Section of Neurobiology, Physiology and Behavior and Center for Neuroscience, University of California, Davis, California 95616
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ABSTRACT |
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Sutter, Mitchell L..
Shapes and Level Tolerances of Frequency Tuning Curves in
Primary Auditory Cortex: Quantitative Measures and Population Codes.
J. Neurophysiol. 84: 1012-1025, 2000.
The shape and level tolerance of the excitatory frequency/intensity
tuning curves (eFTCs) of 160 cat primary auditory cortical (A1) neurons
were investigated. Overall, A1 cells were characterized by tremendous
variety in eFTC shapes and symmetries; eFTCs were U-shaped (~20%),
V-shaped (~20%), lower-tail-upper-sharp (~15%), upper-tail-lower-sharp (<2%), slant-lower (~10%), slant-upper (<3%), multipeaked (~10%), and circumscribed (~20%).
Quantitative analysis suggests that eFTC are best thought of as forming
a continuum of shapes, rather than falling into discrete categories. A1
eFTCs tended to be more level tolerant than eFTCs from earlier stations in the ascending auditory system as inferred from other studies. While
individual peaks of multipeaked eFTCs were similar to single peaked
eFTCs, the overall eFTC of multipeaked neurons (spanning the range of
all peaks) tended to have high-frequency tails. Measurements of shape
and symmetry indicate that A1 eFTCs, on average, tended to have greater
area on the low-frequency side of characteristic frequency (CF) than on
the high-frequency side. A1 cells showed a relationship between CF and
the inverse slope of low-frequency edges of eFTCs, but not for
high-frequency edges. These data demonstrate that frequency tuning,
particularly along the eFTC low-frequency border, sharpens along the
lemniscal pathway to A1. The results are consistent with studies in
mustached bats (Suga 1997) and support the idea that
spectral decomposition along the ascending lemniscal pathway up to A1
is a general organizing principle of mammalian auditory systems.
Altogether, these data suggest that A1 neurons' eFTCs are shaped by
complex patterns of inhibition and excitation accumulating along the
auditory pathways, implying that central rather than peripheral
filtering properties are responsible for certain psychophysical phenomena.
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INTRODUCTION |
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To understand one of the most
fundamental receptive field properties of auditory neurons, frequency
tuning, it is essential to understand how frequency tuning varies with
intensity. Many auditory perceptual phenomena, such as sound
localization, complex spectral processing, and critical band processing
vary little with changing intensity (Comalli and Altshuler
1976; Fletcher 1940
; Seaton
1979
). Suga and colleagues (Suga 1994
,
1995
, 1997
; Suga and Tsuzuki
1985
) elegantly reason that constancy in frequency selectivity
across intensity (called "level tolerance") is essential for
information processing in echolocating mustached bats. Despite the
importance of intensity invariant processing in auditory perception, very little is known about the neurophysiology underlying it. Therefore
investigating the intensity dependence of auditory neurons' frequency
receptive field properties is critical if we are to understand auditory
perception and behavior.
Although frequency tuning traditionally has been measured at a single
intensity (e.g., Calford et al. 1983), this approach cannot reveal level tolerance (Suga 1997
). To quantify
level tolerance one must characterize excitatory frequency tuning curve
(eFTC) "shape," i.e., how frequency tuning varies with intensity.
Characterizing eFTC shapes has provided insight into population codes
of sound. For example, the prevalence of extended low-frequency tails,
and sharp high-frequency cutoffs in auditory nerve (AN) fiber eFTCs (e.g., Kiang et al. 1967
) indicate that more AN fibers
will respond to a loud low-frequency sound than a loud high-frequency
sound. This type of population code cannot simply be determined by
sharpness measures, such as bandwidths or quality (Q) factors, but
rather requires quantifying how low- and high-frequency edges of eFTCs vary with intensity.
An additional advantage of quantifying eFTC shapes is that it
facilitates correlation between eFTCs and other physiological or
anatomical properties. Neurons are frequently categorized based on
their qualitative eFTC shapes to demonstrate different properties between groups of neurons. Usually, these analyses show multiple differences between cells having U-shaped, V-shaped, multi-peaked, circumscribed, and tailed eFTCs (e.g., Calford and Semple
1995; Casseday and Covey 1992
; Sutter and
Schreiner 1991
). Unfortunately, these subjective descriptive
measures can differ between investigators. In fact, the lack of a
quantitative framework to classify cells results in categorization that
is subjective and somewhat arbitrary. Furthermore, whether these
classifications are truly based on discrete classes of neurons, or
rather on arbitrary sub-divisions along a continuum, remains
unanswered. Therefore to make meaningful comparisons across
laboratories and different brain areas, standard reliable quantitative
measures of shape are required. While shape measures have been made on
AN fiber eFTCs (Brugge et al. 1981
; Javel
1994
; Kiang and Moxon 1974
), quantification of
central neurons' eFTC shapes are uncommon (e.g., Salvi et al.
1994
; Sams-Dodd and Capranica 1994
; Wang
et al. 1996
).
In this paper, the coarse shape of A1 neurons' eFTCs are characterized by quantitatively analyzing the level dependence of their low- and high-frequency eFTC borders. With this analysis both eFTC shape and frequency tuning can be addressed in more detail than one obtains with bandwidth measures alone. The results indicate that most A1 eFTCs in cats are slightly shifted toward lower frequencies and are quite level tolerant.
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METHODS |
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Surgical preparation
Surgical preparation, stimulus delivery, and recording
procedures have been described previously (Sutter and Schreiner
1991; Sutter et al. 1999
) and are summarized
below. Single units were recorded from the right hemisphere of 23 cats
and the left hemisphere of 3 cats. After venous cannulation, an initial
dose of pentobarbital sodium (30 mg/kg) was administered. Animals were
maintained at a surgical level of anesthesia with continuous infusion
of pentobarbital sodium (2 mg · kg
1 · h
1) in lactated Ringer solution (infusion
volume: 3.5 ml/h) and, if necessary, with supplementary intravenous
injections of pentobarbital. The cats were also given dexamethasone
sodium phosphate (0.14 mg/kg im) to prevent brain edema and atropine
sulfate (1 mg im) to reduce salivation. The animals' rectal
temperature was maintained at 37.5°C.
After 72-120 h of recording, animals were deeply anesthetized and perfused transcardially with saline followed by Formalin so brain tissue could be processed for histology. Cresyl-violet and fiber staining was used to reconstruct electrode positions from serial frontal 50-µm sections. Electrode positions were marked with electrolytic lesions (5-15 µA for 5-15 s) at the final few recording sites.
Stimulus generation and delivery
Experiments were conducted in double-walled sound-shielded rooms (IAC). Calibrated insert speakers (STAX 54) enclosed in small chambers that were connected to sound delivery tubes sealed into the acoustic meati of the contralateral ear [Sokolich 1981, U.S. Patent 4251686] were used. This sound delivery system was calibrated with a sound level meter (Brüel and Kjaer), and distortions were measured either with waveform analyzers (General Radio) or a computer acquisition system (TDT). The frequency response of the system was essentially flat up to 14 kHz and did not have major resonance deviating more than ±6 dB from the average level. Above 14 kHz, the output rolled off at a rate of 10 dB/octave. The presented intensity values were not corrected for the fluctuation in the transfer function; however, for cells that responded to tones above 14 kHz, we accounted for the roll-off and adjusted intensity values appropriately in the data analysis. Harmonic distortion was better than 55 dB below the primary.
Recording procedure
Parylene-coated tungsten microelectrodes (Microprobe, impedance
1-8.5 M at 1 kHz) were inserted into A1 with a hydraulic microdrive. Penetrations were approximately orthogonal to the brain
surface. Recordings were made at depths from 600 to 1,000 µm below
the cortical surface, as determined by the microdrive. Dimpling of the
cortical surface was usually <100 µm, and thus not a major factor in
determining electrode depth. Histological verification from several
animals indicated that the recording sites were from cortical layers 3 and 4. Electrical signals from the electrode were amplified, and action
potentials from individual neurons were isolated with a window discriminator.
Single-tone frequency response areas
Frequency response areas (FRAs) were obtained for 160 single
neurons. Six-hundred seventy-five tone bursts (50 ms long, 3-ms linear
rise/fall time, and 400- to 1,200-ms interstimulus interval) were
presented in a pseudo-random sequence of different frequency-intensity combinations selected from 15 intensities and 45 frequencies. Intensities were spaced 5 dB apart for a total range of 75 dB. The
frequencies were logarithmically spaced with ranges between 2 and 5 octaves, depending on the estimated frequency tuning curve (FTC) width.
Logarithmic spacing was chosen because of the nearly logarithmic
spacing of frequency in the periphery, and because of the logarithmic
nature of auditory filters (Moore 1995). Typically a
3-octave range, centered on the cells best (most sensitive) excitatory
frequency (BEF) was used, providing 0.067-octave resolution.
The time constraints of single-unit recording necessitated characterizing FRAs on as few stimulus repetitions as possible. If a response was evoked for more than approximately 50% of the stimuli inside of each excitatory band, the FRA was deemed well-defined. In A1, this criterion corresponds roughly to the mean spikes-per-presentation minus 1 SD. If after one presentation per frequency-intensity combination the resulting FRA was not well-defined, the process was repeated with and the resulting responses were added. If necessary, the FRA recording procedure was repeated up to five times.
Single-tone eFTC construction
Excitatory FTCs (the borders of the excitatory spectral
receptive fields), were constructed from the FRAs based on the
estimated spontaneous rate plus 20% of the peak rate (examples of
eFTCs derived from FRAs can be seen in Sutter et al.
1991, 1999
). This criterion was applied
after a weighted response averaging with the eight frequency-intensity
neighbors was applied to each FRA coordinate. This smoothing increased
the effective number of presentations per frequency-intensity
combination by a factor of 2.5 at the expense of frequency resolution.
This method was robust, yielding comparable results across repeated
measurements (see Table 3 of Sutter and Schreiner 1991
).
The first step of eFTC analysis was to identify each excitatory band.
Then, the upper and lower frequency bounds of each excitatory band as
well as of the bounds of the entire eFTC were calculated at all intensities.
Measures of steepness of eFTC edges: inverse-slopes and edge regressions
To quantify the level dependence of eFTCs, the inverse-slopes
(IS) of their low- and high-frequency borders were calculated. Generally IS provides robust characterizations of eFTC borders by
measuring the frequency difference in octaves at two different intensities along an eFTC edge. Figure
1A demonstrates this
calculation for both the lower and upper edge at 15 and 50 dB above
threshold. In this schematized example, the IS for the low-frequency
border, IS15-50_lower, is 0.25
octaves (per 35 dB). Negative numbers denote slopes toward lower
frequencies at higher intensities. For the high-frequency border,
IS15-50_upper was 0.10 octaves (per 35 dB).
IS5-25, IS5-45,
IS5-65, and IS30-60 were
also measured, comparing the frequency of the edges of eFTCs at 5 and
25 dB, 5 and 45 dB, 5 and 65 dB, and 30 and 60 dB above threshold,
respectively.
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In addition to measuring the ISs by sampling two-points along the eFTC edge, the ISs of eFTC edges were also measured by fitting a regression line through each border of the eFTC (Fig. 1B). The spacing for the data points for the regression was identical to that used for FRA collection: i.e., 5 dB. The regression was started at 15 dB above threshold to eliminate any effects near the tip of the eFTC. Regressions were also made starting at 10 dB above threshold.
The IS measure was used, rather than more traditional slope
measurements, because of an instability of slope measurements around
vertical eFTC edges. For example, a cell with an upper edge IS of 0.01 octaves/40 dB has a slope of 4,000 dB/octave (Fig. 1C, ),
while a cell that slightly slants toward lower frequencies with a upper
IS of
0.01 octaves/40 dB (Fig. 1C, - - -) has a slope
of
4,000 dB/octave. So, although the eFTC edges differ by only 0.02 octaves per 40 dB, the slope measures differed by 8,000 dB/octave.
Accordingly, at 40 dB above threshold, the high-frequency borders of
the first and second cells' eFTCs look very similar but have very
different slope measurements because of the instability around infinite
slope. Using inverse slopes circumvents this problem.
Determining strength of intensity tuning
The monotonicity ratio (the number of spikes elicited at the
highest intensity tested divided by the number of spikes elicited at
the maximum of the spike count verse intensity function) was used to
quantify the strength of intensity tuning (Sutter and Schreiner
1995). For each intensity of the spike count versus intensity
function, the number of spikes from a 1/4 octave bin around the
unit's BEF and a 15-dB wide intensity bin were summed. One-quarter octave usually comprised 4 different frequencies and 15 dB covered three intensities, providing a minimum of 12 different stimulus presentations per data point in the spike count versus intensity functions. Therefore a cell that fired maximally at the highest tested
intensity had a monotonicity ratio of 1; a cell that was completely
inhibited at the highest tested intensity had a monotonicity ratio of
0. Only units that were recorded from a minimum of 45 dB above
threshold were analyzed for monotonicity ratio.
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RESULTS |
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General shape of excitatory bands
In general, there was tremendous variety in the shapes and symmetries of eFTCs for the 160 neurons recorded from primary auditory cortex (A1). To characterize eFTC shape, the most commonly employed method of classification was used; eFTCs were classified based on visual inspection of their general appearance. Figure 2 schematically depicts the percentages of different eFTC types. The frequency tuning of U-shaped eFTCs does not depend on intensity and therefore is sometimes called level-tolerant. The frequency tuning of V-shaped eFTCs becomes broader on the low- and high-frequency sides of their eFTCs with increasing intensity. Lower-tail-upper-sharp (LTUS) eFTCs have large "tails" on their low-frequency edges, but have sharp, relatively vertical high-frequency edges. Slant-lower eFTCs have high-frequency edges slanting to lower frequencies. Multipeaked eFTCs have more than one distinct excitatory region separated by a nonexcitatory region. Sharp multipeaked eFTC have two or more level tolerant excitatory areas. Mixed multipeaked or "high heel" eFTCs resemble a high heel shoe and tend to have very broad lower excitatory bands and sharp upper excitatory bands. Circumscribed eFTCs are completely enclosed.
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Although many of these eFTC classes have been reported in the auditory
cortex of several species, the proportions of these classes have not
been extensively examined. Of the recorded neurons that were
classifiable, 22.4% (33/147) had U-shaped eFTCs. This characterization
of U- or V-shaped depends more on the shape of the eFTC at higher
intensities than near the low-intensity threshold (eFTC "tip") and
therefore what this paper refers to as "U-shaped" can include cells
that others call "pencil shaped" (e.g., Suga 1995).
The criteria employed herein would also classify cells with rounded
eFTC tips, but rapidly increasing bandwidth at higher intensities, as
V-shaped. U-shaped curves (e.g., Fig. 3,
A and B) had a range of bandwidths and were
sometimes intensity-tuned (also called nonmonotonic). A large
percentage of cells were classified as having V-shaped eFTCs (19.0%,
28/147). V-shaped eFTCs (Fig. 3, C and D) could
be narrow at the tip and expand only at higher intensities or could be
relatively broad at most intensities. V-shaped eFTCs could be
intensity-tuned and could have complex response profiles within their
eFTC. The cell whose FRA is shown in (Fig. 3D), for example,
preferred intensities between 15 and 30 dB, had a strongly responsive
area from 17-21 kHz, and had weaker responding upper and lower tails
making a V-shaped curve. Circumscribed eFTCs (Fig. 3E) were
also common (20.4%, 30/147) and by definition were intensity tuned.
Circumscribed eFTCs tended to be sharp, although there was some
variability in frequency tuning. Only 13.6% (20/147) of the cells had
LTUS eFTCs (Fig. 3F), which is the most common class of
eFTCs in AN fibers (Kiang and Moxon 1974
). However, the
present classification is not identical to that used in the AN because
there was large variation in the slope of tails, which probably
included shallower tails than are observed in the AN. Surprisingly,
10.2% (15/147) of the cells possessed eFTCs that slanted toward lower
frequencies (Fig. 3, G and H). Most of these
cells were intensity-tuned, and some resembled circumscribed cells with
low-frequency remnants (Fig. 3G). The degree of slant was
variable. Cells with eFTCs slanting toward higher frequencies were
unusual (2.7%, 4/147). Cells with multiple excitatory frequency bands
were also found where the bands were narrow (7.5%, Fig. 3I)
or broad (2.7%, Fig. 3J).
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The results suggest that the eFTC types form a continuum rather than falling into discrete classes. For example, if some broad multipeaked units did not have separation between their excitatory bands, they would look like upper-tail-low-sharp (UTLS) units. Furthermore, some U-shaped eFTCs were close to being V-shaped (Fig. 3K), circumscribed (Fig. 3B), or slanted, while some V-shaped eFTCs were close to upper or lower tail (Fig. 3L).
Analysis of shape: slopes of upper and lower frequency borders of eFTCs
It is advantageous to visually inspect and subjectively score eFTCs because one can assess the entire eFTC, analyze data rapidly, and present qualitatively intuitive data analysis. However, hand-scoring forces one to subjectively determine class boundaries. Therefore to obtain a quantitative measure of eFTC shape, the ISs of the low- and high-frequency borders of every eFTC were calculated. Generally, IS measures how steeply the frequency of an eFTC edge changes or "rolls off" as a function of intensity and is the reciprocal of eFTC edge slope. IS has the advantage over traditional slope measures of being robust for eFTCs with near vertical edges (see METHODS, Measures of steepness of eFTC edges: inverse slopes and edge regressions).
In general, A1 eFTCs were relatively sharp and level tolerant.
Distributions for upper and lower ISs are shown in Fig.
4, which compares the magnitude of change
of the edges at three successively higher intensities. Many eFTC edges
had ISs near zero, confirming that near vertical eFTC edges were
common. Notice how the distributions get flatter with larger mean
magnitudes as one progresses from IS5-25 to
IS5-65, indicating that the eFTC edges on average are broadening with increasing intensity. The IS measurements are converted to units of octaves/40 dB in Table
1 to compare ISs for different intensity
excursions and to allow comparisons to the common bandwidth measure 40 dB above threshold. The mean and median ISs for lower borders were
approximately 0.29 and
0.22 octaves/40 dB, respectively. The more
negative inverse-slope of the mean was because the distributions were
skewed by large negative ISs. The mean and median ISs for upper borders
were approximately 0.19 and 0.10 octaves/40 dB, respectively. It is
noteworthy that the median values of the lower ISs were more constant
across intensity, whereas upper inverse-slopes were larger for measures
near the tip of eFTCs and smaller for measures at higher intensities
(Table 1). This indicates that low-frequency borders had a relatively constant slope across intensity, but high-frequency eFTC borders had
broader tips near threshold and sharper tips at higher intensities.
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Inverse-slopes, as measured by regression fits (Table 1), were similar to other IS measures, although the regression fit, on average, yielded larger tails. The regression measure, however, was not as closely linked to hand scoring as other IS measures (see Analysis of shape: comparisons of hand-scoring to objective measures).
Analysis of shape: comparing upper and lower edges within cells
It is common to read in the literature that cells in a certain
part of the auditory system have mainly U- or V-shaped eFTCs, or that
eFTCs are "level-tolerant," or "have a low-frequency tail and a
sharp high-frequency rolloff." Such classifications hinge on
comparing both eFTC edges. Distributions on a two-dimensional IS space
are needed to determine whether these properties fall into obvious
categories, and if they do not, the degree to which eFTCs are shaped
differently. From Fig.
5 it can be seen
that for most cells both eFTC edges are sharply tuned. The individual lower and upper IS histograms show skewed tails toward more broadly tuned edges and do not indicate a clear dividing line between eFTC
categories. The two-dimensional IS space shares the properties of the
single histograms, except the points appear to fall along a diagonally
oriented distribution. This was confirmed by finding a relationship
between lower and upper edge IS (slope = 0.25, Pslope < 0.01). These data indicate
that if one wishes to formally categorize eFTC types, one must proceed
with further analysis. So the next logical question is: How does
hand-scoring subdivide this space?
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Analysis of shape: comparisons of hand-scoring to objective measures
Quantitatively derived distributions of cell types were similar to those obtained by hand-scoring. The quantitative measures (of IS15-50, IS5-25, etc.) most closely approximating subjective classification were determined to facilitate comparisons of hand-scoring to the two-dimensional IS space. To categorize edges objectively, an "optimal" cutoff criterion in the two-dimensional IS space was determined for each measure by minimizing the error between subjective and quantitative categorization (see APPENDIX 1).
Edges with IS absolute values greater than the criterion were classified as broad tails, whereas edges with IS absolute values less than the criterion were classified as sharp. IS15-50 (with a cutoff of 0.23 octaves/40 dB, Table 2) most closely approximated the percentages of different eFTC types as calculated by hand scoring. Other measures, including those derived by fitting regression lines (10 slope, 15 slope) to eFTC edges, were not as closely linked to hand scoring (Table 3).
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Analysis was also done on a cell-by-cell basis to determine whether the
objective criteria was related to hand scoring. Once again,
IS15-50 most closely resembled hand-scoring.
Eighty percent of eFTCs were classified the same by hand-scoring and IS15-50 with a cutoff criterion of 0.30 octaves/40 dB (Fig. 6; Table 3). The average cutoff from the population
and cell-by-cell optimization was used to divide the two-dimensional IS
space into categories in Fig. 7
(· · ·). Cells with different hand-scored classification are represented by different symbols. The diagonal line
beginning at the origin and continuing in the lower right quadrant with
a slope of 1 marks perfect symmetry that would be characteristic of
U- and V-shaped eFTCs. Any point falling along this line would
represent a perfectly symmetric eFTC. Points further from that line
represent neurons with less symmetric eFTCs. Points above and to the
right of the diagonal line roughly represent eFTCs possessing a larger
response area on the high-frequency side of the BEF. Points below and
to the left of the line (the majority of points) represent neurons with
eFTCs possessing a larger response area on the low-frequency side of
the BEF. As would be predicted from Fig. 5, it is particularly
difficult to distinguish where categorical boundaries should be drawn
without the help of the hand-categorization and fiduciary lines.
Because the drawing of shape boundaries appears relatively arbitrary, it might be better to think of eFTCs shapes as forming a continuum, rather than falling into discrete categories. Nevertheless, this figure
displays the rough correspondence between hand-scoring and
classification using IS15-50. By demonstrating
that categorization using IS15-50 closely
parallel the results obtained by hand-scoring, it is not meant to imply
that this is the best shape measure or that categories exist, but
rather to demonstrate a relationship between subjective and objective
classification using inverse slopes.
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Multi-peaked eFTCs
In the above analysis, inverse-slopes of entire eFTCs were calculated. Thus for multipeaked eFTCs, IS measurements were only applied to the largest possible eFTC interpretation covering all peaks. Under these conditions, multipeaked FTCs (× in Fig. 7) tended to have upper tails. Cells with multipeaked eFTCs had a median IS15-50_upper of 0.25 octaves/40 dB compared with 0.06 octaves/40 dB for other cells. These differences were confirmed statistically (Table 4).
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Each peak within multipeaked eFTCs was also analyzed separately, and the ISs of individual peaks were compared with single-peaked eFTCs. The lower and upper edges of individual peaks of multipeaked eFTCs did not vary significantly from those of single-peaked eFTCs (Table 4).
Relationship of intensity tuning to eFTC shape
Intensity-tuning and eFTC shape were related (Fig.
8). After circumscribed cells, slant
lower cells were the next most intensity-tuned class. For many of these
cells, the slanting of the upper edge caused cells to respond weakly to
loud tones at BEF (e.g., Fig. 3, G and H),
thereby creating intensity tuning for BEF tones. Multipeaked eFTCs were
the next most intensity tuned, possibly due to inhibition in the center
of their eFTCs (Sutter et al. 1999). U-shaped eFTCs were
less intensity tuned, followed by tailed and V-shaped eFTCs. If one
thinks of U-shaped eFTCs as requiring the most inhibition abutting the
excitatory eFTC, and V-shaped the least, the results are consistent
with a relationship between intensity tuning and on-BF or surround
inhibition.
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Symmetry and shape measures
So far, shape classification has been based on a two-dimensional
distribution of eFTC low- and high-frequency ISs. However for
comparative purposes, collapsing the two-dimensional IS space into one
measure would be advantageous. Accordingly, symmetry and shape measures
were derived. U- and V-shaped eFTCs are symmetric because they have
near equal bandwidth above and below BEF, whereas slanted, LTUS and
UTLS eFTCs are nonsymmetric (Fig. 9).
Symmetry was defined as the excess bandwidth, (in octaves) to one side of the eFTC
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Symmetry15-50 has the advantage of quantifying
the degree of eFTC asymmetry in octaves, but the disadvantage of being bandwidth-dependent and, therefore not measuring normalized shape. For
example, negative Symmetry15-50 values can
result from either LTUS or Slant-lower eFTCs. To derive a metric that
could distinguish these two possibilities (and the corresponding
possibilities for UTLS and Slant-upper) a measure of shape was derived,
which is the symmetry measure normalized for bandwidth
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Like Symmetry15-50, if the extent of the eFTC is
predominantly below or above the center frequency,
Shape15-50 is negative or positive
respectively. Unlike Symmetry15-50, Shape15-50 can also distinguish slanted from
tailed eFTCs. If Shape15-50 of an eFTC is more
than 1 or less than 1, the eFTC can be classified as
"slant-upper" slant lower, respectively (Fig. 9, F and
G). Shape15-50 values close to 0 indicate a symmetric eFTC (Fig. 9, D and E). LTUS
eFTCs have shape values more than or equal to
1 and less than 0. UTLS
eFTCs have values less than or equal to +1 and more than 0 (Fig.
9C). For the eFTCs of A1 neurons,
Shape15-50 indicates on average, asymmetric tuning, slightly shifted toward low frequencies (mean
Shape15-50 =
0.26 ± 0.63; median,
0.17, Fig. 10).
Level tolerance of the bandwidth of A1 cells
Suga et al. (1997) defined neurons as
level-tolerant when their eFTC bandwidth (in kHz) at 70 dB above
threshold was less than four times the bandwidth 10 dB above threshold.
Because eFTCs were not generally characterized over a 70-dB range, a
modified metric was created: Bandwidth level intolerance (BLI) = (BW50/BW10), where
BW50 is the bandwidth of the cell, in kHz, 50 dB
above threshold. Adjusting the criterion for the smaller intensity
range used in this study, a cell was defined as level-tolerant if its
eFTC bandwidth (in kHz) at 50 dB above threshold is <3 times the
bandwidth at 10 dB supra-threshold. The median BLI value is 2.23 with
25th and 75th percentile
values of 1.13 and 3.82 (Fig. 10), and 60.6% of A1 cells were
characterized as level-tolerant.
BLI is not normally distributed because of a large percentage of highly
level-tolerant cells with low BLI values (including circumscribed eFTCs
for which BLI = 0), and a long tail caused by cells with high BLI
values because of narrow tuning at 10 dB above threshold (Fig. 10).
This highly skewed distribution is unsuitable for many statistical
analyses, including regression. Therefore another level tolerance
measure was defined: Bandwidth level dependency (BWLD) = BW50 BW10, where the
bandwidths are measured in octaves. By using subtraction rather than
division, the problem of the unstable nature of dividing by small
numbers that creates the tail in the BLI distribution is ameliorated
(see APPENDIX 3). Also, by using octaves, small differences
in the bandwidth 50 dB above threshold are more uniformly distributed,
reducing the compression near zero in the BLI distribution. Because the
resulting BWLD distribution is less skewed and more normal, BWLD is
easier to work with quantitatively.
Frequency dependency of eFTC shape
The IS of the low-, but not high-, frequency edge of eFTCs seemed
to depend on characteristic frequency (CF).
IS15-50_Lower had a regression slope
of 0.085 octaves/40 dB of IS per octave of CF (P < 0.05), indicating that the eFTC edges are sharper in higher CF cells
(Fig. 12A). The ISs of the
high-frequency eFTCs edge did not show a significant dependence of CF.
One should be cautious about the generality of these results because of
a bias against recording cells with lower CFs. It is therefore worth noting that in the inferior colliculus of chinchillas, eFTC shapes are
dramatically different for neurons with very low CFs than for cells
from the middle of the animal's frequency hearing range (Nuding
et al. 1999).
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Level tolerance had a weak nonsignificant dependence on CF (Fig. 12).
Low CF cells tended to be less level tolerant than high CF neurons.
Although not significantly different from zero (P = 0.052), the slope was 0.111 octaves of BWLD per octave of CF. In
other words, for every octave of CF increase, cells would lose roughly
0.111 octaves of bandwidth at 50 dB above threshold compared with the
bandwidth at10 dB above threshold. These results suggest a weak
relationship between level tolerance and CF.
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DISCUSSION |
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A variety of eFTC shapes were found in A1, with most neurons having larger response areas on the low-frequency side of CF than on the high-frequency side. Robust quantitative eFTC shape and level tolerance measures were introduced because more established metrics were not always suitable for A1 cells. Quantitative eFTC measures yielded results comparable to subjective hand-scoring; however, they suggest that eFTC shape forms a continuum. There was a strong relationship between eFTC shape and intensity tuning, but a weaker one between CF and eFTC shape.
Choosing the correct metrics to quantify and compare tuning curves
Historically, choice of metric has a major impact on the
interpretation of neurophysiological data. For example, whether one sees sharpening of frequency tuning as the lemniscal auditory system is
ascended depends critically on one's definition of tuning (Suga
1995). Therefore it is important to discuss the appropriateness of the metrics used in this study. A major advantage of these metrics
is that they provide convenient indexes of shape properties such as
slanted and tailed eFTCs, which traditional bandwidth values cannot
disambiguate. Whereas Q values quantify neuronal bandwidth, IS provides
additional information about how bandwidth is distributed, and shape
and symmetry measures transform this information into one number.
The metrics herein also circumvent problems that ratio metrics
often encounter when the denominator can have small values. For
example, the more traditional measure of slope in dB/octave (Borg et al. 1988; Goldberg and Brownell
1973
) presents problems for many cortical neurons because of
its nonlinear behavior for very sharp edges (see METHODS).
Also, Q (CF/Bandwidth), the most used bandwidth measure in the auditory
system, is inappropriate for intensity-tuned neurons that have zero
bandwidth at high intensities, and thus infinite Q values. For both Q
and slope, performing statistical analyses such as regression against
CF is impossible because of A1 neurons with infinite values. The BLI
(BW50/BW10) measure suffers from a similar problem. Cells with very
narrow eFTC tips have excessively large BLI values because one must
divide by the bandwidth 10 dB above threshold. This creates very skewed
distributions necessitating clipping the very high BLI values. BLI
therefore is far from ideal for statistical analysis, whereas BWLD
(BW10-BW50 in octaves) seems better. Accordingly, the newer metrics
have the flexibility to be applied to make meaningful comparisons
across the wide range of eFTC shapes encountered across brain areas and species.
However, one must not forget that these metrics have limitations. First, the shape measure is a ratio, which like Q, needs modification for circumscribed eFTCs. Also, choosing just two intensities can affect classification. For example the eFTC in Fig. 3C was classified as V-shaped by hand-scoring and LTUS by classification using IS15-50. This difference most likely results from the broadening of the eFTC more than 50 dB above threshold. Another disadvantage is that like any threshold metric, those used herein only quantify the limits of the frequencies to which a cell is sensitive; however, important frequency information is also carried by gradations of responses within a neuron's eFTC. Finally, it should be noted that the metrics derived in this paper are still simple and can only capture gross aspects of eFTC shape and not fine detail that the eye can often see. In conclusion, the measures used in this paper represent a step toward better understanding eFTC shape by providing an incremental improvement over previous approaches.
Comparisons of eFTC level tolerance and shape in A1 of bats and cats
Responses of A1 neurons have arguably been most extensively
studied in cats and the Doppler-shifted constant frequency
(DSCF) area of mustached bat A1. Distributions of quantitative
level tolerance measures have not been reported for A1 neurons;
however, Q10 and Q50 values for mustached bat DSCF neurons have been
(Suga and Manabe 1982), and potentially provide an
estimate of level tolerance. The results of dividing the mean Q50 value
by the mean Q10 value suggests that bat DSCF neurons (Q50/Q10 = 1.28), on average, are more level tolerant than cat A1 neurons
(Q50/Q10 = 2.70). The greater level tolerance in mustached bats
indicates that DSCF neurons in mustached bats are not simply scaled
down, more sharply tuned versions of A1 cells in other animals, but rather, are disproportionately sharper at higher intensities than low.
Unfortunately, quantitative data on the level tolerance of A1
neurons with CFs outside of the 60-kHz DSCF area are not available. However, A1 cells outside of the DSCF area in mustached bat are more
broadly tuned than DSCF neurons (e.g., Suga and Tsuzuki
1985). Therefore neurons tuned to frequencies other than 60 kHz
in bats might have comparable level tolerances to cat A1 cells.
Similarly eFTCs in little and big brown bat A1 tend to be more broadly
tuned than for DSCF mustached bat neurons (Dear et al.
1993
; Shen et al. 1997
). This leaves open the
intriguing possibility that, outside of the DSCF area, level tolerance
might be similar across A1 of many species.
The proportions of slanted eFTCs in cat and bat A1 further support the
notion that there are some common organizational principles responsible
for creating central eFTCs across species. The percentages of
slant-lower eFTCs are similar in bats (Kanwal et al.
1999) to those report here in cats. Slant-upper eFTCs are also
uncommon in both species, implying that the slant-lower eFTC shape is
either functionally or mechanistically advantageous to have in the
auditory system, and that there might be common organizational
principles responsible for creation this eFTC type.
Quantitative measures and comparisons of inverse slopes within the ascending auditory system
The results of this study indicate that A1 neurons are sharper and
more level tolerant than cells at earlier stations in the auditory
system, and that much of this is probably due to sharpening of the
low-frequency border of eFTCs by inhibition. There are a few
quantitative studies of slopes of eFTCs. The slopes of the edges of AN
(Borg et al. 1988) and cochlear nucleus (CN)
(Goldberg and Brownell 1973
) eFTCs strongly vary as a
function of CF. The anterior ventral cochlear nucleus (AVCN)
slope distribution (Goldberg and Brownell 1973
) appears
bimodal, possibly reflecting the convergence of only a few auditory
nerve fibers onto AVCN neurons. The slopes of the edges of AN and CN
neurons appear to be broader and more dependent on CF than A1 neurons,
although a sharpening of the low-frequency edge as a function of CF was
found in A1. Part of this discrepancy might be due to the present
study's use of a more limited CF range than both the Goldberg and
Brownell and the Borg et al. studies. For cells above 2 kHz in these
earlier studies, there is no apparent relationship between CF and upper edge eFTC slopes, and the relationship between CF and lower edge slopes
is weaker than across all CFs (e.g., Fig. 1, Goldberg and Brownell 1973
).
The results of the present study were compared with those from the AN
(Javel 1994; Kiang and Moxon 1974
;
Kiang et al. 1967
) and CN (Goldberg and Brownell
1973
) of anesthetized cats, using only cells in the 5- to
15-kHz range to mitigate CF dependencies. This was achieved by
measuring slopes directly from the published eFTCs. Lower edges sharpen
substantially from a median IS15-50_lower of
approximately
2.10 to
1.70 to
0.20 octaves/40 dB in the AN, CN,
and A1, respectively. Sharpening of eFTC upper edges was less obvious,
going from 0.25 to 0.22 to 0.09 from AN to CN to A1. This suggests a
sharpening of both sides of eFTCs in the ascending auditory system with
more pronounced sharpening of the low-frequency edge.
Hierarchical degradation of eFTC classes
Cortical eFTCs are shaped from convergence and integration of
excitatory and inhibitory inputs. Many brain structures contribute to
this shaping in what appears to be a gradual change with ascension in
the auditory system. This is well exemplified with intensity-tuned and
circumscribed eFTCs. Within several auditory stations some neurons have
intensity tuning that is sharpened by GABAergic or glycinergic
inhibition (e.g., Evans and Zhao 1993; Grothe
1994
; Pollak and Park 1993
; Suga et al.
1997
; Yang et al. 1992
). Additionally, higher
threshold excitatory inputs might be added to eFTCs to overcome the
effects of earlier intensity tuning (Pollak and Park 1993
). Thus each neuron's intensity tuning results from a
differing number of inhibitory sharpening and excitatory integrating stages.
These arguments can be reasonably extended to sharpening of frequency tuning. One can hypothesize that eFTC shapes are also progressively formed along the ascending auditory system. This gradual re-shaping of eFTC properties would be consistent with creating the appearance of shape continua. For example, "discrete" classes, such as multi-peaked eFTCs, could fall along continua related to spectral integration. There are at least two ways in which a continuous change in one variable can produce a gradual change from single- to multipeaked properties. One way is to vary the frequency spacing of convergent excitatory input. When the integrated excitatory bands are closely spaced in frequency, single-peaked eFTCs are created; however, when the frequency spacing between overlaid excitation increases, multipeaked frequency tuning begins to emerge. Alternatively multipeaked eFTCs could be produced if inhibition were placed within an eFTC. Classification of multipeaked eFTCs would result when the strength of inhibition is sufficient to bring the middle of the eFTC below the isoresponse criteria used to judge eFTC edges. This would occur even if the strength of the central inhibition were continuously graded.
Inhibition continuously graded in strength and bandwidth also could create continua in which many eFTC "classes" fall. If inhibition with a CF within the eFTC were broad toward high frequencies, the entire high-frequency side of the tuning curve would be chopped off creating a slant-lower unit. On the other hand, if the inhibition were strong, broad and high-threshold, a circumscribed eFTC might result. But, if the inhibition were weak, it will likely produce an intensity tuned unit that is U- or V-shaped (e.g., Fig. 4C). Thus by continuously varying the properties of inhibition and spectral integration, multiple continuous dimensions can emerge that encompass many eFTC classes.
Under the above scenario, as excitatory and inhibitory spectral
properties are hierarchically integrated in the ascending auditory
system, divisions between classes continue to blur. Auditory nerve
fiber eFTCs have a characteristic LTUS shape with a moderately sharp
tip (~ octaves) that melds into a broad low-frequency tail
40-60 dB above threshold (e.g., Javel 1994
; Kiang and Moxon 1974
). Arguments have been made that CN
eFTCs fall into several categories that are related to cell morphology, and specific patterns of ascending, descending, and internal
connections (e.g., Evans and Nelson 1973
; Joris
1998
; Young and Brownell 1976
; Zhang and
Oertel 1994
). Type I-III CN eFTC are similar to AN eFTCs but
are sharpened by inhibitory domains within and abutting the eFTC
(Evans and Nelson 1973
; Goldberg and Brownell
1973
; Spirou et al. 1999
). Type IV and V eFTCs
have more complex inhibition, with a large variation in the location of
within-eFTC inhibition (Spirou and Young 1991
;
Young and Brownell 1976
). However, in the dorsal
cochlear nucleus (DCN), the complexity and variance in integration, and
the variety of inputs begin to blur the physiological distinction
between classes (e.g., Joris 1998
; Spirou et al.
1999
). In the IC, further transformations occur, and although
categorization has been made based on physiological responses and
hypothesized segregated inputs from the brain stem (Ramachandran
et al. 1999
), it is difficult to discern whether these
categories correspond to clusters in a physiological parameter space.
Qualitative inspection IC central nucleus (ICc) neurons [based on
eFTCs from Ehret and Merzenich (1988)
and Yang et
al. (1992)
] suggests that their eFTCs have properties
somewhere between CN and A1 neurons. In particular, ICc neurons, on
average, look more symmetric, sharper, and more level tolerant than AN
neurons, but less symmetric, broader, and less level tolerant than A1
neurons (Ehret and Schreiner 1997
). The little evidence
that is available from the medial geniculate body (MGB)
indicates that its neurons might fall in the middle of this trend
(based on eFTCs from Imig et al. 1997
). Therefore unlike
in the visual system, where dramatic qualitative receptive field
changes can occur between hierarchical stations, in the auditory system
the changes appear to be more gradual, resulting in populations at
successive stations that overlap substantially in their eFTC properties.
Relationship of average eFTC shape to population codes
Our results indicate that labeled-line population codes of
frequency become more refined as one ascends the auditory system. At
low intensities, every AN fiber responds to a narrow range of
frequencies, and therefore can be assigned as representing a particular
frequency (Javel 1994). However, for high-intensity tones one would expect activity in fibers with CFs up to approximately 2 octaves above the frequency of the presented tone because of their
broad low-frequency tails (Kim and Molnar 1979
). In A1
cells, the low-frequency tail-induced asymmetry should be much less
pronounced than in the AN. At 50 dB above threshold, one would expect
activity in A1 neurons with CFs up to approximately
octave
above the frequency of the presented tone. This frequency range is
remarkably similar to many critical band phenomena and, when combined
with the level tolerance of A1 neurons and other physiological critical
band experiments (e.g., Ehret and Schreiner 1997
), suggests that sharpening of frequency tuning in the
central auditory system contributes to perceptual critical band phenomena.
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APPENDIX 1 |
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To optimize IS cutoff criteria for the population statistics, IS
criteria (x-axis in Fig. 6A)
were varied for different IS measurements (different lines in Fig.
6A). Within an optimization run, the criteria for
defining an edge as a broad tail or as sharp was the same for lower and
upper eFTC edges. Multipeaked and circumscribed eFTCs were not used
because they could not be categorized based on the two-dimensional IS
space. Root mean square (RMS) error was determined by subtracting the
percentages determined by objective scoring from hand-scoring for each
of U-, V-, slant-lower, slant-upper, LTUS, and UTLS shaped eFTC. These
differences were summed and the square root of the sum was taken and
divided by six shapes. Using Table 2, the RMS error for
IS15-50 with a cutoff criteria of 0.23 octaves/40 dB would
be calculated by RMS = {[(24.4 26.0)2 + (17.9
17.9)2 + (9.0
4.9)2 + (2.4
0.8)2 + (14.6
19.5)2 + (1.6
0.8)2]1/2}/6 = 1.1. With
the optimum criterion of 0.23 octaves/40 dB for IS15-50, a
V-shaped eFTC was defined as having IS15-50_upper > 0.23 octaves/40 dB and IS15-50_lower <
0.23
octaves/40 dB. A U-shaped eFTC was defined as having 0.00 > IS15-50_upper < 0.23 octaves/40 dB, and
0.23 < IS15-50_lower < 0.00 octaves/40 dB. Furthermore,
with this criteria, a slant-lower eFTC was defined as having
IS15-50_upper and IS15-50_lower < 0.00 octaves/40 dB. An LTUS eFTC with this criterion was defined as having
its upper edge IS between 0.00 and 0.23 octaves/40 dB and its lower edge having an IS more negative than
0.23 octaves/40 dB, etc.
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APPENDIX 2 |
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The detailed formula for shape measurement is
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APPENDIX 3 |
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One cannot just take the log of BLI and get BLWD. Taking the log
of BLI one gets
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ACKNOWLEDGMENTS |
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I thank K. O'Connor, G. Recanzone, C. Schreiner, W. Loftus, and two anonymous reviewers for useful comments on this manuscript.
This work was supported by National Institute on Deafness and Other Communication Disorders Grant DC-02514 and by the Sloan Foundation (to M. L. Sutter as a Sloan Fellow).
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FOOTNOTES |
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Address for reprint requests: University of California, Davis, Center for Neuroscience, 1544 Newton Ct., Davis, CA 95616 (E-mail: mlsutter{at}ucdavis.edu).
The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
Received 4 January 2000; accepted in final form 3 May 2000.
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REFERENCES |
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