of synaptic currents generated in the apical dendrites
of pyramidal cells (Ketchum and Haberly 1993; Wilson and
Bower 1992
). Additionally, while a study by Bhalla and Bower (1997)
shows mitral cell mean spike rates of 3-20 Hz,
odorant-induced responses in the mitral cells of anesthetized rats show
instantaneous frequencies as high as 100 Hz (Wellis et al.
1989
). Given these observations, one wonders why the spike
trains of pyramidal neurons would not represent inputs in the gamma
frequency range.
From a functional perspective, this lack of fidelity at high frequencies might be explained as follows: 1) Pyramidal cell spike trains do not accurately code frequencies above 30 Hz because the neural processes involved in gamma oscillations do not contain stimulus-related information. 2) Information contained in gamma frequency events is represented in a network-level code rather than in the spike trains of individual neurons. And 3) dendritic processes may transform synaptic inputs in such a way that high-frequency (>30 Hz) information is represented in the spike train despite the bandwidth limitations imposed by the spike initiation zone. Note that these explanations are not mutually exclusive.
Although some researchers have suggested that gamma frequency
oscillations represent information about a stimulus (Bressler 1990; Freeman and Barrie 1994
), others have
proposed that they simply reflect the organization of network activity
(Jefferys et al. 1996
; Wilson and Bower
1992
). Support for the latter hypothesis comes from the
hippocampus, where inhibitory neurons are believed to underlie gamma
oscillations (Jefferys et al. 1996
). Once activated, the
inhibitory cells fire rhythmically and are not affected by any
additional synaptic inputs (Whittington et al. 1995
). A
spiking inhibitory cell can then synchronize the action potentials of individual pyramidal cells in the hippocampus (Cobb et al.
1995
; Whittington et al. 1995
). This phenomenon
has prompted speculation that the gamma frequency generated by these
inhibitory neurons may reflect a "clocking" of the network that is
not stimulus-specific (Jefferys et al. 1996
). If a similar situation
exists in the piriform cortex, one might expect that a pyramidal cell
can ignore high-frequency inputs from inhibitory neurons without
compromising stimulus-related information processing.
A second possibility is that high-frequency information is contained in
a network-level code. Although individual piriform cortex pyramidal
cells may not accurately code stimulus frequencies above 30 Hz, it is
possible that the relative spike timings of different pyramidal cells
may be used to code for high-frequency stimuli. For example, in the
barn owl, axonal delay lines are used to selectively activate different
neurons based on the precise value of an interaural time difference
(Carr and Konishi 1990). It is certainly plausible that
network-level coding in piriform cortex may exceed the temporal
resolution of spike coding in individual pyramidal cells.
Several possibilities exist for dendritic mechanisms that may act to
overcome the bandwidth limitations of the spike initiation zone in
piriform cortex pyramidal cells. Active processes in the dendrite could
initiate a forward-propagating dendritic action potential in response
to high-frequency synaptic inputs. This action potential could then
directly initiate spiking at the spike initiation zone. A similar
process has been demonstrated in neocortical pyramidal cells, where
forward-propagating calcium action potentials in the dendrite can be
induced in response to the pairing of a back-propagating sodium spike
and an input applied to the dendrite (Larkum et al.
1999). The neocortical neuron is thus able to achieve coincidence detection with a temporal resolution of 5 ms. No studies have been done to ascertain the extent to which active processes play a
role in the piriform cortex pyramidal cell dendrite, but given the
presence of voltage-gated channels in the dendrites of neocortical
(Stuart and Sakmann 1994
) and hippocampal (Magee and Johnston 1995
) pyramidal neurons, there is no reason to
rule out their existence in piriform cortex.
One process that is known to exist in piriform cortex is paired-pulse
facilitation, which has been demonstrated along the synaptic pathways
that terminate on the apical dendrite of pyramidal cells. Intracellular
responses to paired shocks separated by 10-200 ms showed a significant
increase in the amplitude of the excitatory postsynaptic potential
(EPSP) generated by the second shock (Bower and Haberly
1986). This effect is most pronounced in the distal-most portion of the apical dendrite, where inputs from olfactory bulb mitral
cells terminate. In contrast, paired-pulse facilitation is less
pronounced in the proximal regions of the apical dendrite, where axons
from other piriform cortex pyramidal cells terminate. This is
interesting because mitral cell spike rates would presumably be higher
than those of other pyramidal cells. Paired-pulse facilitation may
provide a way of coding for higher frequency inputs by selectively increasing the EPSPs associated with high-frequency inputs.
In this paper, we have described how the spike initiation zone of an individual pyramidal cell codes a fluctuating input administered to the soma. As the preceding discussion indicates, this is likely to be a small, but vital, part of neural coding. We believe that an understanding of information processing in the brain requires this kind of micro-dissection of its coding properties. Conceivably, information-theoretic techniques could also be applied to aspects of dendritic and network coding in piriform cortex.
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ACKNOWLEDGMENTS |
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We thank H. Bolouri, C. Chee, and M. Hartmann for useful comments on the manuscript.
This work was supported by a Multi-University Research Initiative from the Army Research Office (Grant DAAG55-98-1-0266).
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FOOTNOTES |
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Address for reprint requests: A. D. Protopapas, Division of Biology, MS 216-76, California Institute of Technology, Pasadena, CA 91125 (E-mail: alexander_protopapas{at}hotmail.com).
Received 31 October 2000; accepted in final form 30 May 2001.
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REFERENCES |
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