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The Journal of Neuroscience, April 1, 1999, 19(7):2780-2788
The Magnitude and Phase of Temporal Modulation Transfer Functions
in Cat Auditory Cortex
Jos J.
Eggermont
Departments of Physiology and Biophysics and Psychology, University
of Calgary, Calgary, Alberta, Canada T2N 1N4
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ABSTRACT |
Temporal modulation transfer functions (tMTFs) in response to
periodic click trains are presented for simultaneous recordings from
primary auditory cortex, anterior auditory field, and secondary auditory cortex in 21 cats. The multiunit records could be
separated in to 215 single-unit spike trains that allowed a reliable
estimate of a group delay, which represents the cumulative delay for
responses to repetitive stimuli. For approximately two-thirds of the
215 single units the group delay was within 7.5 msec of the response latency to the first clicks in the trains. For the remaining units, the
group delay was on average ~14 msec higher, and this may result from
differences in synaptic properties. These findings were similar in the
three cortical areas studied. The findings are modeled based on
presynaptic facilitation and depression and pyramidal cell calcium
kinetics, and a quantitative description of the magnitude of the tMTF
was obtained that resulted in substantially shorter depression time
constants (20 msec) than reported for visual cortex (300 msec). A small
amount (0-5.5%) of facilitation that decayed with a time constant of
60 msec was obtained. Auditory cortical cells apparently have much
faster recovery mechanisms than visual cortical cells. This allows for
the ability of the auditory cortex to reliably track the rhythms that
occur in natural sounds.
Key words:
single unit; temporal modulation transfer functions; cat; primary auditory cortex; anterior auditory field; secondary auditory
cortex; modeling; synaptic depression and facilitation
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INTRODUCTION |
Communication sounds have both
spectral and temporal aspects. The timing aspects are evident in the
onset and offset and in the amplitude and frequency modulation of the
sound. In humans, amplitude-modulated (AM) tones or AM noise produce
various hearing sensations depending on the modulation frequency. These
include rhythm and fluctuation strength for AM frequencies below ~20
Hz and roughness and pitch for AM frequencies above 20 Hz (Zwicker and
Fastl, 1990 ). The ability of neurons to code the AM aspects of sound in
a temporal manner is represented by the temporal modulation transfer
function (tMTF; Schreiner and Langner, 1988). For a fixed modulation
depth of the AM stimuli, the tMTF is equal to the Fourier transform of
the period histograms of the neuronal firings. Generally, only the
magnitude of the Fourier component with a modulation frequency (MF)
corresponding to the period duration of the AM is considered.
Because the Fourier transform is complex, the tMTF is a complex
function and is characterized by its magnitude as well as its phase
dependence on MF. The phase-MF dependence allows calculation of the
group delay at each MF by taking the local slope of the phase-MF
function (Papoulis, 1977). The group delay is a measure over a group of
frequencies. In case the phase-MF function for most of the MF range
can be approximated by a straight line, the group delay is independent
of the MF over that range, represents a pure delay, and can be
interpreted as a neuron property (Anderson et al., 1971).
By using 1-sec-duration periodic click trains as the AM stimulus
followed by 2 sec of silence (Eggermont, 1991), one can independently estimate the latency of the unadapted response to the first click in
each train. The difference between the group delay, which represents the cumulative delay for responses to repetitive stimuli, and the
latency of the response to first clicks in the trains can be
interpreted as the result of temporal filtering. This allows an
estimate of the contribution of this temporal filtering process to the
group delay. The temporal filtering is likely the result of presynaptic
mechanisms such as facilitation and depression (Varela et al., 1997)
and postsynaptic mechanisms such as afterhyperpolarization and
Ca2+ dynamics (Wang, 1998). Facilitation and
depression are presumed to be multiplicative and to have exponential
time courses (Magleby, 1987; Varela et al., 1997). For neocortical
synapses, depression appears to be more pronounced than facilitation
(Markram et al., 1998).
In this paper, the complex tMTFs in response to periodic click trains
are analyzed, and a model based on presynaptic facilitation and
depression and pyramidal cell calcium kinetics is presented that
provides a quantitative description of the magnitude of the tMTF. The
results suggest that recovery time constants are much shorter in
auditory cortex than in visual cortex.
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MATERIALS AND METHODS |
The care and the use of animals reported on in this study was in
accordance with the Guide to the Care and Use of Experimental Animals and was approved (P88095) by the Life and Environmental Sciences Animal Care Committee of the University of Calgary.
Animal preparation. Cats were premedicated with 0.25 ml/kg
body weight of a mixture of 0.1 ml of acepromazine (0.25 mg/ml) and 0.9 ml of atropine methyl nitrate (5 mg/ml) subcutaneously. After ~0.5 hr
they received an intramuscular injection of 25 mg/kg ketamine (100 mg/ml) and 20 mg/kg pentobarbital sodium (65 mg/ml). Lidocaine (20 mg/ml) was injected subcutaneously and rubbed in gently, and then a
skin flap was removed and the skull cleared from overlying muscle
tissue. A large screw was cemented upside-down on the skull with dental
acrylic. An 8-mm-diameter hole was trephined over the right temporal
cortex to expose parts of primary auditory cortex (AI) and secondary
auditory cortex (AII). A 4 mm hole was drilled over the anterior
auditory field (AAF). The dura was left intact, and the brain was
covered with light mineral oil. Then the cat was placed in a
sound-treated room on a vibration isolation frame, and the head was
secured with the screw. Additional acepromazine-atropine mixture was
administered every 2 hr. Light anesthesia was maintained with
intramuscular injections of ketamine at dosages of 2-5
mg · kg 1 · hr1.
The wound margins were infused every 2 hr with lidocaine and, also
every 2 hr new mineral oil was added if needed. The temperature of the
cat was maintained at 37°C. At the end of the experiment the animals
were killed with an overdose of pentobarbital sodium.
Acoustic stimulus presentation. Acoustic stimuli were
presented in an anechoic room from a speaker placed 55 cm in front of the cat's head. The sound-treated room was made anechoic for
frequencies >625 Hz by covering walls and ceiling with acoustic wedges
(3 inch; SONEX, Minneapolis, MN) and by covering exposed parts of the
vibration isolation frame, equipment, and floor with wedge material as
well. Calibration and monitoring of the sound field were done using a
Brüel & Kjær (Atlanta, GA) type 4134 microphone placed above the
animal's head and facing the loudspeaker. A search stimulus consisting
of random frequency tone pips, noise burst, and clicks was used to
locate units. Characteristic frequency (CF) and tuning curve of the
individual neurons were determined with a 50-msec-duration  shape
envelope, tone pips presented randomly in frequency once per second
(Eggermont, 1996). After the frequency tuning properties of the cells
at each electrode were determined, periodic click trains (1 sec
duration followed by 2 sec of silence) were presented once per 3 sec.
The click repetition rates were between 1 and 32 at logarithmically
equal distance with four values per octave and were randomly presented. The sequences of 21 click trains were repeated 10 times, resulting in a
total stimulus ensemble duration of 630 sec. The click trains were
presented at peak intensities of 35, 55, and 75 dB sound pressure level
(SPL), and results are presented for the intensity which resulted in
the highest firing rate.
Recording and spike separation procedure. Three tungsten
microelectrodes (Micro Probe Inc.) with impedances between 1.5 and 2.5 M were independently advanced perpendicular to the AI,
AAF, and AII surfaces using remotely controlled, motorized hydraulic microdrives (Trent-Wells Mark III). The electrode signals were amplified using extracellular preamplifiers (2400; Dagan Instruments, Minneapolis, MN) and filtered between 200 Hz (VBF8; Kemo Ltd., Beckenham, UK; high-pass, 24 dB/octave) and 3 kHz (6 dB/octave, Dagan
rolloff) to remove local field potentials. The signals were sampled
through 12 bit analog-to-digital converters (DT 2752; Data Translation,
Marlborough, MA) into a PDP 11/53 microcomputer, together with timing
signals from three Schmitt triggers. In general the recorded signal on
each electrode contained activity of two to four neural units. The PDP
was programmed to separate these multiunit spike trains into
single-unit spike trains using a maximum variance algorithm (Eggermont,
1996). The spikes from well separated waveform classes, each assumed to
represent a particular neuron, were stored and coded for display.
In addition, the electrode signals were bandpass-filtered between 10 and 100 Hz to obtain spike-free signals of ongoing local field
potentials (LFPs). These signals were also passed through Schmitt
triggers set at ~2 SDs (i.e., at approximately  100 µV) below the
mean value of the ongoing signal during silence. The "spikes" of
these LFPs were processed in the same way as single-unit spike data. We
have shown previously that these level crossings explain most of the
temporal (Eggermont and Smith, 1995) and spectral (Eggermont, 1996)
response properties of the single units recorded at the same electrode.
The boundary between AI and AAF was explored by taking a series of LFP
and multiunit measures from caudal to rostral and assuring that there
was a gradual increase in CF, which reversed in direction when
advancing to the AAF. The AII was identified anatomically and
electrophysiologically based on the broader tuning curves and different
response patterns compared with those in the central and ventral parts
of AI. Recordings in AII were generally made from the ventrorostral
part. Recording electrode positions in the three cortical areas were
chosen such that recordings with approximately similar best frequencies
(within 0.5 octave) at 50-70 dB SPL were obtained. Recordings were
made between 600 and 1200 µm below the cortex surface.
Data analysis. The temporal modulation transfer functions
were obtained by Fourier transformation of the period histograms (Eggermont, 1991). Each modulation period was divided into 16 bins, and
only recordings with at least five counts in the maximum bin per 10 stimulus presentations at a rate of 8 Hz were further analyzed. The
tMTF was estimated from the amplitude of the first harmonic of the
period histogram. The best modulating frequency (BMF) was defined as
the click rate for which the tMTF was maximal. The limiting rate was
defined as the highest click rate at which the response was 50% of
that at the BMF. Phase ( )-click repetition rate (CRR) functions were
approximated by straight lines using linear regression analysis. Only
neurons with R2 > 0.9 for the regression
line calculation were included in the analysis. The slope was converted
in a group delay  = 1/360 /CRR. If is in degrees and CRR is
in hertz, then is in seconds.
Group delay at a certain CRR is defined as the slope of the phase
repetition rate function at that specific CRR. Typically one uses a
group delay if a multifrequency component signal is passed through a
frequency filter, because different frequency components may undergo
different phase delays. This shows up in a nonlinear dependence between
phase and frequency. Most of the phase change occurs around the peak of
the filter response function. If the phase is linearly dependent on
frequency over the entire frequency range of interest, then the system
functions as a pure delay system for signals composed of frequencies
within that range (Ruston and Bordogna, 1986).
The responses at CRRs <5/sec are generally small. Because always 10 trains were presented for each CRR, and the bin width was relative
(1/16) to the period of the CRR, the phase definition was no problem
for those CRRs. And as Figure 1 indicates, the response was always in
the first or second bin. For the higher CRR (>18 Hz), the bin size was
small (1-2 msec), and consequently the distribution was broad.
However, the phase was generally defined within a few bins, and if not
well defined the phase was not entered into the regression line
calculation. The phase at CRRs of >18/sec had hardly any effect on the
slope of the regression line. Again, taking Figure 1 as an example,
deleting the phase entries >18 Hz has no effect on the slope of the
regression line.
All statistical analyses were performed using Statview 4.5. Graphics
and systems analysis were done with Matlab, Powerpoint, and Horizon software.
Perstimulatory adaptation and response to periodic click
stimulation. Spike frequency adaptation in cortical, regular
spiking, pyramidal cells has been described by a model largely based on Ca2+-gated K+ conductances and
manifests itself in an exponential decreasing firing rate with time
after onset of a current pulse (Wang, 1998). Such exponential decay is
also seen in the firing rate of auditory nerve fibers during tone burst
stimulation and has been modeled previously in terms of birth-and-death
Markov processes (Eggermont, 1985; Gillespie, 1992). We summarize that
model here with slight modifications, to allow application to cortical
neurons in response to click trains of fixed duration but variable
number of clicks. For a long tone burst, the normalized firing rate,
R(t), as a function of time after onset,
t, is assumed to decay exponentially:
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(1)
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where Rss is the normalized steady-state
or fully adapted firing rate, the unadapted onset firing rate obtained
after a sufficiently long silent period is normalized to 1, and
adap is the time constant of the exponential decay of
the firing rate. In terms of the birth-and-death model,
adap was equal to the inverse of the sum of a birth and death rate,  and µ, determining the availability of postsynaptic receptor sites. It was assumed that after transmitter release, free
receptor sites (for cortical pyramidal cells this will likely be the
AMPA receptors) were activated at a very fast rate and then converted
at a rate into an inactive or occupied state and subsequently
recovered to the free state with rate µ. This resulted in a fraction
of inactive receptors of /( + µ) and a fraction of free
receptors that determined the steady state Rss = 1 /( + µ) = µ/( + µ). The steady state was
reached with a time constant adap = ( + µ)1. Alternative interpretations of the birth and death
rate in terms of depletion and filling of the immediate release
transmitter store in the presynaptic terminal are also plausible
(Eggermont, 1985). For the adaptation in cortical cells, the
interpretation of these two rates likely has to be different (e.g.,
incorporating postactivation suppression), but the formal description
is assumed to remain the same.
Consider next a forward masking experiment with a masking tone burst
long enough, usually of the order of 100 msec, to allow the neuron to
reach the steady-state firing level Rss and
followed after a silent interval,  t, by a test tone burst
with equal intensity and frequency as the masker. The onset firing rate
to the test tone burst, ron(t),
increases with the length of the silent interval after the masker,
however, with a slower time course than that for the perstimulatory
adaptation:
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(2)
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with recov = (µ)1.
Rss, recov, and
adap are interrelated because they depend only on and µ:
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(3)
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In this model, the knowledge of the perstimulatory adaptation
time constant, adap, and the adapted steady-state
firing level, Rss, is sufficient to
predict the recovery time constant in a forward masking experiment
(Eggermont, 1985).
In case the masker has a short duration, D, the steady-state
firing level, Rss, has to be replaced by
the appropriate adaptation level obtained for that duration. One
obtains:
![r<SUB><UP>on</UP></SUB>(&Dgr;t, D) <UP>=R</UP><SUB><UP>adap</UP></SUB>+(1−R<SUB><UP>adap</UP></SUB>)[1−<UP>exp</UP>(<UP>−</UP>&Dgr;t/&tgr;<SUB><UP>recov</UP></SUB>)],](/content/vol19/issue7/fulltext/2780/img004.gif)
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(4A)
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(4B)
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with:
![R<SUB><UP>adap</UP></SUB>=R<SUB><UP>SS</UP></SUB>[1−<UP>exp</UP>(<UP>−</UP>D/&tgr;<SUB><UP>adap</UP></SUB>)],](/content/vol19/issue7/fulltext/2780/img006.gif)
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(4C)
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d = (1 Radap) can be considered the fraction of
depression produced by a single click.
For repetitive stimulation, generally with short-duration stimuli such
as clicks, the cumulative effects of incomplete perstimulatory adaptation and incomplete recovery has to be taken into account. Under
the assumption that the adaptation and recovery after the second click
in a train are scaled versions of those after the first click, i.e.,
the adaptation starts from the level given by Equation 4B instead of
the unadapted value 1, the onset firing rate for click 3 is given
by:
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(5A)
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Thus, one can write this cumulative effect for stimulation with
a click train with interstimulus interval = t and
consisting of N + 1 ( 2) clicks (N depends on
the CRR for fixed duration click trains), as:
![r<SUB><UP>on</UP></SUB>(N&Dgr;t)=[1−d <UP>exp</UP>(<UP>−</UP>&Dgr;t/&tgr;<SUB><UP>recov</UP></SUB>)]<SUP>N</SUP>.](/content/vol19/issue7/fulltext/2780/img008.gif)
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(5B)
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This is an adaptation in which the effect of subsequent clicks
becomes progressively less. Facilitation can be introduced into this
model. It has been considered additive in modeling adaptation for
visual cortex cells (Varela et al., 1997), but I found a multiplicative update, analogous to that for depression, to provide much better results:
![F(N&Dgr;t)=[1+f <UP>exp</UP>(<UP>−</UP>&Dgr;t/&tgr;<SUB><UP>fac</UP></SUB>)]<SUP>N</SUP>,](/content/vol19/issue7/fulltext/2780/img009.gif)
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(6)
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with f the amount of facilitation per click and
fac the decay time constant of the amount of
facilitation. Assuming further a multiplicative interaction between
facilitation and depression (Magleby, 1987; Varela et al., 1997), the
final model describing the onset firing rate for the (N + 1)th click in a train becomes:
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(7)
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and because the amount of depression and facilitation to
subsequent clicks is described by a geometric series, the summed onset
firing rate for the entire train becomes:
![R<SUB><UP>av</UP></SUB>(&Dgr;t)=[1−R(N&Dgr;t)]<SUP>N</SUP>/[1−R(N&Dgr;t)],](/content/vol19/issue7/fulltext/2780/img011.gif)
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(8A)
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and the average response per click is:
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(8B)
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RESULTS |
Results are presented from 53 simultaneous recordings with
an electrode in each of AI, AAF, and AII in 14 cats. The multiunit (MU)
records could be separated into 169 single-unit (SU) spike trains that
allowed a reliable estimate of a group delay that was independent of
click repetition rate. We also made 17 simultaneous recordings in four
additional cats with two electrodes in AI and one in AAF resulting in
46 single units. The total number of single units presented in this
study is 215 from 21 cats. The following report also includes results
for the simultaneously recorded LFPs.
Group delays and onset latencies for periodic click trains
An example of a complete tMTF is shown in Figure
1. The top part represents the
magnitude (number of synchronized spikes per click train) as a function
of CRR with the actual data points indicated (*) and a cubic spline
curve fit drawn in. The bottom part shows the phase (in
radians) as a function of CRR with a linear regression line drawn in.
The phase of the peak in the period histogram changes as a function of
CRR, and the rate of change can be interpreted as a group delay. The
group delay calculated from the slope of the regression line was 32.8 msec. The limited resolution of the phase, 16 bins in one period
(2 /16 = 0.39 radians), is visible for the low click rates when
the period is long. In theory, this group delay consists of two parts,
a pure transmission delay (conduction time from cochlea to cortex) and
a temporal filter delay, which is likely of synaptic origin. The
transmission delay can be independently estimated from the latency of
the firings to the first click in a train. To allow the assignment of
the first spike latency as a pure delay, several conditions had to be
met. The phase of the response to the train with CRR 1/sec had to be in
the first bin of the period histogram; the first click latency had to
be within 5 msec of the minimum latency to tone pips presented at the
characteristic frequency; and no suppression of spontaneous activity
(reasonably well preserved under ketamine anesthesia) before the
response to the first click should be present. This excludes off
responses for units that are initially inhibited by the click. In the
example in Figure 1 the dependence of the preferred phase of firing on
CRR is fairly linear, and the resulting slope can be converted in a
filter delay that is independent of CRR and can be considered a neuron
property.
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Figure 1.
Magnitude and phase of the temporal modulation
transfer function for periodic click train stimulation for a single
unit from the anterior auditory field. The magnitude is expressed in
the number of synchronized spikes per click train; the phase (position
of the peak response in the period histogram relative to the period
length) is expressed in radians. The data points are indicated by
asterisks; for the magnitude function a cubic spline
interpolation was used, whereas a linear regression line was calculated
for the phase data. The slope of the phase click rate regression line
can be converted in a group delay (in seconds) through division by
2, resulting in 32.8 msec.
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The latency of the first click in each train is not affected by this
filter, provided that the silent period after the click train is long
enough; because its CRR is for all practical purposes equal to 1/3 sec,
it is only the subsequent clicks that experience the delay produced by
synaptic depression. In the absence of a "filter" delay, the group
delay and the response latency to the first clicks should be identical.
The response latency to the first click in the trains was always
independent of the CRR; thus the spikes to the first clicks in the
trains with 21 different CRRs were combined in one poststimulus time
histogram from which the peak latency was measured. Figure
2 shows the comparison between onset
latency and group delay for all units that were recorded in the three
cortical areas. The group delay was on average significantly (p < 0.0001) larger than the first click
response latency in AI (difference, 4.7 msec), AAF (6.2 msec), and AII
(7.0 msec). These values were not significantly different from each
other.
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Figure 2.
Comparison of group delay and first click response
latency for units from three auditory cortical areas. The peak response
latency to first clicks in the various trains was independent of click
repetition rate and between 7 and 31 msec. The group delay was obtained
from the slope of the regression line of the phase (relative position
in one stimulus period) of the peak response as a function of the click
repetition rate (according to the procedure shown in Fig. 1). The group
delay includes the effects of repetition rate on the synaptic responses
on the latency and can be substantially larger than the latency of the
response to first clicks.
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A bivariate plot of temporal filter delay, i.e., group delay minus
first click response latency, against the magnitude of the tMTF at a
CRR of 11.28 Hz (Fig. 3), suggests that
the filter delay consists of two subgroups: one for which the two
latency measures are within 7.5 msec and one for which the group delay is larger than the first click latency by at least 7.5 msec. The dividing line is clearly visible in the bivariate scattergram, but this
scattergram also suggests that there may be another subgroup with
delays of >20 msec. For the moment I will explore the division into
two subgroups and subsequently a division into smaller groups. The
amplitude distribution at the peak of the tMTF is well approximated by
a log normal distribution (drawn in). The mean filter delay for the
small delay group (N = 150) is between 1.3 and 2.0 msec depending on the cortical area and was not significantly different between areas (Table 1). For the large
delay subgroup, the mean filter delays for the individual cortical
areas were between 13.4 and 15.5 msec and not significantly different
(Table 1). For the subgroup with a latency difference >7.5 msec
between group delay and first click latency (N = 65),
the extra delay was independent of first click latency (Fig.
4A). The filter delay
was, as a consequence, linearly related
(R2 = 0.62) to the group delay (Fig.
4B; proportionality constant, 0.65). A potential
dependence of filter delay on stimulus intensity was investigated by
calculating regression lines. None of the slopes was significantly
different from zero (p > 0.5), so an intensity
effect on the filter delays is unlikely. A potential area effect on the
filter delays was explored using a 3 × 3 contingency table (three
areas by three filter delay subgroups, <7.5, 7.5-20, and >20 msec)
and showed that the distribution was as expected from the frequencies
of occurrence. An ANOVA of temporal filter delay on cortical area did
not show a dependence (p = 0.12) either.
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Figure 3.
Bivariate distribution of logarithm of the tMTF
peak magnitude [in number of synchronized (synchr.)
spikes per click train] and temporal filter delay, defined as the
difference between group delay and the response latency to the first
clicks in the train. The bimodal distribution for filter delay suggests
a break point at ~7.5 msec. The magnitude distribution is log normal.
The bivariate plot emphasizes the split in the filter delay
distribution at ~7.5 msec but also suggests that the delays >20 msec
belong to a separate group.
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Figure 4.
Dependence of the "temporal filter" delay on
first click response latency and on group delay. A, The
temporal filter delay for those units in which the group delay is at
least 7.5 msec larger than the first click response latency is
independent of the latency of the response to the first click.
B, Strong correlation between the temporal filter delay
(for the large delay subgroup) and the group delay.
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Temporal modulation transfer functions and latency
The average tMTF for the groups with a difference in first click
response latency and group delay of <7.5 msec had a smaller peak
magnitude than that for the subgroup with latency difference >7.5
msec. Because of the potential of a third subgroup with filter delays
>20 msec, an ANOVA of peak tMTF amplitude on three filter delay groups
(delays <7.5, 7.5-20, and >20 msec) was performed and showed that
the mean amplitude in the intermediate delay group was significantly
larger than that for the small delay group (p < 0.0001) but not significantly different from the large delay group
(p = 0.17). The small and large delay groups
showed no significant difference either (p = 0.94). A linear regression analysis between BMF and temporal filter
delay was performed per area and combined across areas. Across all
areas the slope of the regression line (BMF = 7.61 Hz + 0.06 *
filter delay) was not significantly different from zero. Calculated per
individual area, the slopes of the regression lines were not
significantly different from zero for AI and AII but showed a positive
slope for AAF (BMF = 7.15 Hz + 0.11 * filter delay), which was
significantly different from zero (p = 0.025). Because the temporal filter delays were indistinguishable in the three
cortical areas, I assume that the finding of the small dependence between BMF and temporal filter delay in AAF has minimal implications. To explore this more systematically, mean tMTFs were constructed (magnitude and phase) for five subgroups differing by increments of 5 msec in the amount of cortical filter delay. Because there were no
significant differences between cortical areas, the tMTFs were averaged
across units from all areas. Figure
5A shows that the largest
magnitude (close to five spikes per click train) was found for the
group with cortical filter delays of 15-20 msec. For filter
delays >20 msec the magnitude was similar to that for the small filter
delay groups. One observes that the best modulation frequency (peak of
the magnitude function, BMF) is at 9.52 Hz, except for the 15-20 msec
delay group, where it is 11.28 Hz. The limiting rate (the click rate
for which the response magnitude is 50% of that at the BMF) was higher
for the groups with filter delays of 10-15 and 15-20 msec than for
the other groups. Figure 5B shows the mean phase plots for
these groups, reflecting the increased group delay. In this
representation the phase is expressed in degrees, and the click rate
axis is logarithmic.
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Figure 5.
Magnitude and phase components of the mean tMTFs
for subgroups of temporal filter delays. Results are shown for five
subgroups. The subgroup with filter delay <5 msec comprised 142 units;
the subgroup with filter delay from 5-10 msec comprised 38 units, the
10-15 msec filter delay group comprised 31 units; the 15-20 msec
group comprised 22 units; and the group with filter delays in
excess of 20 msec comprised 10 units. The magnitude function
(A) is very similar for filter delays <10 and
>20 msec, whereas the peak magnitude is larger for the subgroups with
filter delays of 10-20 msec. The phase functions show the gradual
increase in slope expected from this subdivision in temporal filter
delays (B).
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A subsequent regression analysis between the tMTF magnitude of the
individual unit at every CRR and the value of the cortical filter delay
(by cortical area) showed no significant dependence for CRRs <8 and
>16 Hz. In the CRR region of 8-16 Hz there was a significant
(p < 0.005) positive correlation between tMTF
magnitude and cortical filter delay. In other words, with increasing
magnitude the delay in this CRR range increased.
Of 106 multiunit recordings with at least two well separated single
units, 69 recordings consisted of units that were all from the low
filter delay group (<7.5 msec), 12 recordings comprised units with
only large filter delays (>7.5 msec), and 25 recordings were composed
of units from both groups. This percentage of mixed recordings (24%)
is expected on basis of independence of finding low or high filter
group units: the product of their occurrence rates in the overall
population (0.70 and 0.30) predicts a 21% co-occurrence of recording
them on the same electrode. This was not significantly different from
the observed value.
Modeling the magnitude of the tMTF in terms of
synaptic mechanisms
In Figure 6 the number of spikes per
10 clicks is presented as a function of the CRR for the five filter
delay groups. This is an appropriate representation for estimating and
discussing the synaptic depression and facilitation mechanisms
responsible for the "adaptation." Figure 6A shows
that for all groups the functions are low-pass and have approximately
the same shape. Curves based on twice smoothing the data are drawn in
as well. Figure 6B presents the same data normalized
on their mean response for CRRs between 1 and 4 Hz. One observes that
for the groups with the 15-20 msec extra filter delay the CRR
dependence has a different shape and, as observed before, shows an
enhanced response in the 8-16 Hz range. The slope of the low-pass
filter functions is for all groups steeper than 12 dB/octave and
steepest for the 15-20 msec delay group.
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Figure 6.
Adaptation functions expressed as number of spikes
per click. A, These adaptation functions are low-pass
functions of click repetition rate that have similar shape regardless
of temporal filter delay. B, After normalizing the data
on the mean values of the response between 1 and 4 Hz, the curves are
similar, with the exception of the two groups with temporal filter
delays between 10 and 20 msec. The high-frequency slope is steeper than
12 dB/octave.
|
|
For repetitive stimuli the model for the normalized steady-state
response to a train with interstimulus interval, t, was given in Materials and Methods, and is repeated here for the summed response across the entire train:
![R<SUB><UP>av</UP></SUB>(&Dgr;t)=[1−R(N&Dgr;t)]<SUP>N</SUP>/[1−R(N&Dgr;t)],](/content/vol19/issue7/fulltext/2780/img013.gif)
|
(8A)
|
and for the average response per click:
|
(8B)
|
Recall that there is a multiplicative interaction between
depression and facilitation, so that the response to the (N + 1)th click becomes:
![R(N&Dgr;t)=[1−d <UP>exp</UP>(<UP>−</UP>&Dgr;t/&tgr;<SUB><UP>recov</UP></SUB>)]<SUP>N</SUP>[1+f <UP>exp</UP>(<UP>−</UP>&Dgr;t/&tgr;<SUB><UP>fac</UP></SUB>)]<SUP>N</SUP>,](/content/vol19/issue7/fulltext/2780/img015.gif)
|
(9)
|
The data-fitting procedure was done in Horizon, using the
nonlinear least squares fitting procedure, which provides a
 2 as an estimate of fit. To fit the data for the short
filter delay group, the facilitation, f, was set equal to
zero, and the amount of depression by a single click, d, and
the recovery time constant was estimated. Introducing facilitation at
this point only increased the 2, indicating a less
acceptable fit. The 10-15 and 15-20 msec filter delay group tMTFs
were subsequently modeled by introducing a small amount of
facilitation, f, but leaving the other fit parameters the
same as estimated for the short delay group. The results are shown in
Figure 7, A and B.
Figure 7A presents the tMTFs for the short delay group
(open circles), the 10-15 msec delay group (open squares), and the 15-20 msec delay group (filled
squares) on a linear ordinate, and Figure 7B presents
the response per click on log-log scale. Without spontaneous activity,
the model fitted the data well up to 13.44 Hz but for higher click
rates underestimated the data. Introducing a small amount of
spontaneous activity, identical for all click rates but slightly
different for the three filter delay groups, made the model fit quite
well. This residual activity may result from off responses that
frequently are observed for the higher click rates and that were
automatically incorporated in the calculation of the tMTF whenever they
were within one interclick interval from the last click. The fit curves
for the short filter delay group are shown with the
full lines (no facilitation, f = 0; strong depression, d = 0.9; fast recovery,
recov = 20 msec; spontaneous activity, 0.04 spikes per
click), for the 10-15 msec delay group with
wide-spaced dashed lines (f = 0.045; fac = 60 msec; d = 0.9;
recov = 20 msec; spontaneous activity, 0.04 spikes per
click), and for the 15-20 msec filter delay group with closely spaced dashed lines (f = 0.055;
fac = 60 msec; d = 0.9;
recov = 20 msec; spontaneous activity, 0.045 spikes per
click).
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Figure 7.
Modeling the magnitude of the tMTF on the basis of
synaptic mechanisms. A, tMTFs for three groups of units
together with the fit curves based on Equation 8A with the parameters
shown in B. B, Adaptation functions
together with the fit curves based on Equation 8B. C,
Estimates of the asymptotic adaptation functions (for 30 clicks) for
depression, facilitation, and the combination thereof. For comparison
an adaptation function for visual cortex is shown.
|
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These fit curves are for average values per filter delay group. Figure
3 showed that for each group there is a large range of peak tMTF
amplitude values. This variation reduces the amplitude range by a
factor of 30 (~1.5 log unit) when the peak amplitude is normalized on
the average firing rate for CRRs between 1 and 4 Hz. This suggests that
the overall firing rate of the units is a major factor in this
variation. For the group with filter delays in the 10-20 msec range
the variation in peak amplitude can be further explained by a small
variation in the amount of facilitation. For instance, tMTFs with the
largest amplitudes (1.25 log units or ~18 synchronized spikes per
click train) can be fitted by using f = 0.07. For
f = 0, the peak amplitude is approximately two spikes
per train. To model individual unit tMTFs with smaller peak amplitude,
for all filter delays, the depression time constant has to be increased
slightly. For instance, an increase to 24 msec is sufficient to fit a
tMTF with a peak amplitude of 0.5 spikes per train. However, the
overall variation found in the number of synchronized spikes per train
for low CRRs, which accounts for at least half of the variation in the
peak amplitude, cannot be explained by changes in the amount of
short-term depression or facilitation.
These model results suggest that the recovery time constant for the
auditory cortex is approximately a factor of 4 smaller than for other
neocortical areas and that relatively small amounts of synaptic
facilitation can account for most of the observed quantitatively large
tMTF magnitude changes for the various temporal delay groups.
The model parameters can in turn be used to generate asymptotic values
for a constant number of clicks in the train instead of a constant
train length. In Figure 7C the asymptotic values after 30 clicks are shown for depression only (Eq. 5B; time constant, 20 msec),
for facilitation only (Eq. 6; time constant, 60 msec; 5.5%
facilitation), and for depression and facilitation combined (Eq. 9).
Note the enhancement between 3 and 10 Hz. For comparison, model data
for visual cortex cells under periodic stimulation (Chance et al.,
1998) are shown as well.
Local field potentials
For the simultaneously recorded LFPs, magnitude tMTFs, onset
latency, and group delay measurements were obtained in the same way as
for the single units. As shown previously, the magnitude tMTF for LFP
triggers is, save for a scale factor, identical to those for
simultaneously recorded units (Eggermont and Smith, 1995), suggesting
that the tMTF magnitude is determined at the input level to the
neurons. Figure 8 shows some comparisons
between LFP and SU measures for onset latency and group delays,
suggesting that factors contributing to the SU filter delays are acting
at the spike generation level. Figure 8A presents
latency of the response to first clicks for SU as a function of that
for LFP triggers for the low and high filter delay category for the
SUs. The slopes of the regression lines for the two groups are not significantly different, and neither is significantly different from
one. Thus LFP latencies to first clicks are highly predictive of
the SU latencies to first clicks. Figure 8B compares
the group delays for LFPs and SU spikes. One observes that there still
is a good correlation for the small filter delay group but no
correlation for the high filter delay group. In the latter group the
mean group delay difference between SU and LFP is 14.5 msec. This
suggests that the extra delay for the SU arises at the spike generation level and not from the specific afferent input to the neurons.
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Figure 8.
Relationships between LFP and single-unit
latencies for first click responses (A) and for
group delays (B). There is a close correlation
for first click latencies across both filter delay groups. For the
group with short temporal filter delays, the two estimates of group
delay are correlated, but there is no correlation between LFP and SU
group delays for the long SU temporal delay group.
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DISCUSSION |
For approximately two-thirds of the 215 single units the group
delay calculated from the phase-MF dependence was within 7.5 msec of
the response latency to the first clicks in the trains. For the
remaining one-third of the units, the group delay was on average ~14
msec higher. The overall amplitude distribution is unimodal and has
higher values for filter delays in the 10-20 msec range. These
findings were similar in the three cortical areas. Schulze and Langner
(1997) compared group delays in primary auditory cortex to AM tones
with latencies to unmodulated tone burst and found a similar dependence
as in the present study. The difference in group delay and first click
latency is interpreted here as a temporal filter delay. For
intermediate values of the temporal filter delay an enhancement of the
magnitude of the tMTF was observed, resulting in increased limiting
rates. This enhancement was the same for units and LFPs. For the long
delay group, the temporal filter delay for single units was ~14.5
msec longer than for LFPs, suggesting that the temporal filter delay is
related to spike generation.
Systems analysis
The differences between the various filter delay groups can be
elucidated by comparing the average magnitude and phase of the tMTF for
the low (<7.5 msec) and high (>7.5 msec) filter delay groups (Fig.
9A,B) and calculating the
magnitude ratio and phase shift between the two groups (Fig.
9D,E). As suggested above, the additional phase shift only
occurs at >8 Hz, and the extra magnitude gain occurs largely between 8 and 16 Hz. The impulse responses for the low and high filter delay
groups, calculated by inverse Fourier transformation of the complex
spectrum, formed by combining the magnitude and phase data, are shown
in Figure 9C and indicate the peak latencies expected from
the group delays for the two groups. The extra gain and phase shift,
needed to convert the tMTF of the low filter delay group into the high
delay tMTF, shown in Figure 9, D and E, can be
interpreted as resulting from the action of an "amplifying filter"
with impulse response shown in Figure 9F. The nature of the
filter is not immediately obvious. Generally, increased group delays
correspond to steeper filters, which does not fit the increase in the
magnitude of the tMTF with increasing group delay, unless an
amplification aspect is introduced. This amplification could be akin to
that observed in reducing the damping of a bandpass system. Concurrent
with the increase in output at the "resonant" frequency, the phase change is more rapid across the frequency range of the peak response than for a more damped resonator (Bendat and Piersol, 1971). The group
delay introduced by a filter with otherwise the same characteristics would thus be much larger in the more resonant, less damped, filter. In
our data the observed phase changes are of the order of 2-3 radians, and the slope of the tMTF filter is ~18-24 dB/octave, suggesting that the filter is of approximately fourth order.
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|
Figure 9.
Magnitude (A) and phase
(B) for the group with filter delay <7.5 msec
(*) and that with longer filter delays ( ). The corresponding impulse
responses are shown in C. D,
E, Magnitude ratio and phase shift between the two
groups, which can be interpreted as the action of an amplifying filter
with impulse response, as shown in F.
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|
For LFPs, filter delays were also split into two groups; however, the
vast majority showed a delay that was <5 msec. The SU filter delays
were independent of the LFP filter delays; for the short filter delay
group the mean difference was 1.5 msec, and for the long delay group it
was 14.5 msec. This suggests that the long group delays for the SU are
the result of effects additional to those for the EPSPs of which the
LFPs are an extracellular representation (Mitzdorf, 1985; Varela et
al., 1997). The finding of an independent distribution of units
belonging to the two temporal delay groups suggests that the
explanation for the long filter delays is in individual, not
spatially segregated, neuron properties. The observation that the
distribution of low and high filter delay neurons is similar in all
three cortical areas corroborates this.
After the subdivision of the population into groups of ascending
temporal filter delay in 5 msec steps, the groups with filter delays
between 10 and 20 msec stand out as a separate group with enhancement
of the tMTF. The group with larger delays had a tMTF similar to
that for the groups with temporal filter delays <10 msec. Putting the
separation boundaries at 7.5 and 20 msec made no difference in the
findings. This suggests that the temporal filter is not a minimum phase
system, with its unique relationship between the magnitude and the
phase functions of the tMTF, allowing one to be calculated from the
other (Papoulis, 1977). The linearity of the phase-CRR dependence
suggests that it can be treated as a system that results in a pure
delay for the neural responses. This delay is likely the result of
cumulative effects of depression and recovery mechanisms. The
enhancement in the tMTF magnitude can be seen as resulting from an
independent mechanism, notably presynaptic facilitation.
Modeling on the basis of synaptic mechanisms
The observed enhancement in the magnitude of the tMTF could be
explained by a modest amount of facilitation. This puts the amplification at the input site of the neuron. Previous findings (Eggermont and Smith, 1995) that the LFP-based tMTF is a scaled version
of those for SU and MU also suggest this. Initially, the tMTFs were
fitted using time constants for visual cortex neurons. Modeling the
data using the published adaptation time constant of 33 msec and the
recovery time constant of 80 msec (Wang, 1998) required also 90%
facilitation with a time constant of 87 msec, comparable to what was
reported for visual neurons (Varela et al., 1997) to obtain some
resemblance to the tMTF. This did, however, not result in an acceptable
fit to the data, because the residuals were not spherically
distributed, and the steep decrease for CRR could not be obtained. The
next step, as described in Results, was to assume very little
facilitation as is common for neocortical cells (Markram et al., 1998)
and to estimate the time constants by a least mean squares
curve-fitting procedure. The best results for the short filter delay
group (Fig. 7) were obtained with a model that provided a short
adaptation time constant of 8 msec, a short recovery time constant of
20 msec, ~90% of depression, and no facilitation. It was impossible
to obtain a good fit for the tMTFs in the 10-20 msec filter delay
groups without incorporating a small amount of facilitation. A
multiplicative combination of effects of previous stimuli, for
depression as well as facilitation, was the only way to obtain a good
fit to the data. The variance in the response for low CCR, which
accounts for up to half of the variance at the tMTF peak, cannot be
explained by this model.
Comparison with other studies
The decrease in the number of spikes per click as a function of
click rate can theoretically (see Materials and Methods) be described
by three time constants, adap,
fac, and recov. The adaptation
time constant, adap, reflects fast adaptation
properties and was identified by Wang (1998) as depending on the
[Ca2+] extrusion and buffering properties of the
neuron, quantified by Ca, and on the product of
the spike-evoked [Ca2+] influx size and the
conductance of the afterhyperpolarization. Differences in adaptation
(adap values from 10 to 50 msec) for pyramidal cells in
visual cortex have been reported for superficial and deep layers (Ahmed
et al., 1993). In the model a value as short as 8 msec was needed. As a
result of this very short perstimulatory adaptation time constant the
fraction of depression introduced by a single click was 0.94. This
value is not unreasonable in light of the very short transient response
of cells in auditory cortex to a single click, which typically consists
of one to three spikes within 10 msec, followed by a 60-150 msec
period of suppressed spontaneous activity. The recovery time constant
for visual cortical cells, recov, was considered
by Wang (1998) to be solely dependent on Ca and to be
smallest in the dendrites (80 msec) and much larger for the soma (240 msec). Our tMTFs and adaptation functions could only be fitted using a
recovery time constant that was approximately four times smaller than
the one used by Wang (1998) for the dendrites. Response facilitation
has also been demonstrated in neocortex, especially under low quantal
release conditions (Varela et al., 1997). A small amount of
facilitation, <7%, in agreement with values for neocortical cells
(Markram et al., 1998), appeared to explain most of the changes in the
magnitude of the tMTF. For visual neocortical synapses (Varela et al.,
1997) the facilitation time constants were somewhat larger (90-120
msec) than the 60 msec obtained from our curve fit procedure.
This model result indicates that auditory cortical cells may have much
faster recovery mechanisms than visual cortical cells on which previous
temporal modeling was based (Varela et al., 1997; Chance et al., 1998;
Wang, 1998). This fast recovery may be required for the ability of the
auditory cortex to reliably track the fast amplitude modulations that
occur in natural sounds.
| |
FOOTNOTES |
Received Sept. 9, 1998; revised Dec. 2, 1998; accepted Jan. 19, 1999.
This work was supported by grants from the Alberta Heritage Foundation
for Medical Research, the Natural Sciences and Engineering Research
Council of Canada, and the Campbell McLaurin Chair for Hearing
Deficiencies. Kentaro Ochi, Mutsumi Kenmochi, and Makiko Kimura
assisted with the data recording. Greg Shaw assisted with the data analysis.
Correspondence should be addressed to Dr. Jos J. Eggermont, Department
of Psychology, University of Calgary, 2500 University Drive Northwest,
Calgary, Alberta, Canada T2N 1N4.
| |
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TOP
ABSTRACT
INTRODUCTION
