Spike Coding in Pyramidal Cells of the Piriform Cortex of Rat

Alexander D. Protopapas and James M. Bower

Division of Biology, California Institute of Technology, Pasadena, California 91125


    ABSTRACT
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ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

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.


    INTRODUCTION
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

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.


    METHODS
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ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

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.

Patch electrodes with impedances of 4-8 MOmega were filled with the following solution (in mM): 120 potassium gluconate, 10 KCl, 10 EGTA, 10 HEPES, 2 MgCl2, 2 CaCl2, and 2 Na2ATP, with pH 7.3 (adjusted with KOH) and osmolarity 290 mosm (Major et al. 1994). The solution was passed through a 0.02-µm filter prior to use. Neurons used in our analysis maintained resting potentials of less than -50 mV from the beginning to the end of the recording.

An Axoclamp 2A amplifier (Axon Instruments, Foster City, CA) controlled by custom software was used to inject current and record membrane potential. Data was digitized using a MetraByte A/D converter and stored to videotape or to the hard disk of a PC (Micro Q 66 MHz 486).

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 (gamma ) equals one when the reconstruction perfectly matches the stimulus. When gamma  = 0, the reconstruction is no better than noise.

To measure coding accuracy as a function of the stimulus frequency, we calculated the gain (or coherence function) (Theunissen et al. 1996). A gain value of 1 indicates that the stimulus in a particular frequency band is perfectly represented in the reconstruction.

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.

The bias correction had a small effect that was partially dependent on the frequency characteristics of the stimulus. The bias in the mean value for mutual information was 0.5-1.6% for the 0- to 5-Hz stimulus, 0.4-2.0% for the 0- to 10-Hz stimulus, 1.3-7.4% for the 0- to 50-Hz stimulus, and 3.2-14.6% for the 0- to 100-Hz stimulus. In the case of the 0- to 400-Hz stimulus, the bias for information measures was substantially larger (19.3-38.8%). For this reason, and the very poor representation of frequencies in the hundreds of Hertz, we focus on responses to stimuli with frequencies of <= 100 Hz.

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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Table 1. Spectral properties of physiological events in olfactory system


    RESULTS
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ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

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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Fig. 1. A: to ensure that our equipment did not distort the Gaussian distribution of stimulus values, the stimulus (0-400 Hz) was recorded from the current monitor of our amplifier and then separated into bands 50-Hz wide. Different shapes represent histograms (bars not shown for clarity) for the various frequency bands. The overlap between the stimulus histogram and the gray line (ideal Gaussian) suggests that the Gaussian distribution of values is maintained at all frequencies in the current stimulus. B: an example of stationarity in the response of a pyramidal cell. A stimulus segment was repeated within an otherwise constantly varying current waveform. The raster plot shows that the cell responded consistently (noise excepted) each time it was exposed to this repeat. Mean firing rate was measured for the 10-s segments of novel (circles) and repeated (asterisks) stimuli and is plotted to the right. Stability in mean firing rate appears to imply stationarity. C: test for possible contribution of nonlinear terms in the reconstruction of the stimulus. Data for C and D come from a typical cell responding to a 0- to 100-Hz stimulus. The plot shows reconstruction values plotted against stimulus values. For clarity, each circle represents the average of all data points within a bin that was 0.0025 nA wide. Bins at extreme values contained fewer points, which may account for the perceived deviation from linearity in those regions. The linearity of this graph suggests that a linear coding scheme implied by the use of KW filters is appropriate. D: this plot tests the possibility that different stimulus frequencies may interact nonlinearly to change the accuracy of coding. Because points (i.e., different symbols) do not cluster above or below the linear regression line, it is unlikely that such nonlinearity plays a role in spike coding. Symbols indicate dominant frequency: circles, 0.5-20 Hz; x's, 20.5-40 Hz; dots, 40.5-60 Hz; asterisks, 60.5-80 Hz; and triangles, 80.5-100 Hz. See text for further explanation.

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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Fig. 2. Examples of filters and reconstructions achieved with stimuli that have bandwidths of 0-5, 0-10, 0-50, and 0-100 Hz. Dotted lines are the stimuli and solid lines are the reconstructions. Very small hash lines on the KW filters are error bars.

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 (gamma ) 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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Fig. 3. Coding fraction (A), mutual information (B), and mutual information per spike (C) are shown as functions of mean spike rate. Data come from 32 different cells. Error bars are insignificant at the scale of the the 3 graphs. D: gain as a function of spiking frequency. Thick solid line shows the average gain vs. stimulus frequency for 12 cells. Error bars are not shown because the average is taken over many mean spike rates. The bottom curve represents the mean gain for cells with firing frequencies from 0.9 Hz to the median value of 4.3 Hz. The top curve shows the mean gain for cells with spike rates above the median to 11.6 Hz.

When mutual information is plotted against spike rate (Fig. 3B), the relationship is again linear; however, in contrast to gamma , 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 gamma  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.


    DISCUSSION
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ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

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.


    ACKNOWLEDGMENTS

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).


    FOOTNOTES

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.


    REFERENCES
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

0022-3077/01 $5.00 Copyright © 2001 The American Physiological Society