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The Journal of Neuroscience, May 15, 2002, 22(10):4114-4131
Nonlinear Spectrotemporal Sound Analysis by Neurons in the
Auditory Midbrain
Monty A.
Escabí1, 2 and
Christoph E.
Schreiner1
1 W. M. Keck Center for Integrative Neuroscience
and University of California San Francisco/University of California
Berkeley Joint Bioengineering Graduate Group, University of California,
San Francisco, California 94143, and 2 Department of
Electrical and Computer Engineering, Biomedical Engineering Program,
University of Connecticut, Storrs, Connecticut 06269
 |
ABSTRACT |
The auditory system of humans and animals must process information
from sounds that dynamically vary along multiple stimulus dimensions,
including time, frequency, and intensity. Therefore, to understand
neuronal mechanisms underlying acoustic processing in the central
auditory pathway, it is essential to characterize how spectral and
temporal acoustic dimensions are jointly processed by the brain. We use
acoustic signals with a structurally rich time-varying spectrum to
study linear and nonlinear spectrotemporal interactions in the central
nucleus of the inferior colliculus (ICC). Our stimuli, the dynamic
moving ripple (DMR) and ripple noise (RN), allow us to systematically
characterize response attributes with the spectrotemporal receptive
field (STRF) methods to a rich and dynamic stimulus ensemble.
Theoretically, we expect that STRFs derived with DMR and RN would be
identical for a linear integrating neuron, and we find that ~60% of
ICC neurons meet this basic requirement. We find that the remaining
neurons are distinctly nonlinear; these could either respond
selectively to DMR or produce no STRFs despite selective activation to
spectrotemporal acoustic attributes. Our findings delineate rules for
spectrotemporal integration in the ICC that cannot be accounted for by
conventional linear-energy integration models.
Key words:
inferior colliculus; spectrotemporal; receptive field; nonlinear; ripple; naturalistic; reverse correlation
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INTRODUCTION |
The central nucleus of the inferior
colliculus (ICC) is an obligatory station in the lemniscal auditory
system that receives convergent inputs from numerous brainstem
structures and sends its highly processed outputs to the auditory
thalamus and, subsequently, to the primary auditory cortex. Neurons in
the ICC are sensitive to systematic manipulations of temporal,
spectral, binaural, and intensity stimulus attributes (Rees and
Møller, 1983 , 1987; Schreiner et al., 1983; Langner and Schreiner,
1988; Schreiner and Langner, 1988; Irvine and Gao, 1990; Kuwada et al.,
1997; Ramachandran et al., 1999; Krishna and Semple, 2000). These
properties have been studied extensively with pure tones, modulated
tones, and noise stimuli; however, the overall capabilities of the ICC
for processing dynamic, spectrally complex acoustic stimuli remain unknown. Clearly, because natural sounds have structurally rich acoustic spectra and can simultaneously vary along spectral, temporal, intensity, and aural acoustic dimensions, it is essential to understand how these are jointly processed and represented within the ICC.
The concept of a stimulus-response function or receptive field (RF) is
a mathematical construct that describes the stimulus features that are
encoded by a sensory neuron. A widely used RF description that measures
the response of a neuron to pure tones of varying frequency and sound
pressure level (SPL) is the frequency-tuning curve (FTC; Schreiner and
Langner, 1988; Nelken et al., 1997; Ramachandran et al., 1999).
Although this descriptor continues to be important, it cannot
characterize the dynamic behavior of a neuron in response to an
arbitrary, spectrally complex, time-varying stimulus. Consequently,
secondary analyses are often used that measure the ability of a neuron
to respond to other stimulus aspects, such as the ability to
follow successively presented stimuli of different rates (Rees and
Møller, 1983, 1987; Schreiner et al., 1983; Møller and Rees, 1986;
Langner and Schreiner, 1988; Eggermont, 1999; Krishna and Semple,
2000).
Recently, the use of reverse correlation techniques to estimate the
spectrotemporal receptive field (STRF) in the auditory system (Aersten
et al., 1980; Yeshurun et al., 1985; Eggermont, 1993; Nelken et
al., 1997; de Charms et al., 1998; Klein et al., 2000; Theunissen et
al., 2000; Depireux et al., 2001; Miller et al., 2001, 2002) has
allowed scientists to overcome some of the practical limitations posed
by conventional auditory RFs and the stimuli used to derive them (e.g.,
pure tones and modulated tones). The STRF describes the
stimulus-response function of an auditory neuron along both the
spectral and temporal acoustic dimensions, to a rich stimulus ensemble,
and makes no assumptions about independence of spectral and temporal
response attributes.
Most RF methods, including the STRF procedure, operate under the
assumption that the system under investigation integrates information,
be it acoustic or visual, in an approximately linear manner. This
requires that the spiking output of a sensory neuron be described as a
linear or quasilinear function of its inputs. Although this is often a
reasonable assumption, it may not always hold. For instance, direct
STRF (referred to as spatiotemporal receptive field for visual neurons)
approaches are readily applicable for simple cells in the primary
visual cortex (Jones and Palmer, 1987; DeAngelis et al., 1993,
1999; Victor and Purpura, 1998; Anzai et al., 1999; Reich et al.,
2000) but fail for visual complex cells and neurons outside of
VI (Emerson et al., 1987; Szulborski and Palmer, 1990; Livingstone et
al., 2001). Other stimulus-dependent limitations are observed for
sensory neurons in acoustically specialized animals, where central
sensory neurons are often highly nonlinear and specifically tuned to
behaviorally relevant vocalizations (Suga and Jen, 1976; Suga, et al.,
1978; Margoliash, 1983; Doupe, 1997; Portfors and Wenstrup, 1999;
Theunissen et al., 2000).
Theoretically, the STRF procedure requires the use of white noise as a
probing stimulus. Practically, however, because sensory neurons in
central stations respond to a limited range of spectrotemporal (spatiotemporal) modulations and are often inhibited by white noise, it
is necessary to synthesize acoustic or visual sequences that are
optimized for any particular station (de Charms et al., 1998; Klein et
al., 2000). Often this is achieved with randomly arranged
spectrotemporal tone pips in the auditory system (de Charms et al.,
1998; Theunissen et al., 2000) and spatiotemporally interleaved bars or
spots of light in the visual system (Emerson et al., 1987; DeAngelis et
al., 1993, 1999; Anzai et al., 1999; Reich et al., 2000).
Recently, some of the stimulus-dependent limitations associated with
such stimuli have been overcome with the use of natural sounds
(Theunissen et al., 2000) in the avian auditory cortex homolog.
In this study, we recorded single-unit activity from neurons in the ICC
of cats in response to dynamic spectrotemporally complex stimulus
sequences. Our synthetic stimuli, the dynamic moving ripple (DMR) and
ripple noise (RN), are designed to stringently satisfy a number of
theoretical requirements for use with the reverse correlation STRF
methods. Furthermore, these sounds share various properties with
natural sounds that allow us to overcome some of the practical
limitations of white noise, randomly interleaved tone pips, and other
synthetic reverse correlation stimuli. Compared with natural signals,
these stimuli offer the advantage that they can be parametrically
manipulated, allowing for a systematic assessment of nonlinear response
characteristics within the ICC. Our findings demonstrate the presence
of distinct spectrotemporal nonlinearities in the ICC and identify
possible mechanisms used for complex sound analysis, source
segregation, and signal detection.
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MATERIALS AND METHODS |
Surgical preparation
Cats were initially anesthetized with a mixture of ketamine HCl
(10 mg/kg) and acepromazine (0.28 mg/kg, i.m.). After an intravenous infusion line was inserted, a surgical state of anesthesia was induced
with ~30 mg/kg Nembutal and maintained throughout the surgery with
supplements. Body temperature was measured with a rectal probe and
maintained with a heating pad at ~37.5°C. An incision was made in
the intercartilaginous area of the trachea, and a tracheotomy tube was
inserted. After performing a craniotomy, the ICC was exposed by
removing the overlying cerebrum and part of the bony tentorium using a
dorsal approach. On completion of the surgery, the animal was
maintained in an areflexive state of anesthesia via continuous infusion
of ketamine (2-4
mg · kg 1 · h1)
and diazepam (0.4-1
mg · kg1 · h1)
in lactated Ringer's solution (1-4
mg · kg1 · h1).
The state of the animal was monitored (heart rate, breathing rate,
temperature, and periodically checked reflexes) throughout the
experiment, and the infusion rate was adjusted according to physiological criteria. Every 12 hr, the cat received an injection of
dexamethasone (0.14 mg/kg, s.c.) to prevent brain edema and atropine to
reduce salivation (0.04 mg · kg1 · d1,
s.c.). All surgical methods and experiment procedures followed National
Institutes of Health and US Department of Agriculture guidelines and
were approved by the committee on animal research of the University of
California, San Francisco.
Neuronal recording
Data were obtained from n = 81 single units in
the central nucleus of the inferior colliculus of three anesthetized
cats. One or two closely spaced parylene-coated tungsten
microelectrodes (Microprobe Inc., Potomac, MD; 1-3 M at 1 kHz) were
advanced with a hydraulic microdrive (David Kopf Instruments, Tujunga, CA). Action potential traces were recorded onto a digital audiotape (CDAT16; Cygnus Technologies, Delaware Water Gap, PA) at a sampling rate of 24.0 kHz (41.7 µsec resolution) for off-line analysis. Off-line analysis consisted of digital bandpass filtering (0.3-10 kHz)
and individually spike sorting the action potential traces using a
Bayesian spike-sorting algorithm (Lewicki, 1994).
Electrode penetration trajectories were at ~20-30° relative to the
sagittal plane. Electrodes were initially advanced through the external
nucleus and onto the central nucleus while audiovisually determining
single neuron and multiunit characteristic frequencies (CFs).
The boundary between the external and central nucleus of the inferior
colliculus (IC) was confirmed physiologically (Merzenich and Reid,
1974) by a reversal or discontinuity in the CF trend and by
monotonically increasing CFs as a function of depth (over a range of
~1-20 kHz and ~1.5-5.0 mm relative to the surface of the IC),
consistent with the central nucleus. All electrode
recordings throughout the remainder of the experiment were taken from
this physiologically defined region. Except for the depth and CF
constraints, recording locations were randomly distributed within the ICC.
Acoustic stimuli
RN and DMR stimulus waveforms were designed on a digital
computer using the MATLAB (Mathworks) programming environment. The spectrotemporal envelopes shown in Figure 1C,D define the
energy modulations, in time and frequency, that are used to modulate a
bank of sinusoidal carriers of frequencies
fk. As with natural signals, the
envelope of these sounds is time-varying and probes spectral and
temporal neuronal response preferences. Furthermore, analogous to
various classes of natural signals (Fig. 1A,B), these sounds have unique short-term statistics (Fig. 2D,E)
and yet their long-term statistics are identical (Fig.
2D,E, far right; see Stimulus correlation
statistics). Therefore, both sounds satisfy the necessary requirement
for use with the reverse correlation procedure that we use to estimate
auditory spectrotemporal receptive fields (see Spectrotemporal
receptive field).
Dynamic moving ripple envelope. The DMR envelope is designed
as a dynamic sinusoidal grating on a octave frequency and decibel amplitude axis. Two parameters defined the DMR envelope: the
instantaneous ripple density, (t), defines the number of
spectral peaks per octave at a given time instant; and
Fm(t) defines the
instantaneous modulation rate. The DMR spectrotemporal envelope is
expressed as:
![S<SUB><UP>DMR</UP></SUB>(t, X<SUB><UP>k</UP></SUB>)=M/2 · <UP>sin</UP>[2&pgr;&OHgr;(t)X<SUB><UP>k</UP></SUB>+&PHgr;(t)],](/content/vol22/issue10/fulltext/4114/img001.gif)
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(1)
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where M = 30 or 45 is the modulation depth of
the envelope in decibels, Xk = log2(fk/f1)
is the octave frequency axis relative to the lowest stimulus frequency
(f1 = 500 Hz), and
 (t) =   Fm( )d controls the time-varying temporal modulation rate,
Fm(t). Spectral [(t)] and temporal
[Fm(t)] parameters are
independent and slowly time-varying random processes (maximum rates of
change, 1.5 Hz for Fm and 3.0 Hz for
). The time rate of change of both parameters was heuristically
chosen so that they coincide with the observed range of values for
similar acoustic features in speech and vocalizations (Greenberg,
1998). To guarantee that the stimulus space was covered in a
statistically unbiased manner, both parameters were designed with
uniformly (flat) distributed amplitudes in the intervals 0-4 cycles
per octave for and  350 to +350 Hz for
Fm.
The time-varying stimulus parameters were generated in the MATLAB
programming environment. First, the parameters were generated as a
random sequence of normally distributed samples (randn function in
MATLAB) using a sampling rate of 3 Hz for
Fm(t) and 6 Hz for (t). These sequences had maximum frequency contents of
1.5 and 3 Hz, respectively (because the maximum signal frequency is
half of the sampling frequency). To generate the acoustic sound
waveforms at a sampling rate of 44.1 kHz (Eq. 4) it was necessary to
resample both of the parameter signals to an equivalent sampling rate. Therefore, we upsampled both signals to 44.1 kHz using a cubic interpolation procedure (interp1 function in MATLAB; "cubic"
option; upsampling factor, 14,700 for modulation rate and 7350 for
ripple density). Next we needed to convert the parameter amplitudes
from a normal to a uniform distribution so that the probability of occurrence of each parameter is statistically unbiased within the
selected intervals. This normalization was performed with the error
function:
This function converts normally distributed amplitudes to
uniformly distributed amplitudes over the interval 1 to +1 and a
subsequent linear rescaling of the amplitudes to the selected interval.
This operation had only a subtle effect on the spectrum of these
signals and is necessary to guarantee that the signal parameters are
statistically unbiased (flat distribution) within their predefined range.
Ripple noise envelope. The RN envelope is first
generated as a linear superposition of L = 16 independently chosen DMR envelopes, SDMRl(t,
Xk):
|
(2)
|
where the sum is normalized so that the SDs of the RN and DMR
are identical. Although this guaranteed that the average contrast of
the DMR and RN envelopes be the same (i.e., identical SD), the RN
amplitude distribution had long tails and resembled a Gaussian distribution, whereas the DMR envelope is approximately uniform and
confined to the interval [M/2, M/2].
Instances at the high- and low-intensity tails of the distribution of
the RN envelope can therefore potentially activate undesirable
intensity- and contrast-dependent nonlinearities. We overcame this
possibility by compressing the RN envelope so that its amplitude
statistics resemble those of the DMR. The compressed RN envelope is
given by:
![S<SUB><UP>RN</UP></SUB>(t, X<SUB><UP>k</UP></SUB>)=f[<A><AC>S</AC><AC>&cjs1171;</AC></A><SUB><UP>RN</UP></SUB>(t, X<SUB><UP>k</UP></SUB>)],](/content/vol22/issue10/fulltext/4114/img005.gif)
|
(3)
|
where f(x) = M/2 · erf(x/ DMR) and
erf(·) is the error function. This envelope covers a
relative intensity range of [M/2, M/2] dB
as for the DMR envelope. This procedure allows us to isolate
spectrotemporal nonlinearities from intensity- or contrast-dependent ones. A second concern was that the erf(·) function
significantly distorts the RN envelope by introducing high-frequency
envelope modulation components, and this in turn could compromise
experimental results. We found, both analytically (data not shown) and
through simulation, that the ripple spectrum and spectrotemporal
autocorrelation (see Fig. 2D,E, far right;
shown for compressed RN) of the uncompressed and compressed RN were in
close agreement (2.1% rms error for both the ripple spectrum and autocorrelation).
Acoustic waveform. From the DMR and RN spectrotemporal
envelopes, the acoustic sound pressure waveforms,
s(t), are constructed by modulating
L = 230 sinusoidal carriers that are added
together:
|
(4)
|
where  k is a randomly chosen phase
(0-2 ), which gives s(t) a noise-like
character, and SLin(t,
Xk) is a transformed version of the
DMR or RN envelopes that describes the amplitude modulations in linear
amplitude units. The linear envelope is bounded between 10M/20 and 1. It is related
to the decibel envelopes by (here we use SdB in place of
SDMR and
SRN):
|
(5)
|
Frequency carriers are geometrically spaced at a resolution of
43 carriers per octave: fk =  · fk 1 ( = 1.01617) over a
range of 5.32 octaves (500-20,000 Hz). Although the resultant power
spectrum is not flat, this guarantees that the primary sensory
epithelium is uniformly excited and equal energy is provided per unit octave.
Sound presentation. All recordings were made with the animal
in a sound-shielded chamber (IAC, Bronx, NY), with stimuli delivered via a closed, binaural speaker system (electrostatic diaphragms from
Stax). Single neurons or clusters of neurons were initially isolated
audiovisually by presenting pure tones, white noise, or both. FTCs were
derived in two of the three experiments with a pseudorandom sequence of
pure tones presented at 15 intensities and 45 geometrically spaced
frequencies. In one experiment, rate-level functions were measured
with the RN stimulus as a function of SPL and contrast. After these
initial tests, DMR and RN stimuli were presented binaurally with an
independent sound sequence for each ear. The DMR stimulus was presented
for 10-20 min, followed by 10-18 min (full length presented for
~95% of the recording sites; identical stimuli for all experiments)
of the RN at ~30-70 dB/carrier greater than the neuron response
threshold (as determined by the FTC or rate-level functions). Because
the RN and DMR stimuli are each composed of 230 sinusoid carriers, the
effective SPLs were 10 · log10(230) = 23.6 dB greater than these values (i.e., ~53-93 dB greater than
threshold; SPL range, 75 ± 19 dB SPL, 64 ± 19 dB/one-third
octave, or 51 ± 19 dB/carrier). Both RN and DMR were presented at
identical intensities and contrast so that they covered an identical
range of amplitudes and fall well within the intensity response area of
the neuron. Sixteen neurons were also tested with a short 5 sec segment
of the DMR and RN that was presented 40 consecutive times. This was
used to construct response rastergrams for each stimulus (see Fig. 10).
Finally, for six neurons that did not respond to the RN, the DMR
stimulus was again presented at the end of the recording session to
verify that the given neurons were still responsive and to verify the stability of the electrode placement.
Stimulus correlation statistics
The long-term and instantaneous spectrotemporal correlation
statistics of the RN and DMR stimulus constitute an essential aspect of
the stimulus design and the experimental approach. These were evaluated
in closed form and rigorously tested via simulation. Only a brief
account is provided.
A spectrotemporal Gaussian window,
wi(t, X),
of SD x = 0.5 octaves and
t = 5, 10, or 20 msec and centroid about
t = ti was used to
localize the RN or DMR spectrotemporal envelope,
S(t, X). The instantaneous
spectrotemporal autocorrelation function was obtained by evaluating the
localized autocorrelation:
![R<SUB><UP>ss</UP></SUB>(&tgr;, &xgr;‖t<SUB><UP>i</UP></SUB>)=E[S(t, X)w<SUB><UP>i</UP></SUB>(t, X)S(t−&tgr;, X−&xgr;)w<SUB><UP>i</UP></SUB>(t−&tgr;, X−&xgr;)],](/content/vol22/issue10/fulltext/4114/img008.gif)
|
(6)
|
where the expectation operator, E[·], is taken
with respect to time, t, and the spectral distance variable,
X [Eqs. 1, 3 are substituted for S(t,
X)]. The variable
ti corresponds to the time instant
when the autocorrelation is evaluated, and and  correspond to
the temporal lag and spectral displacement, respectively.
In closed form the solutions for the RN and DMR are given by:
|
(7)
|
![R<SUB><UP>RN</UP></SUB>(&tgr;, &xgr;)=[&sfgr;<SUP>2</SUP><SUB><UP>RN</UP></SUB> · <UP>sinc</UP>(2&OHgr;<SUB><UP>Max</UP></SUB>&xgr;) · <UP>sinc</UP>(2F<SUB><UP>Max</UP></SUB>&tgr;)+e(&tgr;, &xgr;)] · R<SUB><UP>ww</UP></SUB>(&tgr;, &xgr;),](/content/vol22/issue10/fulltext/4114/img010.gif)
|
(8)
|
where  = M2/8 and  = M2/12 are the variance of the
DMR and RN, respectively, and Rww(, ) is the autocorrelation function of the Gaussian window (which is
itself a Gaussian window of SD  2x and
2t). The parameters i = (ti)
and Fm,i = Fm(ti) are the
instantaneous DMR parameters evaluated at
ti. Because the stimulus parameters
dynamically vary with time at a nominal rate of 3 and 1.5 Hz (Fig.
2A,B), the DMR instantaneous spectrotemporal
autocorrelation likewise varies with time (Fig. 2D).
Accordingly, its spectrotemporal envelope is nonstationary at these
time scales. The term e(, ) is a spectrotemporal noise
term, and the parameters Max = 4 cycles per
octave and FMax =350 Hz are the
maximum ripple parameters.
The long-term autocorrelation for both sounds was obtained by
performing a time average of the instantaneous autocorrelation: RSS (, ) = E[RSS (,
|ti)] (E[·] is
now evaluated with respect to ti). The
autocorrelation is identical in form for both sounds:
|
(9)
|
The autocorrelations only differ in the SD by a multiplicative
factor of 20% (RN, S = RN = M12 dB; DMR,
S = DMR = M8 dB).
Spectrotemporal receptive field
STRFs are computed by averaging the pre-event spectrotemporal
envelope. For a sequence of N neural events at times,
tn (sampled at 41.7 µsec
resolution), contralateral and ipsilateral STRFs are obtained as [here
we use SdB(t,
Xk) in place of
SDMR(t,
Xk) or
SRN(t,
Xk)]:
|
(10)
|
where T is the experimental recording time in
seconds, is the temporal delay of the stimulus relative to the
neural event time (0-100 msec), and  is the
variance of the decibel spectrotemporal envelope for the DMR or RN.
During the DMR and RN stimulus presentation, independent sound
sequences were binaurally presented to each animal. This allowed us to
independently estimate the contralateral and ipsilateral STRFs by
replacing the contralateral and ipsilateral spectrotemporal envelopes
into Equation 10 (Marmarelis and Naka, 1974).
Stimulus envelopes were sampled at 4.0 kilosamples/sec (temporal) and
43 samples per octave (spectral). The STRF is formally given in units
of spikes per second per decibel. We use a rate-normalized version of
the STRF, STRFr(,
Xk) = s
· STRF(, Xk), which corresponds to the average driven output produced at time 0, in units of spikes per
second, for the average differential stimulus (decibels) presented within the receptive field of the neuron.
Statistically significant STRF
We devised a procedure for measuring the statistically
significant STRF by considering a null condition in which N
randomly chosen spikes are put through Equation 10. This procedure
consists of adding random sound waveforms to construct a control STRF
from which statistical significance can be determined. Solutions for this procedure were derived analytically in closed form (data not
shown). The distribution of amplitudes for the control STRF quickly
approached a normal distribution (with as little as N = 50 spikes). Therefore, a simplification was made in which we determined
the two-tailed probability of exceeding a threshold relative to the
control STRF under the assumption of a normal distribution. The
statistically significant portion of the STRF (p < 0.002) is obtained by keeping all values of the STRF that exceed
3.09 SD of the control noise STRF and setting all other values to 0. Analytically this is expressed as | · T · STRF(, )/N| > 3.09 · s. No smoothing was performed before or after
thresholding. This procedure was tested against the analytically derived solutions, and we found that actual significance values were
always slightly smaller (e.g., actual significance value of
p < 0.0019 for N = 50).
To determine relative significance of STRFs, on an equal spike basis,
we further evaluated significance by recomputing all STRFs using 100 action potentials and determining all pixel values that exceeded the
p < 0.002 confidence intervals. For these pixel values, the average and maximum signal-to-noise ratio (SNR) was computed. Average and peak SNRs were computed as:
and
where 100 is the SD of the noise
control STRF derived for 100 random spikes. Thus, for any given pixel,
the SNR determines the number of SDs by which STRF pixels stand out
above the noise.
Null hypothesis
Response nonlinearities are tested against the expected results
for an ideal linear model neuron. Given that the long-term spectrotemporal autocorrelation functions for the DMR and RN are identical, it follows that for a purely linear neuron
STRFDMR = STRFRN (for
proof, see Appendix A). Significant differences between the RN and DMR
STRFs can be attributed to response nonlinearities. To quantify
response differences, we use the statistically significant portion of
the STRFs and use this to compute a number of response metrics for the
DMR and RN: similarity index, rate and magnitude disparity index, and
the phase-locking index (see below).
Quantifying DMR and RN response differences
Neural responses for DMR and RN were compared in three
complementary ways. First the STRF similarity index (SI; DeAngelis et
al., 1999; Reich et al., 2000) was used to quantify shape
differences between STRFDMR and
STRFRN. Using the STRF pixel values that exceeded the statistical significance threshold of p < 0.002 for either condition, we treated the STRFs as vectors (including
significant contralateral and ipsilateral pixels). The vectorized RFs
were then used to evaluate the similarity index:
|
(11)
|
where RFDMR and
RFRN are the significant STRFs,
 ·, · is the vector inner product, and  · designates
the vector norm operator. The SI is numerically identical to the
Pearson correlation coefficient.
We devised two metrics to evaluate differences in firing rate and
driven activity independently of STRF shape. First we computed the rate
disparity index (RDI):
|
(12)
|
where s = sign(rDMR rRN), and the mean spike rates for
each condition are rDMR and
rRN. The magnitude of the RDI is
numerically equivalent to the percent change in firing rate between DMR
and RN. Its sign tells us which condition, DMR or RN, had a higher firing rate (+, DMR; , RN). To quantify differences in driven activity, we used a third metric, the magnitude disparity index (MDI).
The MDI is identical in form to the RDI, where the mean firing rates,
rDMR and
rRN, are replaced by the
rate-normalized STRF energies, EDMR
and ERN, for the corresponding
conditions. Here the STRF energy is computed as:
|
(13)
|
Because the response of the neuron could be fractionally
distributed between the contralateral and ipsilateral ears, the energy
of the contra- and ipsi-STRFs was measured independently, and the
cumulative sum was taken as:
where Ec and
Ei are the contra- and ipsi-STRF
energies. The STRF energy measures phase-locked activity (units of
spikes per second) and is equivalent to the average phase-locked output
for a linear integrating neuron (for proof, see Appendix B).
Phase-locking index
The phase-locking index (PLI) quantifies the ability of a neuron
to phase lock to the spectrotemporal envelope. This metric is obtained
by dividing the peak-to-peak STRF amplitude (in spikes per second) by
the mean spike rate, r:
|
(14)
|
and normalizing this quantity by a theoretically derived factor,
 , that corresponds to the theoretical maximum peak-to-peak rate-normalized STRF amplitude (confining this index to the range of
0-1). For the DMR, = 8, and for the RN,
= 12 (for proof, see Appendix C).
Frequency domain analysis: ripple transfer function and conditioned
response histogram
As an alternative to the STRF, we further evaluated neuronal
response preferences to DMR and RN in the frequency domain. These approaches are useful, because they can be used to quantify neural responses as a function of ripple frequency and temporal modulation rate parameters.
The ripple transfer function (RTF) is one such descriptor. It is
obtained directly from the STRF by performing a two-dimensional Fourier
transform on the statistically significant STRF
(p < 0.002), discarding the phase, and keeping
the magnitude (see Fig. 5A,B). From the RTF, the best ripple
density and best modulation rate parameters were determined for all
phase-locking neurons. These are chosen by the location in the
magnitude response with the peak amplitude. In instances in which two
responses are observed (for negative and positive modulation rates),
the secondary response was selected only if its response magnitude
exceeded 50% of the maximum response magnitude. Positive (negative)
modulation rates designate downward (upward)-going stimulus features;
however, because the STRF is a time-reversed version of best stimulus
of the neuron, this convention is flipped for the neuron and its RTF
(positive, upward sweep; negative, downward sweep).
Although this approach was successfully applied for many neurons, other
neurons did not show statistically significant STRFs; therefore, it was
impossible to estimate their RTFs directly. We therefore approximate
the probability distribution function of observing a given set of
parameters given a spike at time tn, P(Fm,
|tn), by performing a
spike-triggered average with respect to the time-varying DMR
parameters, (t) and
Fm(t):
![P<SUB><UP>kl</UP></SUB>=<LIM><OP>∑</OP><LL>n=1</LL><UL>N</UL></LIM>I[k&Dgr;F<SUB><UP>m</UP></SUB>≤F<SUB><UP>m</UP></SUB>(t<SUB><UP>n</UP></SUB>)≤(k+1)&Dgr;F<SUB><UP>m</UP></SUB>] · I[l&Dgr;&OHgr;≤&OHgr;(t<SUB><UP>n</UP></SUB>)≤(l+1)&Dgr;&OHgr;],](/content/vol22/issue10/fulltext/4114/img024.gif)
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(15)
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where Pkl is the discrete
version of P(Fm,
|tn), and I[·] is the
identity function. The identity function takes a value of unity
whenever the condition inside its argument is satisfied. Otherwise, it
assumes a value of 0. Thus for any given bin of Pkl, this conditioned response
histogram (CRH) is incremented by +1 if and only if the instantaneous
parameters,
Fm(tn)
and (tn), fall within the required
intervals, kFm  Fm(tn) (k + 1)Fm and
l (tn) (l + 1), at the time of the neuronal spike,
tn (see Fig. 5C,D). Bin
width resolutions of Fm = 15-35 Hz
and = 0.2-0.4 cycles per octave were used. The exact
position used to estimate the parameters relative to the neuronal spike time, tn, did not alter the resulting
histogram (tested for a time lag of 0-50 msec), because the
parameters vary at a slow rate (1.5 and 3 Hz) compared with the
integration time of ICC neurons (usually tens of milliseconds).
As for single units, it was also useful to characterize population
responses in the frequency domain, and we therefore extended these
methods to include population statistics. By averaging the RTFs of
individual neurons, we estimated the population ripple transfer
function (pRTF) for those neurons with significant STRFs. To avoid
biasing the pRTF because of systematic differences in firing strength,
the RTFs of individual neurons were equally weighted so that the
cumulative area of each was exactly 1.
For neurons that did not produce statistically significant STRFs, a
modified approach was applied. We normalized the CRH of each neuron so
that its cumulative sum was exactly 1. An average was then taken over
the entire population, thereby producing the "population" CRH
(pCRH). To facilitate comparisons, the pCRH was interpolated using the
interp2 function (spline option) in MATLAB to identical resolution as
for pRTF.
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RESULTS |
We studied 81 single neurons with the intent of understanding how
dynamic spectrotemporal signals are processed within the central
nucleus of the inferior colliculus. Specifically, we address whether
single neurons integrate spectrotemporal information according to a
linear integration model and whether dynamic stimulus aspects significantly affect neuronal encoding. Our complex stimuli constitute an integral part of the experimental protocol, and we fully
characterize several pertinent properties of the stimulus ensembles. By
design, both test sounds have identical average statistics and,
therefore, equally sample the relevant spectrotemporal stimulus
dimensions for this study. As a first-order test of evaluating
spectrotemporal response nonlinearities, we compute and compare the
spectrotemporal receptive field for each sound type. We also
characterize higher-order response attributes that are not directly
accessible with the STRF descriptor.
Stimulus statistics: average versus dynamic spectrotemporal
characteristics of the dynamic moving ripple and ripple noise
To test the possibility that individual auditory neurons in the
ICC are selective for structural features prevalent in natural sounds
(Fig. 1A,B), complex
broadband stimuli (Fig. 1C,D) were designed that allow us to
systematically identify nonlinear processing capabilities of auditory
neurons. These stimuli fulfill a number of theoretical and ecological
constraints: first, both sounds were designed to stringently meet a
number of necessary requirements for use with the STRF. Second, both
sounds incorporate a number of pertinent acoustic stimulus attributes
that are prevalent in various natural signals [e.g., spectral energy
peaks, frequency modulation (FM) sweeps, and temporal modulations] and
that determine important perceptual qualities (Plomp, 1970, 1983; Van
Veen and Houtgast, 1983).
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Figure 1.
Synthetic sound sequence used for reverse
correlation analysis (C, D) and some corresponding
natural sound counterparts (A, kitten vocalizations;
B, babbling brook). The DMR (C) is
designed to mimic spectral profiles created by formants (spectral
energy peaks) and temporal modulations in speech production and animal
vocalizations. The ripple density parameter,
(t), corresponds to the number of energy peaks
(cycles per octave) along the spectral axis at time t.
The temporal modulation rate,
Fm(t), describes the
repetition rate of the envelope in hertz. The second stimulus, the RN
(D), has noise-like properties that uniformly
cover the ripple dimensions. The DMR and RN are shown for a maximum
temporal modulation rate of 70 Hz, although a value of 350 Hz was used
for the experiments.
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The DMR stimulus (Fig. 1C) is an extension of the rippled
spectrum noise used to characterize spectral and temporal response properties in the ferret and cat auditory cortex (Schreiner and Calhoun, 1994; Kowalski et al., 1996; Klein et al., 2000). This sound
is constructed so that its spectrotemporal envelope is dynamic and
coherently modulated ("structured") in time and frequency. As for
speech and animal vocalizations (Fig. 1A), the DMR
has strong short-time spectrotemporal correlations. These are
determined by two independent parameters that vary randomly in time:
the temporal modulation rate,
Fm(t), and ripple density,
(t) (see Materials and Methods; Figs. 1C, and
2). The temporal modulation parameter
determines the number of onsets and offsets per unit time (units of
hertz) (Fig. 1C, top right). At any given time, the DMR sound produces a sinusoidal energy excitation pattern along the
sensory epithelium, where the number of peaks per octave frequency is
determined by the ripple density at that instant (Fig. 1C,
top right). To efficiently excite neurons in the range characteristic for vocalizations, these parameters continuously vary at
a nominal rate of 3 Hz (ripple density) (Fig. 2A) and 1.5 Hz (temporal modulation rate) (Fig. 2B) (in
speech, for instance, similar features change at a rate of ~2-8 Hz;
Greenberg, 1998).
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Figure 2.
Stimulus dynamics and spectrotemporal correlation
statistics of the DMR and RN. The DMR parameter trajectories
(t) (A; ripple density, 0-4
cycles per octave) and
Fm(t)
(B; modulation rate, 350-350 Hz) are shown for a
short 15 sec segment. The spectrotemporal parameters efficiently cover
the ripple space (C; shown for the 15 sec segments of
A, B). The instantaneous correlation function of the DMR
(D) and RN (E) are shown
for three distinct time instants,
t1-t3
[D; left to right,
(t1) = 1 cycle per octave;
Fm(t1) = 0 Hz; (t2) = 2 cycles per
octave;
Fm(t2) = 150 Hz; (t3) = 0.15 cycles
per octave;
Fm(t3) = 60 Hz]. The RN instantaneous correlation function consists of a
narrow central peak and a noisy surround (E). The
global autocorrelation is identical for both sounds, consisting of an
impulse-like central peak of width 3 msec and one-fourth octave
(D, E, far right).
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By averaging 16 independently chosen DMR envelopes, we designed a
second stimulus, the RN. This sound is locally weakly correlated ("unstructured"), resembling background and environmental noises such as wind and rain (Fig. 1B). Visually, its
spectrotemporal envelope (Fig. 1D) has a noisy
profile both along time and along the spectral axis and lacks coherent
modulations as present in the DMR and many vocalization sounds (Voss
and Clarke, 1975; Attias and Schreiner, 1998; Nelken et al., 1999;
Theunissen et al., 2000).
To characterize and compare the instantaneous versus the average
behavior of these stimuli and their suitability for the reverse correlation method, the spectrotemporal autocorrelation function was
evaluated for each stimulus. Dynamic properties were evaluated over
short intervals of 10, 20, and 40 msec, which are comparable with
integration times for ICC neurons. Global correlation statistics were
evaluated for the ensemble as a whole (consisting of a 20 min
continuous sound segment; see Materials and Methods). Both the local
(shown for 10 msec analysis interval) and global spectrotemporal autocorrelations are depicted in Figure 2D,E.
The local autocorrelation depicts the spectrotemporal modulations that
are present at a given time instant over a 10 msec segment. For the DMR
stimulus, these take the form of tapered oscillations at a
characteristic ripple density, modulation rate, and frequency sweep
direction (Fig. 2D). Comparing the DMR and RN, it is
clear that the local stimulus statistics are markedly different.
Although the DMR has strong local correlations over the defined 10 msec
intervals, the RN lacks any definitive spectral and temporal
oscillations (Fig. 2E). Accordingly, its local
autocorrelation is qualitatively similar at all time instants,
consisting of a narrow central peak with a noisy surround. Therefore,
the RN appears to be stationary or locally time-invariant. By
comparison, the DMR has local envelope statistics that are dynamic;
that is, they continuously vary with time.
By averaging the instantaneous autocorrelation function over all 10 msec time instants, it is possible to characterize the average
statistics for the DMR and RN stimulus ensembles, which are identical
(Fig. 2D,E, far right). In both cases, the
average spectrotemporal autocorrelation assumes a narrow impulse-like character, which is the essential requirement for deriving receptive fields with the reverse correlation method (Eggermont, 1993; Klein et
al., 2000).
Linear spectrotemporal receptive fields for DMR and RN
Neuronal data were evaluated by computing the STRF for neurons in
the ICC and comparing neuronal responses to the spectrotemporally structured (DMR) and unstructured (RN) sounds. The STRF is a
mathematical construct that describes the integrating area of the
neuron along time and along the sensory epithelium (i.e., the frequency
axis) and that depicts the spectrotemporal arrangement of neuronal
excitation (red domains) and inhibition (blue domains). Figure
3 illustrates the spike-triggered average
procedure we use to derive STRFs in response to DMR and RN. The STRF
procedure requires that the probing stimulus have an unbiased
modulation spectrum (both in time and along the sensory epithelium) or,
equivalently, an impulsive spectrotemporal autocorrelation function
that fully covers the physiologically relevant limits. Both the RN and
DMR were designed with this constraint in mind; by limiting the
temporal modulation rate to 350 Hz and the ripple density to 4 cycles
per octave, we should be able to characterize 90-95% of the neurons
in the ICC (Langner and Schreiner, 1988; Krishna and Semple, 2000)
without biasing their STRFs.
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Figure 3.
Spike-triggered average and the STRF. At each
instant of an action potential, the pre-event sound segment (up to 100 msec before spiking) is extracted and averaged for the entire stimulus
ensemble. Red regions indicate stimulus patterns that
were likely to be present whenever a neural response occurred at delay
of 0. Blue indicates stimulus patterns that tended to be
off at a moment before spike initiation. Functionally, these are
interpreted as excitation (red) and inhibition
(blue).
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This essential property, which makes the RN and DMR stimuli suitable
for reverse correlation, also permits the identification of
spectrotemporal response nonlinearities. Given that both stimuli have
identical low-order statistics (matched in intensity, contrast, and
average envelope modulations), it is expected that a linear integrating
neuron would have an average neural response that is similar for the RN
and DMR conditions. That is, because both the RN and DMR stringently
satisfy the necessary requirements for reverse correlation, we expect
that STRFDMR = STRFRN if
the neuron behaves as a linear integrator (see Materials and Methods and Appendix B for proof). By comparing DMR and RN responses, we find
that 60% (n = 49) of the neurons in our ICC sample met this requirement (Fig. 4). For reference,
pure tone FTCs are shown alongside the RN and DMR STRFs when available
(Fig. 4A,D). A red bar designates the mean
sound pressure level (per one-third octave) for DMR and RN.
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Figure 4.
Spectrotemporal receptive fields of neurons that
responded to DMR and RN. Neurons were tested with pure tones (A,
D, left column), DMR (B, E, G, I,
middle column), and the RN (C, F, H, J,
right column) stimuli (individual neurons are shown by
row). Frequency-tuning curves depict the frequency
versus intensity response area of a neuron (A, D). The
red horizontal line designates the mean stimulus level
(per one-third octave) used for RN and DMR. STRFs have similar shapes
(similarity index: B, C, 0.94; E, F,
0.76; G, H, 0.77; I, J, 0.7) and strength
(magnitude disparity index: B, C, 13%; E,
F, 178%; G, H, 74%; I, J, 4%;
rate disparity index: B, C, 6%; E, F,
35%; G, H, 24%; I, J, 53%). To
facilitate comparisons, STRFs are shown on identical color scales for
RN and DMR. STRFs for each neuron are drawn on individually chosen
spectral and temporal scales. Significant patterns of the STRF are
denoted by red contours (p < 0.002 contour).
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Neurons in our sample showed a variety of preference to stimulus
patterns in the DMR and RN, including suppressive side bands, obliquely
oriented excitatory or inhibitory regions, and distinct temporal
response profiles (e.g., on-off, off-on, and off-on-off). Typically, excitatory and inhibitory STRF features were consistent between DMR and RN, although in some cases, inhibitory features were
less pronounced for the RN (Fig. 4E,F). DMR
and RN firing rates were generally high (mean spike rate, 11.2 spikes/sec for DMR and 11.8 spikes/sec for RN) and significantly
correlated [correlation coefficient, 0.85 ± 0.08 (mean ± SE)] for this subset of neurons. Likewise, all neurons had
comparable STRF energies. The neuron of Figure 4B,C,
for instance, had a spike rate of 34.0 spikes/sec for the DMR and 36.2 spikes/sec for the RN (difference, 6%) and comparable STRF energies
(EDMR, 2.6 spikes/sec; ERN,
3.0 spikes/sec; difference, 13%). The presence of well defined,
statistically significant STRFs (p < 0.002) for
both DMR and RN indicates that neurons efficiently phase locked to the
stimulus spectrotemporal envelope. To distinguish these functional
properties from those of other neurons in our sample, we refer to these
as type I responses.
Frequency domain RF analysis
Complementary to the STRF, we also evaluated neuronal data in the
frequency domain to extract physiologically meaningful parameters from
the STRF and to describe neuronal preferences in terms of low-pass and
bandpass filtering (Depireux et al., 2001; Klein et al., 2000).
First, we converted the STRF to an RTF (Fig.
5A,B). The RTF maps a the
preferences of a neuron as a function of the temporal (modulation rate)
and spectral (ripple density) stimulus parameters (see Materials and
Methods). Whether a neuron integrates spectral or temporal information
in a low-pass or bandpass manner depends strongly on the
spectrotemporal relationship between neural excitation and inhibition
in its STRF. For instance, the neuron of Figure 4B,C,
has an on-off temporal response pattern; therefore, its RTF resembles
a bandpass filter along the temporal modulation axis (Fig.
6A) that is centered at
a best temporal modulation rate (bTM) of 45 Hz. Likewise, along the
spectral axis, this neuron has a weak but significant inhibitory region
alongside an excitatory region. Therefore its response as a function of
ripple density also has a bandpass response profile with the dominant
response peak centered at a best ripple density (bRD) of 0.6 cycles per octave. Neurons that lack interleaved patterns of excitatory (on) and
inhibitory (off) subfields in their STRFs generally have low-pass response characteristics (Fig. 4I,J)
along the spectral and temporal dimensions. The STRF of this example is
marked by an off-on-off temporal response pattern, but its spectral
STRF patterns lack interleaved excitatory and inhibitory subfields.
Accordingly, its RTF (Fig. 6B) shows a bandpass
response pattern in time (bTM, 200 Hz) and a low-pass response pattern
along the spectral axis (bRD, 0 cycles per octave).
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Figure 5.
Frequency domain response analysis. The auditory
STRF (A; shown for RN) is used to compute the RTF
(B; shown for RN) by applying a two-dimensional Fourier
transform. The RTF depicts time-locked energy in the neural response as
a function of temporal modulation rate,
Fm, and ripple density, .
Red indicates parameter combinations that evoked a
strong time-locked response, and blue indicates a weak
response. The CRH (D) characterizes nonlinear
neuronal responses that do not show up in the STRF. For each neural
event, the spectral and temporal DMR parameters,
(tk) and
Fm(tk),
are determined at the time instance of the neural spike,
tk. The values of and
Fm are then used to increment the
corresponding bin in the histogram by +1
(D).
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Figure 6.
Neuronal preferences determined with the RTF
(left column) and CRH (right column)
shown for the neurons of Figures 4B,I and
7J,G (A-D, respectively). The RTF and
CRH depict the spectrotemporal frequency combinations (modulation
frequency and ripple density) that preferentially activate a neuron.
These can show either a low-pass or bandpass tuning profile along the
temporal modulation or ripple density axis. Generally, neuronal tuning
is similar for the RTF and CRH.
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In a second related approach, a CRH was used to evaluate neuronal
selectivity by tabulating the number of action potentials as a function
of ripple parameters (see Materials and Methods). Unlike the STRF and
RTF, this method accumulates the stimulus parameters, as opposed to the
averaging stimulus waveforms, and is therefore insensitive to spike
timing jitter. Figure 5C,D illustrates this approach.
Generally, we find that RTF and CRH are in close agreement (Fig. 6).
However, the CRH also reflects nonspecific activity, that is, action
potentials that fall outside the dominant RTF boundaries and presumably
do not contribute to the construction of the STRF (Fig.
6A,B).
Nonlinear spectrotemporal receptive fields for DMR and RN
One question addressed in this study is whether ICC neurons
require specific acoustic features to be efficiently activated and
whether these features can be identified using the STRF method. One
reason why it may be difficult to identify the preferred acoustic features of a neuron using a direct approach is because conventional reverse correlation stimuli (such as the RN or spectrotemporal tone
pips) seldom contain isolated sound patterns during a typical recording
period. As an example, the DMR stimulus has pronounced energy peaks and
FM sweeps that appear in isolation in its spectrotemporal envelope
(Fig. 1C). These same features are much more subtle in the
RN (Fig. 1D), because they are superimposed with
other components. How do such stimulus characteristics affect the
ability of a neuron to respond, and which of these stimuli is better
suited for identifying neuronal preferences in central auditory
stations? Presumably, if a neuron exhibits substantial nonlinearities,
significant differences could be expected between DMR and RN.
Not all studied neurons responded equally well to the DMR and RN. A
small but significant (14%; n = 11) subset of neurons responded selectively to the DMR stimulus (Fig.
7; type II neurons). In
general, type II neurons had low firing rates to the DMR and little or
no response to the RN. Average firing rates for either stimuli were
significantly lower than for type I responders (mean DMR, 0.61 spikes/sec; t test, p < 0.003; mean RN,
0.13 spikes/sec; t test, p < 0.0025).
Surprisingly, despite the low spike rates, STRFs derived with the DMR
were highly significant (p 0.002) and
exceptionally clean.
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Figure 7.
Spectrotemporal receptive fields of
neurons that responded specifically to the DMR sound (B, D, G,
J, middle column) but responded weakly or had no
response to the RN (C, E, H, K, right
column). Frequency-tuning curves derived with pure tones are
shown for reference (A, F, I, left
column). Red lines designate the mean stimulus
level (per one-third octave) used for DMR and RN. Significant STRF
patterns are denoted by red contours. All neurons are
shown at distinct spectral and temporal scales.
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Figure 7 depicts typical responses for these neurons. Some neurons
(Fig. 7B-E) responded to both the DMR (0.24 and 1.4 spikes/sec) and the RN (0.14 and 0.2 spikes/sec) sounds, although their
DMR firing rate was significantly stronger. DMR STRFs were highly significant (p < 0.002), with well defined
excitatory and inhibitory subfields. However, the RN STRFs of these
type II neurons were weak, with no distinguishable boundaries and
excitatory and inhibitory subregions. Furthermore, the DMR STRF energy
was 725% (Fig. 7B,C; EDMR, 0.100 spikes/sec; ERN, 0.012 spikes/sec) and 1280%
(Fig. 7D,E; EDMR, 0.276 spikes/sec;
ERN, 0.020) stronger, respectively, than for RN.
Although these neurons did respond weakly to RN, other neurons
responded exclusively to the DMR (Fig. 7G,H,J,K). Again, these neurons had extremely low spike rates (0.45 and 0.11 spikes/sec, respectively) to the DMR and no response to the RN (0 spikes). These STRFs were constructed using 276 (Fig. 7G)
and 139 (Fig. 7J) spikes for the DMR over a 10 and 20 min recording period, respectively. Nevertheless, their STRFs are as
noise-free as those of type I responders that typically had thousands
to tens of thousands of action potentials.
Interestingly, response characteristics for type II neurons are
consistent with the idea that they are highly selective for some of the
DMR stimulus features. The fact that we can compute highly significant
DMR STRFs from very few spikes further suggests that the acoustic
features leading to spike initiation must be precisely aligned in time
and frequency; otherwise, STRFs would not accurately build up. To
determine whether this is so, we recomputed all DMR STRFs using a
subset of 100 randomly chosen action potentials for each neuron and
determined the mean and maximum SNRs of those pixel values that
exceeded a significance criterion of p < 0.002 (see
Materials and Methods). The SNR of these conditioned DMR STRFs was
approximately twice as strong for type II neurons (average maximum SNR,
8.7 for type II vs 4.0 for type I; paired t test, p < 3.5 × 105;
average mean SNR, 4.7 for type II vs 2.8 for type I; paired t test p < 0.003). This suggests that the
spectrotemporal waveforms added to compute the STRF are more consistent
from spike to spike for type II neurons compared with type I neurons.
Consequently, type II neurons are highly sensitive for particular
stimulus features in the DMR stimulus, resulting in exceptionally clean
STRFs that can be obtained with very few action potentials. Response
specificity is also reflected in the CRH for these neurons. Compared
with type I responses, CRHs for type II responses show highly localized peaks (Fig. 6C,D, far right) and lack nonspecific
activity. Together, the low firing rates, high response specificity to
the DMR, and unresponsiveness to RN demonstrate that these neurons are
extremely nonlinear and highly selective for isolated spectrotemporal
sound patterns.
It may be argued that the seemingly low spike rates and sparse
responses of these neurons are simply attributed to stimulus levels
near or below the response threshold of the neuron. We tested for this
possibility in 6 of the 11 neurons by computing FTCs with pure tones
(Fig. 7A,F,I). The FTCs are shown alongside DMR and
RN STRFs, with a red line depicting the mean intensity per
one-third octave during DMR and RN stimulation (mean ± SE SPL per
one-third octave, 69 ± 9 dB). In all cases, the DMR and RN
intensity operating points were well above the response threshold of
the neuron, thus arguing against potential thresholding effects. Many
of these neurons had bandwidths exceeding one-third octave. Therefore,
the actual energy exceeded the one-third octave estimate by up to 12 dB
(Fig. 7G). For the five neurons for which frequency-tuning curves were not available, it is unlikely that these were near or less
than the threshold, because DMR and RN were presented for these at
moderately loud SPLs (58, 58, 78, 78, and 88 dB/one-third octave, respectively).
STRF shape, energy, and firing rate differences between DMR
and RN
Differences in response activity between DMR and RN for type I and
II responses were quantified with three metrics to independently assess
STRF shape, mean firing rate, and STRF energy differences. STRF shape
differences were quantified with the STRF SI (DeAngelis et al., 1999;
Reich et al., 2000). The SI assumes values between 1 and 1. Values of
1 indicate that the STRFs have identical shapes. Values near 1
indicate that the STRFs have identical shapes but are of opposite
polarity, and SI values near 0 occur only for STRFs that have nothing
in common. The RDI and the STRF MDI quantify the percent change in mean
firing rate and STRF energy between the RN and DMR. Values of 0 for the
RDI indicate that the mean firing rates are identical
(rDMR = rRN), whereas values >0 indicate that
rDMR > rRN. Values <0 indicate that
rDMR < rRN. The magnitude of the RDI is
numerically equivalent to the percent difference between
rDMR and
rRN. The MDI is identical in form to
the RDI, where the STRF energies, EDMR
and ERN, are now substituted for the
mean firing rate, rDMR and
rRN, respectively. This metric therefore characterizes phase-locked or driven activity as depicted by
the STRF.
In extreme scenarios, neurons either responded equally well to both
sounds or responded only to the DMR. This was evident from both the
similarity index statistics and the rate and magnitude disparity index.
Figure 8B shows the
similarity index distribution for all neurons that had significant
STRFs for the DMR or RN stimulus conditions or both. The distribution
of SI values is bimodally distributed. Most neurons (n = 49) had similar DMR and RN STRFs and therefore high SI values, >0.5
(mean SI, 0.75). These were classified as type I neurons. The remaining
neurons (n = 11) had SI values of <0.5. Of these, two
neurons had values of SI that were nearly 0.5 (0.48 and 0.49) (Fig.
7D,E), and six neurons had SI values that were identically 0 (Fig. 7G,H,J,K). Neurons in the latter subset
responded to the DMR sound and produced statistically significant STRFs
but did not respond to the RN sound. Therefore, although most neurons
had similar integration areas for RN and DMR, significant differences
in STRF shape were usually attributed to improper activation by RN.
Consequently such neurons were classified as type II responses.
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Figure 8.
Response statistics comparing the DMR versus the
RN. The MDI and RDI quantify differences in mean firing rate and driven
activity for the DMR and RN (A). Type II neurons
have RDI and MDI values that exceed the 500% contour. STRF shape
differences are quantified with the SI, which usually takes values from
0 (not similar) to 1 (very similar). The population similarity index
distribution (B) is bimodally distributed, with
the majority of neurons falling at ~0.7.
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Although the SI index statistics are consistent with the observed
response types of Figures 4 and 7, they do not tell us anything about
the driven and average activity to these stimuli. The rate and STRF
magnitude disparity index corroborate the results of Figures 4 and 7.
Although most neurons (n = 49; type I) had
RDI and MDI centered about 0 (|RDI| < 500% and |MDI| < 500%; mean MDI, 49.1%; mean, 2.7%), a large subset of neurons
(n = 11; type II) had values for either of these
metrics that exceeded +500% (mean MDI, 896%; mean RDI, 712%; cluster
verified post hoc, link tree cluster analysis) (Fig.
8A). Thus, the average activity or phase-locked
activity of these neurons tended to be significantly higher for the DMR
stimulus, consistent with type II response characteristics and the
examples of Figure 7. Five of these neurons had MDI values between 500 and 1000%. For three neurons, the RDI values were <500%, and
observable response differences manifested themselves only as a
significant change in driven activity (MDI > 500%) (Fig.
7B,C). An additional six neurons had very large values of
RDI and MDI, because they responded to the DMR stimulus but produced
zero spikes for the RN sound (Fig. 7G,H,J,K). These are shown collectively as a single point centered about MDI of +1000%
and RDI of +1000%.
STRF construction and the effects of phase locking
A basic requirement for computing the STRF is that the action
potential linearly time lock or phase lock to the stimulus
spectrotemporal envelope. Sinusoidal amplitude modulation studies have
demonstrated that many ICC neurons phase lock to the stimulus
modulation waveform (Rees and Møller, 1983, 1987; Møller and Rees,
1986; Langner and Schreiner, 1988; Krishna and Semple, 2000).
Accordingly, a large percentage of neurons in this study phase locked
to the spectrotemporal envelope and consistently produced statistically
reliable STRFs (n = 61 of 81).
The remaining neurons (n = 20 of 81), failed to produce
statistically reliable STRFs (p < 0.002) with a
distinct spectrotemporal patterning (Fig.
9), despite a significant overall firing
rate (mean firing rate, 7.5 spikes/sec). We labeled these neurons type III. One possible explanation is that these neurons were spontaneously firing and did not respond in a time-dependent manner to the DMR and
RN. One of a number of possible alternatives is that these neurons
responded selectively to energy fluctuations of the DMR and RN but did
not linearly phase lock to their spectrotemporal envelope. Therefore,
waveform averaging to estimate neuronal receptive fields would be of
little use.
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Figure 9.
Neurons for which the STRF procedure
fails. STRFs derived with DMR (B, E, G, middle
column) show no significant spectrotemporal patterns
(p < 0.002) and, therefore, provide little
information about stimulus features being encoded. Pure tone tuning
curves are shown for reference (A, D, left
column). Spectrotemporal feature selectivity is established
with the conditioned response histogram (C, F, H,
right column), which always shows a tuned response not
observed directly from the STRF or the RTF.
|
|
To test this possibility, we computed the CRH for these neurons. This
procedure allows us to test whether type III neurons respond
selectively to complex sound attributes even if they do not posses the
necessary timing precision in their stimulus-response alignment for
producing STRFs. The CRH of all of these neurons revealed strong
responses to particular stimulus parameter combinations (Fig.
9C,F,H) despite the lack of linear time locking to
the spectrotemporal envelope (resulting in no STRF in Fig.
9B,E or a very weak STRF in Fig. 9G). Thus, the
responses of these neurons do not linearly follow the fast
spectrotemporal modulations of the stimulus envelope (up to 350 Hz) but
were able to track very slow changes of the stimulus parameters (1.5 Hz
for the temporal modulation rate and 3 Hz for the ripple density) with
changes in firing rate. On the basis of the STRF and mean firing rate
alone, one would conclude that these neurons are only spontaneously
firing without functional consequences for encoding stimulus
information. However, the cumulative analysis of the stimulus-response
relationship reveals that these neurons do respond selectively to
pertinent stimulus parameters (Fig. 9C,F,H).
In the few instances in which significant STRFs
(p < 0.002) were observed (n = 6 of 20) for type III neurons, these were diffuse and weak (Fig.
9G), despite the fact that the CRH was strong and tightly
tuned (Fig. 9H). For comparison purposes, the color
scale on all STRFs including those of Figures 4 and 7 are normalized so
that the minimum and maximum values correspond to half of the mean
firing rate (in the case in which the STRF amplitude exceeded these
limits, the maximum absolute value of the STRF was used). Most neurons
had STRF magnitudes that fell below this range of values, although
these limits were often exceeded for neurons with type II responses (as
is the case for all the neurons of Fig. 7). In the case in which the
STRFs are absent, this observation indicates that the sound waveforms
that were used to construct the STRF were not phase-aligned and,
therefore, do not add constructively. In the case of type I responses,
the sound waveforms are presumably moderately aligned, whereas for type
II, they are tightly aligned (allowing the peak-to-peak rate of the
STRF to exceed the mean firing rate of the neuron).
Examples depicting the different phase-locking scenarios for the three
neural types are depicted in Figure
10B-D for a short 5 sec segment of the DMR stimulus. The type III neuron (Fig.
10D; same neuron as in Fig. 9A-C) had an
elevated firing rate but showed no obvious correspondence between the
occurrence of action potentials and the DMR stimulus spectrotemporal
pattern (Fig. 10A, far right). The type I
neuron of Figure 10B (same neuron as in Fig.
4A-C) had a high spike rate and a phasic response
raster. Similarly, the type II neuron of Figure 10C (same
neuron as in Fig. 7F,G) showed precisely aligned phasic
response components; however, this neuron had a low spike rate to the
DMR and no spontaneous background activity. By comparing its STRF (Fig.
7G), its response raster (Fig. 10C, far
right), and the DMR stimulus sound pattern (Fig. 10A, far right), it is evident that the
neuron responds specifically if the spectrotemporal sound patterns
closely match the STRF of the neuron. This level of temporal
specificity is less pronounced for the type I neuron (Fig.
10B) and absent for the type III neuron (Fig.
10D).
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Figure 10.
Phase-locking statistics for the DMR
stimulus. A, Left, A 5 sec segment of the
DMR stimulus was presented to each neuron. Rastergrams
(B-D, left) show individual response
traces for 40 consecutive presentations for type I
(B), II (C), and III
(D) neurons. The occurrence of each action
potential is shown as a single dot (1 msec resolution).
A-C, Far right, Cutout
(red) detailing the stimulus spectrotemporal envelope
(A, far right) and the response
rastergrams of each neuron (B-D, far
right). E, The PLI measures the ability of a
neuron to phase lock to the spectrotemporal envelope of a sound. A PLI
of 0 indicates minimal linear phase locking, and a PLI of 1 indicates
perfect phase locking. PLI distribution is skewed toward low values
(mean PLI, 0.24) but extends over a broad range of 0-0.75.
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|
We quantified the phase-locking abilities of all neurons by computing
the PLI (see Materials and Methods; Fig. 10E) for the DMR stimulus. This metric can assume values between 0 and 1 (observed range, 0-0.75), where 0 indicates no linear phase locking and 1 indicates maximal linear phase locking. Results for the population are
consistent with the examples of Figures 4, 7, and 9. Type III neurons,
which have no STRFs, had the lowest PLI values (mean PLI, 0.076 ± 0.02; bootstrap p < 0.01 confidence interval; Fig. 9B, 0.028, E, 0.09, G, 0.093), and
neurons with type II responses had the highest values (Fig.
7B, 0.46, D, 0.42, G, 0.64, J, 0.65). As postulated for type II responses, high PLI
values (mean, 0.50 ± 0.13; bootstrap p < 0.01 confidence interval) suggest that the sound waveforms used to construct
STRFs add constructively and are tightly aligned. In contrast, type I
responders had intermediate PLI values (Fig. 4B,
0.22, E, 0.20, G, 0.14, I, 0.13; mean,
0.24 ± 0.04; bootstrap p < 0.01 confidence
interval), indicating that sound waveforms are moderately aligned.
Spectrotemporal filtering statistics
As noted previously, neuronal preferences to features of the DMR
and RN depend strongly on the spectrotemporal arrangement and size of
excitatory and inhibitory receptive field regions. These, in turn,
determine the range of spectral and temporal preferences of each neuron
and whether their filtering characteristics are bandpass or
low-pass.
To evaluate the processing capabilities of all neurons and to
characterize any systematic differences among type I-III responses, we
measured the bRD and bTM parameters of each neuron (Fig.
11A). Because most
neurons (77 of 81, ~95%) responded symmetrically to upward-going
(positive temporal modulation) and downward-going (negative temporal
modulation) ripples, two values of the best parameters were extracted
(one for each quadrant of the RTF; i.e., one for the positive and one
for the negative modulation rate value). For type III responses, these
were estimated directly from their CRH. bTM and bRD show a distinct
covariation for time-locked responses (types I and II). There is a
strong negative correlation between the absolute magnitude of bTM and
bRD (type I, r = 0.6 ± 0.06 bootstrap SE;
p < 1 × 105; type
II, r = 0.5 ± 0.1 bootstrap SE;
p < 1 × 105).
Evidently, time-locking neurons that prefer fast temporal modulations also prefer stimuli with broad spectral features, and neurons that
prefer slow temporal modulations can respond efficiently to stimuli
with narrow or broad spectral features. This trend was significantly
different for type III responses, in which the absolute magnitude of
bTM and bRD showed no correlation (r = 0.1 ± 0.16 bootstrap SE; p > 0.78).
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Figure 11.
pRTFs and best ripple parameter
statistics. A, Scatter plot of the bRD and bTM for the
observed neural responses (triangles, type I;
circles, type II; squares, type III). The
pRTF of type I (B), II (C),
and III (D) neurons depicts the filtering
profiles of each neural response type. Black
contours designate the 95th percentile interval (boundaries
that account for 95% of the area under the pRT).
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We characterized the overall spectrotemporal filtering capability of
the ICC by averaging the DMR RTFs of individual neurons to estimate the
pRTF (see Materials and Methods). The composite pRTF depicts a clear
trend in the spectrotemporal filtering profile. Neurons with type I and
II responses had similar response profiles (pRTF correlation
coefficient, 0.765 ± 0.015; p < 0.01 bootstrap confidence interval) in which spectral resolution appears to be traded
for temporal resolution (Fig. 11B,C). At low
modulation rates, filtering profiles extended to intermediate ripple
densities (up to two cycles per octave); however, at high modulation
rates, neurons are sensitive only to low ripple frequencies. Overall, spectral filtering is low-pass, whereas temporal filtering
characteristics are bandpass. This was true for both type I and II
responses; however, the pRTF of type II responses is more compact, as
evident from the 95th percentile contours (Fig.
11B,C, solid line). By direct comparison,
the filtering profile of type III responses (Fig.
11D) is diffused and shows no systematic patterns as
for type I and II responses (pRTF correlation coefficients: I vs III, 0.44 ± 0.016; II vs III, 0.2695 ± 0.015; p < 0.01 bootstrap confidence interval). Accordingly, spectrotemporal
filtering characteristics differ significantly between neurons with
strong and weak phase locking.
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DISCUSSION |
Neurons in the central auditory system respond selectively to both
spectral and temporal stimulus attributes (Rees and Møller, 1983,
1987; Schreiner et al., 1983; Langner and Schreiner, 1988; Schreiner
and Langner, 1988; Nelken et al., 1997; Eggermont, 1999; Ramachandran
et al., 1999; Krishna and Semple, 2000). Although this is well
described for narrow-band stimuli, clicks, and modulated tones, only a
few studies have addressed how these acoustic dimensions are jointly
processed by the brain. This is of interest, because natural sounds are
composed of both spectral and temporal sound components, and because,
in general, the response to complex stimulus ensembles cannot be
extrapolated directly from the neuronal responses to simpler sounds.
Our data demonstrate that ~60% of neural responses to complex
auditory stimuli in the ICC are consistent with a linear integration
model (type I neurons). However, we also identified conditions in which
this model fails at fully describing neural responses. This result is
true for type II and III neurons. Type II neurons phase lock well and
respond selectively to spectrotemporal stimulus features. However,
these neurons are not efficiently activated with the RN stimulus. In
contrast, type III neurons do not phase lock tightly to the stimulus
envelope, but they respond selectively to both spectral and temporal
stimulus parameters.
Recent studies have demonstrated the usefulness of the STRF procedure
for studying neural processing of complex sounds in the auditory cortex
(de Charms et al., 1998; Klein et al., 2000; Miller et al., 2002) and
its avian homolog (Theunissen et al., 2000). They have shown that it is
indeed possible to approximate the stimulus-response function of some
central auditory neurons as linear functions of their inputs. As for
the related visual STRF, the auditory STRF can be used to identify the
spectrotemporal features of the stimulus that a neuron prefers (de
Charms et al., 1998). Because this method describes neural processing
in terms of time and the sensory epithelium receptor surface, it has
become a valuable and intuitive experimental tool. Despite its general utility, nonlinear aspects of neural integration are often difficult to
identify and cannot be fully accounted for with the STRF (Young, 1998;
Theunissen et al., 2000). Our results build on those findings, suggesting that the STRF is useful in various respects, but it does not
fully account for all response nonlinearities. Therefore, to
systematically identify nonlinear aspects of processing, complementary approaches and acoustic stimuli must be examined. For instance, approaches that extend the STRF method by performing a second-order reverse correlation (with respect to the spectrotemporal envelope) could be used. These methods, however, generally require a substantial amount of data and can easily fail, especially if the types of nonlinearities are not compatible with the approach (i.e., they must be
of even order with respect to the envelope of the sound). Furthermore,
results from any such methods may depend strongly on the stimulus
ensemble used (Theunissen et al., 2000).
As outlined in the introductory remarks, limitations encountered with
the STRF technique can be either stimulus-dependent or methodological
in nature. Stimulus-dependent limitations are characterized by the
inability of a stimulus to efficiently activate highly nonlinear
sensory neurons. For instance, high-level auditory neurons in the avian
forebrain in bats and other acoustically specialized animals exhibit
complex nonlinearities and respond efficiently to acoustic features
found in their vocalizations. Such high-level sensory neurons are
likely optimized to analyze acoustic features and combinations found in
natural signals (Suga and Jen, 1976; Suga et al., 1978; Margoliash,
1983; Doupe, 1997; Portfors and Wenstrup, 1999; Theunissen et al.,
2000). Therefore, when these animals are studied using synthetic
stimuli, such as conventional reverse correlation sequences, neural
responses are generally weak, and, consequently, a quantitative
evaluation of the stimulus response function is not possible
(Theunissen et al., 2000). However, by presenting natural stimuli that
contain pertinent stimulus correlations, some of these limitations can be overcome (Theunissen et al., 2000).
Our findings in the ICC further demonstrate the importance of the
probing stimulus characteristics and how these may interact with the
sensory system. The fact that significant response differences exist
between DMR and RN is evidence that, for some neurons, a direct STRF
procedure using conventional stimuli may be insufficient. Neurons with
type II responses, for instance, cannot be characterized with RN
stimuli, despite the fact that this stimulus contains the essential
characteristics required to estimate auditory STRFs. The DMR, which is
by all accounts a nontraditional reverse correlation sound, allowed us
to characterize receptive field of these neurons. These differences
suggest that high-order acoustic features in the DMR efficiently drove
such neurons, whereas RN did not. By simply comparing responses between
DMR and RN, we have therefore taken a significant step toward
identifying some of the acoustic features that are necessary to
efficiently activate such neurons. At the same time, this comparison
allows us to dissociate linear from nonlinear spectrotemporal interactions.
By controlling for multiple stimulus parameters (including SPL,
contrast, and global second-order correlations), we show that instantaneous correlations of the probing stimulus are essential for
activating some neurons. The DMR stimulus dynamically and efficiently
probes the entire acoustic ripple space by providing maximal driving
force over short periods (Fig. 2). Our finding that some neurons
require strong time-limited correlations to activate them is not
unexpected, because ICC neurons integrate stimulus information over a
restricted temporal extent of less than ~50 msec. Similar processing
principles are likely operative for natural signals (Theunissen et al.,
2000); however, the large number of degrees of freedom necessary to
describe natural stimuli makes their identification difficult.
Neurons with type II responses consistently produced highly significant
STRFs despite low spike rates for the DMR. In fact, when the level of
significance was compared for an equal number of action potentials,
STRFs of neurons with type II responses were more significant and had a
higher signal-to-noise ratio than for type I. Therefore,
spectrotemporal acoustic features in the DMR were added effectively
during the construction of these STRFs. This finding indicates that
type II neurons precisely phase lock to particular stimulus features of
the DMR, as reflected by the higher phase-locking index values (Fig.
10). These observations support the idea that type II neurons
selectively respond to particular stimulus features within the DMR,
whereas type I neurons integrate stimulus information in a quasilinear manner.
Although we cannot speak directly about the exact mechanisms underlying
these nonlinear response characteristics, the general nature of the
observed effect points to several possibilities. For instance, active
engagement of inhibitory and excitatory neuronal inputs combined with
intracellular thresholding in the ICC (Kuwada et al., 1997) could
account for the low spike rates and observed differences between DMR
and RN in type II neurons. If the inhibitory inputs are sufficiently
strong, broadband stimulation would significantly reduce firing rates,
because stimulus energy would almost always overlap inhibitory RF
domains. This is especially true for RN, because it has a short but
constant correlation width of ~3 msec and one-fourth octave. This
possibility is supported by the fact that the fraction of inhibitory
STRF energy was larger for type II responses than type I (mean ± SE, 40 ± 6 vs 36 ± 8%; paired t test,
p < 0.05). Even if subthreshold summation is strictly linear, a high intracellular reversal potential would drastically reduce overall spike rates. Under such conditions, the neuron would be
most likely to fire only when the stimulus modulations precisely
overlap the excitatory and inhibitory RF of the neuron. Such active
engagement of excitation and disengagement of inhibition would allow
the intracellular potential of the neuron to reach the spike initiation
threshold. The strong instantaneous spectrotemporal correlations of the
DMR stimulus could, under such circumstances, provide the necessary
driving force to selectively activate and deactivate excitatory and
inhibitory inputs. Preliminary modeling results (data not shown) are
consistent with our findings and suggest that such mechanisms could
serve as a general basis for selectivity enhancement, similar to
feature selectivity mechanisms observed in other species and modalities
(Casseday et al., 1994; Moore and Nelson, 1998; Bringuier et al.,
1999).
Methodological limitations of the STRF are evident for type III neurons
that, despite significant firing rates, showed no significant STRFs. We
overcame these limitations by devising an alternate functional
descriptor, the CRH. This consisted of performing a spike-triggered
histogram with respect to the time-varying DMR parameters, as opposed
to the stimulus spectrotemporal envelope. The fact that we do not
obtain STRFs despite selective activation to both spectral and temporal
attributes points to several mechanisms. On the one hand,
dominant even-order nonlinearity would render the STRF method useless,
because this technique only characterizes suitable projections from
odd-order nonlinearities. For example, a simple squaring operation
would cause a linear neuron to phase lock to both stimulus onsets and
offsets, the average of which is precisely zero. Therefore, the average
pre-event stimulus (i.e., its STRF) would be zero. Such nonlinearities
are well described for complex cells in the primary visual cortex,
which have strong even-order nonlinearities and consequently do not
produce linear spatiotemporal receptive fields (Emerson et al., 1987;
Szulborski and Palmer, 1990). A number of alternate mechanisms,
however, could also produce a similar result.
One such possibility is random spike-timing jitter, a mechanism
likely responsible for loss of temporal synchrony at fast temporal
modulation rates (Epping and Eggermont, 1986; Langner and
Schreiner, 1988; Schulze and Langner, 1997; Krishna and Semple, 2000).
If spike-timing jitter is comparable in its time scale with that of the
preferred stimulus feature of the neuron (by as little as half of the
STRF period), the spectrotemporal patterns that are added during the
STRF computation would be randomly out of phase and would, therefore,
not add constructively. This is especially true at high temporal
modulation rates, at which the time scales for neural integration of
fast stimulus features are at the limits of the internal precision of
the spike generation mechanisms (on the order of a few milliseconds).
Under such conditions, a small amount of jitter would abolish the STRF.
If, on the other hand, a neuron prefers slow temporal modulations, a
small amount of temporal jitter would distort or blur the STRF of the
neuron but would not abolish it in its entirety. This possibility is supported by the fact that bTMs were significantly higher for neurons
with type III responses than for those with type I and II responses
(mean bTM, 190 vs 75 Hz; paired t test, p < 2 × 107). Our modeling results
(data not shown) suggest that both of these mechanisms produce results
identical in character to those observed for type III responses.
Although we have chosen to break up our data into functionally defined
subgroups of neurons, our methods cannot distinguish between
anatomically defined neural populations (Oliver and Morest, 1984) and
functionally defined neural inputs into the ICC (Ramachandran et al.,
1999). Our findings, however, show that the ability of a neuron to
respond to DMR versus RN is ultimately reflected in other response
properties, such as its phase-locking ability, its SNR, and even its
preferred spectrotemporal parameters. Differences in the
spectrotemporal filtering abilities of each neural type were determined
from the best spectral and temporal parameters of each neuron or from
the population transfer functions. Type I and II neurons had similar
spectrotemporal preferences in which the preferred ripple density and
modulation rate showed a strong negative correlation. Furthermore, the
range of modulation rates and ripple densities were more restricted for
type II neurons, indicating that the STRFs of these neurons were
typically larger. Type III neurons, by comparison, showed no systematic
filtering pattern; however, the observed modulation rates were
significantly higher than for type I or II neurons. These differences
in filtering ability argue for distinct coding strategies within the
ICC according to differences in the spiking output (e.g., the degree of
phase locking).
Advances in the STRF mapping techniques using natural sounds and other
naturalistic stimuli (Klein et al., 2000; Theunissen et al., 2000) are
providing the means to study complex nonlinearities that are necessary
for the brain to efficiently processes sensory information from the
outside world. Our findings delineate rules for spectrotemporal sound
processing in the ICC that cannot be accounted for by linear
integration models and that can, in general, not be characterized alone
with narrowband stimuli, conventional reverse correlation stimuli, and
direct STRF methods. Because of the dynamic spectrotemporal nature of
natural sounds, such processing principles likely play an important
role for natural sound analysis.
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FOOTNOTES |
Received Sept. 18, 2001; revised Jan. 22, 2002; accepted Jan. 25, 2002.
This work was supported by National Institutes of Health Research
Grants DC02260 and NS34835 and a grant from the Ford Foundation (M.A.E.). We thank two anonymous reviewers for many insightful comments
and M. P. Stryker, J. A. Winer, and A. J. Doupe for
comments on previous versions of this manuscript. We also thank L. M. Miller and H. Read for numerous discussions and help during
experiments and M. Kvale for the use of his SpikeSort1.2 analysis tool.
Correspondence should be addressed to Monty A. Escabí, 260 Glenbrook Road, U-157, University of Connecticut, Storrs, CT 06269. E-mail: escabi{at}engr.uconn.edu.
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APPENDIX A |
Nonlinear response characteristics are tested against the expected
response of an idealized linear neuron. Because the RN and DMR both
have identical autocorrelation functions, a hypothetical linear neuron
would produce identical STRFs and RTFs for these sounds.
To prove this, we consider a multi-input, single-output linear filter
bank (Marmarelis and Naka, 1974) as a model representation for auditory
neuronal filtering. This representation is motivated by the fact that
the primary sensory epithelium performs a spectrotemporal decomposition
of incoming sounds, and consequently, all further processing along the
auditory system is constrained by this output pattern.
The spectrotemporal filter bank model consists of a set of L
octave spaced linear modulation filters,
[h1(),
h2(), . . . , hL()], where
hk() = STRF(,
Xk) is the impulse response of a
linear filter centered about the frequency band
Xk, and corresponds to the
temporal lag of the filter. The expected firing rate of the neuron,
r(t), is obtained by summing the firing rate
contribution for each of the tonotopically arranged frequency
channels:
|
(16)
|
where r0 is the mean firing rate
of the neuron (zero-order kernel), and the output of its kth
frequency band is given by the convolution integral:
|
(17)
|
where sk(t) = S(t, Xk) is the
modulation input to the kth filter channel, and
ek(t) is a noise term that
arises from measurement error and the internal noise of the neuron. For
the nonlinear case, ek(t)
contains the nonlinear response contributions that cannot be accounted
for by the linear description (Klein et al., 2000). For practical
reasons, we assume that
ek(t) is statistically independent of the input,
sk(t) and has 0 mean and SD
of ek.
To compute the STRF from the experiment data, we perform a
cross-correlation between the input and output. For the linear model
neuron, this procedure is expressed as:
![E[(r(t)−r<SUB>0</SUB>) · s<SUB><UP>l</UP></SUB>(t−&sfgr;)]=<LIM><OP>∑</OP><LL>k=1</LL><UL>L</UL></LIM>E[r<SUB><UP>k</UP></SUB>(t) · s<SUB><UP>l</UP></SUB>(t−&sfgr;)]](/content/vol22/issue10/fulltext/4114/img027.gif)
|
(18)
|
where:
is the time average operator, and
RSS(, ) is the stimulus average
spectrotemporal autocorrelation function. For a sufficiently large
recording period, T, the error cross-correlation
E[ek(t) · sl(t ]
approaches 0, because ek(t)
and sl(t) are statistically independent and both have 0 means. Because the above equation is
strictly a function of the stimulus long-term spectrotemporal autocorrelation function, RSS(,
), and is independent of the stimulus local statistics, an idealized
linear neuron ought to produce identical STRFs for both sounds as
hypothesized. This is expected, because the global spectrotemporal
autocorrelation is identical for both stimuli (Eq. 9, Fig. 2).
To show that Equation 18 degenerates into a spike-triggered average, we
consider the impulse-like correlation properties of the RN and DMR. If
the spectrotemporal autocorrelation of the stimulus has the unique
property that it has impulse-like characteristics, that is,
RSS(, )  ·  () · (), then the
spectrotemporal cross-correlation between the stimulus and the output
simplifies to:
![E[(r(t)−r<SUB>0</SUB>) · s<SUB><UP>l</UP></SUB>(t+&sfgr;)]=&sfgr;<SUP>2</SUP><SUB><UP>s</UP></SUB> · <LIM><OP>∑</OP><LL>k=1</LL><UL>L</UL></LIM>∫&dgr;(&tgr;−&sfgr;) · &dgr;(X<SUB><UP>k</UP></SUB>−X<SUB><UP>l</UP></SUB>) · h<SUB><UP>k</UP></SUB>(&tgr;)d&tgr;=&sfgr;<SUP>2</SUP><SUB><UP>s</UP></SUB> · h<SUB><UP>l</UP></SUB>(&sfgr;),](/content/vol22/issue10/fulltext/4114/img031.gif)
|
(19)
|
where is to the variance of the
spectrotemporal envelope. The spectrotemporal receptive field for the
model neurons is instantly derived as:
![<UP>STRF</UP>(&sfgr;, X<SUB><UP>l</UP></SUB>)=h<SUB><UP>l</UP></SUB>(&sfgr;)=<FR><NU>1</NU><DE>&sfgr;<SUP>2</SUP><SUB><UP>s</UP></SUB></DE></FR> · E[(r(t)−r<SUB>0</SUB>) · s<SUB><UP>l</UP></SUB>(t−&sfgr;)].](/content/vol22/issue10/fulltext/4114/img032.gif)
|
(20)
|
Therefore, for both RN and DMR, the STRF can be estimated by
performing a cross-correlation between the response of the neuron, r(t), and each of its L inputs,
Sk(t), for
k = 1, . . . , L. Although the
spectrotemporal correlation of the RN and DMR is not strictly an
impulse (temporal correlation width, ~3 msec; spectral correlation width, one-fourth octave), it is in general significantly tighter than
the spectrotemporal integration areas of ~95% of ICC neurons (Rees
and Møller, 1987; Langner and Schreiner, 1988; Schreiner and Langner,
1988; Krishna and Semple, 2000) and can therefore be approximated as such.
For a spiking neuron with an action potential sequence
r(t) =  i(t ti) of N neuronal event
times, ti, Equation 20 can be easily
expanded as a spike-triggered average:
|
(21)
|
In practice, T corresponds to the experimental
recording period (600-1200 sec for these experiments).
Therefore if the grand average spectrotemporal autocorrelation function
of the stimulus has impulse-like properties, it is possible to estimate
the STRF of the neuron via Equation 21. Other stimulus aspects, such as
high-order statistics, and stimulus dynamics have no bearing on this
result under the assumption of quasilinear integration. Both the RN and
DMR satisfy the global correlation requirement and therefore should
produce identical results for a linear integrating neuron.
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APPENDIX B |
Consider the linear model neuron of Equations 16 and 17, where the
filter for the kth input channel is related to the STRF of the neuron by hk() = STRF(,
Xk). We would like to derive a metric that quantifies the energy in the response of the neuron that is
captured by the STRF of the neuron. We do this by computing the
expected output SD or, equivalently, the firing rate variance of the
neuron that is predicted by its STRF. The predicted firing rate
variance is expressed as:
![&sfgr;<SUP>2</SUP><SUB><UP>r</UP></SUB>=E[(r(t)−r<SUB>0</SUB>)<SUP>2</SUP>]=<LIM><OP>∑</OP><LL>i=1</LL><UL>L</UL></LIM><LIM><OP>∑</OP><LL>k=1</LL><UL>L</UL></LIM>E[r<SUB><UP>j</UP></SUB>(t) · r<SUB><UP>k</UP></SUB>(t)],](/content/vol22/issue10/fulltext/4114/img034.gif)
|
(22)
|
where r(t) is the predicted firing rate of
the neuron (Eq. 16), r0 is the mean
firing rate of the neuron, and
rk(t) is the predicted
output for the kth filter channel. Substituting Equation 17
into the expectation of Equation 22 yields:
![E[r<SUB><UP>j</UP></SUB>(t) · r<SUB><UP>k</UP></SUB>(t)]=E[∫s<SUB><UP>j</UP></SUB>(t−&tgr;<SUB>1</SUB>) · h<SUB><UP>j</UP></SUB>(&tgr;<SUB>1</SUB>)d&tgr;<SUB>1</SUB> · ∫s<SUB><UP>k</UP></SUB>(t−&tgr;<SUB>2</SUB>) · h<SUB><UP>k</UP></SUB>(&tgr;<SUB>2</SUB>)d&tgr;<SUB>2</SUB>]](/content/vol22/issue10/fulltext/4114/img035.gif)
|
(23)
|
where
RSS(1 2, Xj Xk) = · sinc[2Max(Xj Xk)] · sinc[2FMax(1 2)] is the RN and DMR autocorrelation (Eq. 9). Given the arguments presented in Appendix A, the autocorrelation
function is approximated by a spectrotemporal impulse,
RSS(1 2, Xj Xk) = · (Xj Xk) · (1 2). Substituting into Equation 23
yields:
![E[r<SUB><UP>k</UP></SUB>(t)<SUP>2</SUP>]=<LIM><OP>∬</OP></LIM>&sfgr;<SUP>2</SUP><SUB><UP>S</UP></SUB> · &dgr;(&tgr;<SUB>1</SUB>−&tgr;<SUB>2</SUB>) · h<SUB><UP>k</UP></SUB>(&tgr;<SUB>1</SUB>) · h<SUB><UP>k</UP></SUB>(&tgr;<SUB>1</SUB>)d&tgr;<SUB>1</SUB>d&tgr;<SUB>2</SUB>=&sfgr;<SUP>2</SUP><SUB><UP>S</UP></SUB> · ∫h<SUB><UP>k</UP></SUB>(&tgr;)<SUP>2</SUP>d&tgr;,](/content/vol22/issue10/fulltext/4114/img038.gif)
|
(24)
|
for k = j and:
![E[r<SUB><UP>j</UP></SUB>(t) · r<SUB><UP>k</UP></SUB>(t)]=0,](/content/vol22/issue10/fulltext/4114/img039.gif)
|
(25)
|
for k  j. Combining with Equation 22, the firing rate variance that is captured by the STRF of the neuron
is expressed as:
|
(26)
|
The predicted firing rate energy, E = r, is therefore computed directly from the
STRFr by computing its RMS value via
Equation 26.
| |
APPENDIX C |
The theoretical maximum peak-to-peak amplitude of the
rate-normalized STRF is obtained by considering perfectly aligned sound waveforms that add constructively. This theoretical value is used as a
reference normalization factor for the phase-locking index. Consider
the amplitude normalized STRF:
|
(27)
|
where Equation 10 is substituted for STRF(,
Xk). Because STRF is described in
units of spikes per second, STRFn is unit-less. Substituting the measured firing rate, r = N/T, we have:
|
(28)
|
where  = S/S
is a ripple envelope with unit variance. The maximum peak-to-peak
amplitude of (t,
Xk) is 8 for the DMR, because the
peak-to-peak amplitude of S(t,
Xk) is M, and because S = M/8. For the RN,
S = M/12; therefore, the maximum
peak-to-peak amplitude is 12. The theoretical maximum peak-to-peak
amplitude of STRFn is obtained as:
|
(29)
|
under the assumption that the N spectrotemporal
waveforms used to construct the STRF are perfectly aligned. This
yields:
|
(30)
|
for the DMR and = 12 for the RN.
| |
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TOP
ABSTRACT
INTRODUCTION
![<UP>SNR</UP><SUB><UP>Mean</UP></SUB>=<RAD><RCD>E[<UP>STRF</UP><SUP>2</SUP><SUB>100</SUB>]/&sfgr;<SUP>2</SUP><SUB>100</SUB></RCD></RAD>](/content/vol22/issue10/fulltext/4114/img016.gif)
![=<LIM><OP>∑</OP><LL>k=1</LL><UL>L</UL></LIM>∫E[s<SUB><UP>k</UP></SUB>(t−&tgr;) · s<SUB><UP>l</UP></SUB>(t−&sfgr;)] · h<SUB><UP>k</UP></SUB>(&tgr;)d&tgr;+E[e<SUB><UP>k</UP></SUB>(t) · s<SUB><UP>l</UP></SUB>(t−&sfgr;)]](/content/vol22/issue10/fulltext/4114/img028.gif)
![E[ · ]=<LIM><OP><UP>lim</UP></OP><LL>T → ∞</LL></LIM><LIM><OP>∫</OP><LL><UP>−</UP>T/2</LL><UL>T/2</UL></LIM> · dt](/content/vol22/issue10/fulltext/4114/img030.gif)
![<LIM><OP>∬</OP></LIM>E[s<SUB><UP>j</UP></SUB>(t−&tgr;<SUB>1</SUB>) · s<SUB><UP>k</UP></SUB>(t−&tgr;<SUB>2</SUB>)] · h<SUB><UP>j</UP></SUB>(&tgr;<SUB>1</SUB>) · h<SUB><UP>k</UP></SUB>(&tgr;<SUB>2</SUB>)d&tgr;<SUB>1</SUB>d&tgr;<SUB>2</SUB>](/content/vol22/issue10/fulltext/4114/img036.gif)
