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HEARES 01944

Excitation effects on LSO unit sustained responses: Point process characterization

M. Zacksenhouse ‘, D.H. Johnson a and C. Tsuchitani b ’ Carnputer and Information Technology institute, Department of Electrical and Computer Engineering, Rice University, Houston, Texas, USA and

’ Sensory Science Center, Graduate School of Biomedical Sciences, The lJniL,ersity of Texas Health Science Center, Houston. Texas, USA

(Received 1 September 1992; Revision received 26 February 1993; Accepted 7 March 1993)

LSO units recover from a spike discharge in a characteristic way, modeled by an intrinsic recovery function that is stimulus invariant up to a scaling factor and a shifting constant. Data analysis shows that the effect of increasing excitatory stimulus level can be described by amplifying the intrinsic recovery function and by shifting it toward shorter intervals. The shifting process secondarily interacts with the absolute deadtime to produce the response characteristics of the three LSO unit types. Decreased excitation is clearly distinguished from inhibition, which affects the scaling, but not the time origin, of the recovery. We conclude that both excitatory and inhibitory stimulus levels are encoded in the timing of LSO unit discharges.

Point process models; Lateral superior olive; Excitation

Introduction

The lateral superior olive (LSO) is the first nucleus in the ascending auditory pathway involved in the binaural processing of mid-to-high frequency ( > 1 kHz) sounds. LSO units having characteristic frequencies (CFs) greater than 1 kHz are excited by stimulation of the ipsilateral ear and inhibited by simultaneous stimu- lation of the contralateral ear. As the first stage in high-frequency binaural processing, the LSO is be- lieved to play a crucial role in extracting high-frequency information necessary for sound localization and signal discrim~ation in noise. Binaural cues relevant at high frequencies include the interaural-level-difference (ILD) and the interaural time difference between high-frequency transients and between the envelopes of complex high-frequency stimuli. We developed a point process model (Johnson et al., 1986; Zacksen- house et al., 1992) to characterize the encoding of ILD in the sustained discharges of LSO units. Extending this model to predict the time course of LSO unit transient responses, however, necessitates explicit char- acterization of how monaural (excitatory) stimulus level affects the underlying point process. In this report, the effects of excitatory tone burst stimulus level on the sustained discharges of cat LSO units are studied and

Correspondence to: M. Zackenhouse, Computer and Information Technology Institute, Department of Electrical and Computer Engi- neering Rice University Houston, TX 772.51-1892, USA.

modeled as parametric changes in the previously devel- oped point process model.

The potential role of LSO units in extracting tempo- ral cues is suggested by their highly structured initial chopping discharge patterns in response to tone burst stimuli. The initial discharges in the response are time locked to stimulus onset and produce peaks in the poststimulus-onset time histograms (PST histograms illustrate the times of occurrence of spike discharges relative to stimulus onset time) that become wider and eventually obscured with time (Boudreau and Tsuchi- tani, 1970; Tsuchitani, 1982, Tsuchitani, 1988a). The width and spacing of these peaks are used to differenti- ate between two LSO unit types (Tsuchitani, 1982): Slow choppers produce PST histograms with relatively broad and widely spaced peaks (Fig. l), and fast chop- pers produce PST histograms with multiple narrow and closely spaced peaks (Fig. 2). The discharge rates of the sustained response that follow the initial whopping response are correlated with the unit classes: Slow- choppers respond at low sustained discharge rates (< 300 spikes/s) and fast-choppers respond at higher rates. While most of the slow and fast chopping units produce unimodal histograms of interspike intervals, some LSO units produce bimodal interval histograms and are therefore classified separately as bimodal units.

A point process generates a sequence of event times according to its intensity, which may depend on the time and on the history of the process (Snyder and Miller, 1991). Applied to neural spike trains, the inten- sity function describes the recovery of the spike gener-

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Slow chopper

0 PST (ms)

(I Interval (Ins) ?I)

0 Interval T,, (ms) 20

Fig. 1. Effects of excitatory stimulus level on statistical measures of the responses of a slow-chopper LSO unit (CF 11.0 kHz). The

poststimulus-onset time (PST) histograms (binwidth 500 ps) elicited under three different excitatory stimulus levels are shown on the left. The

monaural excitatory stimulus level expresses in dB above unit threshold is indicated at the top of each graph and is assigned a letter for further

reference. The interval histograms (top row), recovery functions (middle row), and conditional mean functions (bottom row) elicited by the same

three excitatory stimulus levels (referred to by the assigned letters) were computed from the sustained discharges of the unit’s responses,

specifically from the PST interval (50-100 ms) with binwidth 100 ps. The histogram and recovery functions are normalized relative to the

binwidth. The conditional mean function elicited by the highest stimulus level is shifted upward and superimposed (thin lines) on each of the

conditional mean functions elicited by the lower stimulus levels to demonstrate the constancy of shape of the conditional mean functions.

ating process and its dependency on both the stimulus level and the timing of the previous spikes. The point

process model of LSO unit discharges describes the intensity by an intrinsic recovery function, which is shifted as a function of the previous interspike interval to account for the observed negative serial dependency and is scaled proportionally by the contralateral in- hibitory stimulus level. Because this model is based on LSO discharges to a fixed ipsilateral stimulus level, variations of the intensity function with excitatory level have not yet been quantified. In this report, we de- scribe the effect of ipsilateral excitatory stimulus level

on LSO unit discharges as operations on the intrinsic recovery function. In this way, we quantify the differ-

ences between excitatory and inhibitory processes.

Methods

Experimental and data analysis methods

Action potentials were recorded extracellularly from single-units in the LSOs of adult cats anesthetized with sodium pentobarbital. The location of each of the 18 LSO units used in this study was verified histologically

using electrolyte deposits of the recording electrode. Stimulating and recording procedures were similar to those detailed elsewhere (Tsuchitani and Johnson, 1985; Tsuchitani, 1988a).

The ipsilateral excitatory tuning curve (one-spike- discharge threshold level as a function of stimulus frequency) was measured for each unit. The frequency to which the unit was most sensitive defined its excita- tory CF. Tone bursts, set to the excitatory CF, were presented monaurally to the ear ipsilateraf to the recording site. The excitatory stimulus level is ex- pressed relative to the LSO unit’s threshold to the CF tone. The discharges elicited by 100-200 presentations of CF tone bursts ~100-200 ms duration, 1 to 2.5 ms rise-fall times and repetition rates of 1 per s to

1 per 6 s) were recorded. The time at which a stimulus code or spike occurred was calcuiated (clock quantiza- tion of 1 ius) and stored in digital formal.

Relevant statistical measures of LSO unit discharges were computed off-line from the digitized data. The PST histogram represents the times of occurrence of discharges relative to the stimulus-onset time under repeated presentations of the same stimulus (Johnson, 1978). The PST histograms are normalized with respect to the binwidth and number of stimulus repetitions and described as a rate expressed in spikes/s. This normal- ization procedure reduces the dependency on binwidth and facilitates the comparisons of PST histograms of responses to different numbers of stimuli. The PST histograms were used to select the more stationary,

Fast chopper

11wrval (Ins)

0 PST (ms) Interval 7, (ms)

Fig. 2. Effects of excitatory stimulus level on statistical measures of the responses of a fast-chopper LSO unit (CF 11.0 kHd. The PST histograms (bin~idth 500 ps) elicited under three different excitatory stimulus Ievels are shown on the left. The interval histograms (top row), recovery functions (middle row>, and ~nditional mean functions (bottom row> eficited by the same three stimulus conditions are compared in the panefs

on the right (binwidth 50 us). The stimulus conditions and statistical measures are marked as in Fig. 1.

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sustained portion of the tone burst response from

which interval statistics were computed.

Three measures of the interval statistics were com- puted from the data: the interval histogram, the recov- ery function associated with the interval histogram, and

the conditional mean function. The interval histogram describes the probabilistic distribution of interspike interval durations: the relative number of interspike

intervals having a given duration. The interval his-

tograms are normalized with respect to the binwidth

and described as a rate. The recovery function, some-

times called the hazard function, is derived from the interval histogram and describes the probability of an

immediate spike occurrence given that no spike has occurred in the elapsed interval (Tsuchitani and John-

son, 1985). While the interval histogram describes the number of intervals with a given duration relative to

the total number of intervals, the recovery function describes the number of intervals with a given duration relative to the number of intervals having longer dura-

tions. The conditional mean function estimates the mean interspike interval as a function of the previous

interval’s duration. Similarly, the conditional interval

histogram and the conditional recovery function de- rived from it describe the statistics of those intervals that immediately follow a conditioning interval of a

specified length. These statistical measures are quanti- fied in the next section.

Theoretical methods

After it has generated a spike, a neuron takes some time to “recover” before it is ready to generate an-

other. During this refractory period, the probability of the next spike occurrence is affected. In some cases,

the effect of a spike may not be diminished by the time

the next spike occurs, and a cumulative effect on the probability of firing may result. Point processes for which the occurrence of an event has an after-effect are referred to as self-exciting point processes (Snyder

and Miller, 1991). The complete characterization of a general self-exciting point process may depend on the complete history of the process. The description of such processes rests on the conditional probability of an event occurring in the immediately following in-

finitesimal interval given the process’s history

Pr(n+ I” intervalin [7,r+,,7,,+,+dt)lN,=n,‘)

=F(T,,+,; n; T)At

The intensity of the process fi(~,+ i; n; I) depends implicitly on the time t (t = ZT,~), on the counting process N, (the number of events up to time t>, and on the vector of interevent intervals E observed prior to time t.

In the simplest case, the intensity depends only on

the time since the last spike T,,,,. The intensity then

equals the recovery function (a term we adopt here). Elsewhere in the literature, the terms hazard function

(Cox, 1962) and spike rate function (Tuckwell, 1989) are used. In this simple case, the intensity function is

directly related to the probability density function of

the interspike intervals, the quantity estimated by the interval histogram (Johnson et al., 1986).

When a first-order serial dependence exists between

successive interspike intervals, the intensity is related

to the first-order conditional interval histogram and is

equivalent to the first-order conditional recovery func-

tion, wherein the statistic is conditioned on the dura- tion of the previous interspike intervals.

Thus, to reveal the underlying structure of processes

having first-order serial dependence, as in all LSO

discharges, the first-order conditional interval his- tograms must be measured; the usual interval his-

togram p,(. 1 is not powerful enough.

The data processing procedure presented above- measuring a sequence of event-times, computing the

interval histogram, and deriving the recovery function from it-can be reversed. Given an intensity function,

a simulated spike train can be generated that is charac- terized by a recovery function having the same shape

as the underlying intensity function (Johnson et al., 1986; Ozaki, 1979). Similarly, a simulated spike train

exhibiting serial dependency and having the desired

conditional recovery functions can be generated by specifying a family of conditional intensity functions, which in the general case can be arbitrarily complex. A parsimonious method for specifying a family of first- order conditional intensity functions has been devel-

oped based on a single underlying recovery function and a rule for generating the conditional intensity functions from that function. This single underlying recovery function describes the history independent

recovery characteristics of a LSO neuron and is termed the intrinsic recovery function (Zacksenhouse et al., 1992). Note that while some rules for generating the conditional recovery functions preserve the shape of the intrinsic recovery function, others may introduce distortions so that the resulting conditional intensity functions have different shapes. In the later case, ex- tracting the intrinsic recovery function from the mea- sured recovery function or from the measured condi- tional recovery functions may not be straightforward. Understanding the distortion mechanism helps extract the shape of the intrinsic recovery function in those

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cases in which distortion prevails under all conditions. In previous work we have restricted the shapes of the intrinsic recovery functions to the space of non-de- creasing, piecewise-linear functions having at most four segments (Johnson et al., 1986; Zacksenhouse et al., 1992). However, we have found that the shapes of the intrinsic recovery functions can be further re- stricted to the space of saturating linear functions (as shown in Fig. 5) and have thus been able to simplify the simulation process.

The analysis of LSO unit discharges presented in this report reveals that the major effect of increasing excitatory stimulus level is to shift and scale the intrin- sic recovery function. To demonstrate this effect, we first shifted the recovery function elicited by the lower excitatory stimulus Ievel to the left (to shorter inter- vals), and then estimated the scaling factor with respect to the recovery function elicited by the higher excita- tory stimulus level. The magnitude of the shift was determined by comparing the durations of the appar- ent deadtime when the apparent deadtime exceeded the absolute deadtime or by visual inspection. The scaling factor was determined by an homogeneous lin- ear regression technique (~cksenhouse et al., 1992). The recovery function measured from the discharges elicited by the higher excitatory stimulus level, which corresponds to a relativety narrower interval distribu- tion, was assumed exact. The interval histogram of the discharges elicited by the lower excitatory stimulus level was used to estimate the uncertainty in the corre- sponding recovery function. The regression analysis was limited to those intervals where both recovery functions were nonzero and distortion effects, due to the suppress-and-rebound phenomenon (Zacksenhouse et al., 19921, were not apparent. To verify the hypothe- sized excitatory effect, we formulated the shift-and- scale effect on the intrinsic recovery function, and used it to generate the appropriate conditional intensity functions and to drive the simulations. Comparison between the statistics of the simulated discharges and the measured discharges under a series of monaural stimulus conditions provide a measure of the validity of the h~othesized model.

Results

Excitatory effects - apparent uariability between units Recent studies of the effects of excitatory stimulus

level on the discharge patterns of LSO units (Tsuchitani and Johnson, 1985) indicate that the relationships be- tween stimulus level and response measures depend on the unit type. Figs. 1 and 2 illustrate this observation. The mean sustained discharge rates of both the slow choppers and fast choppers increase with excitatory stimulus level, as indicated in the series of PST his-

tograms in these figures. Superficially, the effects of the excitatory stimulus level on the interval histograms and recovery functions derived from the sustained dis- charges do not appear to be consistent from unit to unit. The slow chopper interval histograms are mostly symmetric at all stimulus levels (Fig. I, top right). In contrast, those of fast choppers (Fig. 2, top right) become more highly skewed as level increases. Conse- quently, the shapes of the recovery functions produced by slow choppers remain fairly constant, almost inde- pendent of the stimulus level (Fig. I. middle right), while those produced by fast choppers vary with level. In particular, a step-like change appears at higher stimulus levels immediately after the deadtime (Fig. 2, middle right). Examination of the recovery functions produced by slow choppers (Fig. 1) reveals that the interval at which the likelihood of a discharge first departs from zero (the apparent deadtime) shifts to shorter intervals as stimulus level increases. In con- trast, the apparent deadtime exhibited by the fast chopper recovery functions do not depend strongly on the stimulus level (Fig. 2, note the recovery function time scale differs from that in Fig. 1). The above examples are typical and illustrate the general observa- tions drawn from a monaural population study (Tsuchitani and Johnson, 1985): As a function of the mean discharge rate, the duration of the apparent deadtime measured from different units decreases at low discharge rates, reaches a limiting value at mid discharge rates, and exhibits little change at higher discharge rates. Thus, units that can generate a very high sustained (or initial) discharge rate cannot pro- duce interspike intervals that are shorter than some limit. This observation further supports our previous postulate (Zacksenhouse et al., 1992) of an absolute deadtime during which the unit cannot discharge. Based on this population study, the duration of the absolute deadtime is expected to vary within a narrow range under different excitatory stimulus levels and across different units.

When a unit is driven fast enough to produce inter- vals as short as the absolute deadtime, any potential discharge is suppressed during the absolute deadtime and a rebound in the firing rate occurs immediately after the absolute deadtime (Zacksenhouse et al., 1992). This process, termed the ‘suppress-and-rebound’ pro- cess, distorts the shape of the measured recovery func- tion immediately after the deadtime and may obscure the effect of the stimulus level. Hence, the effect of the excitatory stimulus level on the conditional recovery function can be best revealed by studying monaural response series of slow choppers or slowly driven fast choppers in which the apparent deadtime is longer than the absolute deadtime. Once the excitatory pro- cess is thereby extracted, it can be combined with the suppress-and-rebound process to produce the observed

excitatory effect for the monaural response series of fast choppers.

Shifting and umplifying effects The effect of the excitatory stimulus level on the

recovery functions of two slow choppers is demon- strated in Fig. 3. As the stimulus level increases down each column, the likelihood of a discharge first be- comes nonzero at shorter intervals (shorter apparent deadtime) and increases thereafter at a higher rate. Most importantly, however, the shape of the recovery function appears to be invariant to the stimulus level

SIOV!

(+12)

(+22) AT = 2.3ms A = 2.2 (+30) A? = 0.Sm.s A = 2.6

(+30) AT = 3.3ms A = 3.1 (+3(J) Ar = 1.Sm.s A = 2.2

0 Intcrvai (ms)

207

for each LSO unit: Only its scale and origin vary. To demonstrate this observation, the recovery function at the lowest discharge rate (Fig. 3, top row of graphs) is shifted to the left, amplified, and then superimposed (thin line) on the recovery functions at the higher discharge rates (thick line, lower two rows). The magni- tude of the shift AT and the amplification factor A are indicated above each graph. When shifted and ampli- fied, the recovery functions produced by sustained dis- charges to different ipsilateral stimulus levels match well. Analysis of the responses of other slow choppers and slowly driven fast choppers support the postulates

choppers

(+20)

(i Interval T,, (ms) IS’ Fig. 3. The shifting and amplifying effects of the ipsilateral excitatory stimulus level on the recovery functions of two slow-chopper LSO units are

illustrated (binwidth 100 ps). The stimulus level increases down each column and is indicated, in dB above unit threshold, within the parentheses

at the upper left of each graph. For each unit, the recovery function generated by the sustained discharges elicited under the lowest stimulus

level (top row) is shifted toward shorter intervals and amplified before being superimposed (thin line) on each of the recovery functions produced

by the higher stimulus levels (thick lines). The magnitude of the shift AT (in ms) and the amplification factor A are indicated at the top middle

and top right of each graph, respectively. A good match is demonstrated. The stimulus and processing conditions for the unit illustrated in the

left column are described in the caption for Fig. 1. The CF of the unit illustrated in the right column is 10.0 kHz and the recovery functions were

computed from the PST interval 40-100 ms.

that a stimulus independent intrinsic recovery function defines the recovery process of a given unit and that the main effect of increasing the excitatory stimulus level is to shift and amplify the intrinsic recovery function. Note that these conclusions are apparent even when studying the overall recovery function; be- cause no distortion occurs, we can conclude that a similar effect occurs in the conditional recovery func- tion.

Interaction with the rebound process The effect of the excitatory stimulus level on the

recovery functions of a fast chopper and a bimodal unit

Fast chopper

(+ZO

1

Az = lms A = 3.0

1+30‘) A% = 1Sms A = 4.5

0 Interval (ms) 10

are shown in Fig. 4. As the excitatory stimulus levci increases down each column, the shape of the recovery function appears to change. Consequently, when the recovery function at the lowest discharge rate is shifted and amplified (as suggested by the conclusion drawn from the analysis of slow choppers), it does not match well the recovery functions at higher rates (thin vs. thick lines, two lower rows of Fig. 4). We attribute the observed discrepancies to the interaction of the shifting recovery function with the absolute deadtime according to the suppress-and-rebound process. We note that the discrepancies between the shifted and amplified recov- ery functions at the lowest discharge rate and those at

Bimodal unit it31

t+141 AZ = 3ms A =2.1 -I i

i?st = 5ms A = 7.5 25fK)

0 lntcrval T” (ms) 15

Fig. 4. The shifting and amplifying effects of the ipsiiateral excitatory stimulus level on the recovery functions of a fast chopper (binwidth 50 ps) aud a b&nodal unit (binwidtb 75 PSI are illustmted. The stimulus tevel increases down each column and is indicated in dB above unit threshold within the parentheses at the upper left of each graph. For each unit, the recovery function generated by the sustained discharges elicited under the lowest stimulus level (top row) is shifted toward shorter intervals and amplified before being superimposed (thin line) on each of the recovery functions produced by the higher stimulus level (thick lines). The magnitude of the shift AT (in ms) and the amplifiiation factor A are indicated at the top middle and top right of each graph, respectively. The match is good at long intervals, but fails at short intervals. The stimulus and processing conditions for the fast chopper are described in the caption for Fig. 2. The CF of the bimodal unit is 31.5 kHz. and the recovery

functions were computed from the PST interval 100-400 ms.

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higher discharge rates occur mainly at short intervals immediately before and after the deadtime; the match at longer intervals is adequate. As the recovery func- tion is shifted toward shorter intervals, it eventually reaches the absolute deadtime. Discharge probability is reduced to zero in that portion of the recovery function shifted into the absolute deadtime. When this suppres- sion occurs, the recovery function after the deadtime increases beyond the level expected by a pure shift. This “rebound” in the probability of a discharge fol- lowing the absolute deadtime has been shown to be approximately equal to that suppressed (Zacksenhouse et al., 1992). We formulate the suppress-and-rebound process and its interaction with the excitatory process in the next section and present simulation results for final verification.

The suppress-and-rebound process is commonly ac- tivated in the discharges of fast choppers and bimodal units. The conditional recovery functions of fast chop- pers are often shifted into the absolute deadtime be- cause of the high discharge rates, while the conditional recovery functions of bimodal units are often shifted into the absolute deadtime because of a combination of slowly increasing intrinsic recovery functions and large values of negative serial dependency. Conse- quently, as the excitatory stimulus level increases and the intrinsic recovery function shifts toward shorter intervals, recovery function shapes for fast choppers and bimodal units seem to change. In contrast, the suppress-and-rebound process is rarely activated in the discharges of slow choppers because they respond at low rates, and the recovery function shapes are main- tained independent of the stimulus level.

Modeling

Excitatory effects Point process models for spike trains are defined by

an intensity function, which describes the probability of an immediate occurrence of a spike in an infinitesimal interval given the relevant history of the spike train. Previous point process modeling of LSO unit dis- charges concluded that l The effect of the history of the spike train on the

recovery process is mainly attributed to a first-order serial dependence. Thus, a point process description of LSO unit discharges necessitates the specification of the conditional intensity functions, which depend on the duration of the preceding interspike interval T,, as well as the time elapsed since the last discharge 7 n + 1 (Johnson et al., 1986).

l The effect of the serial dependence can be described by conditional intensity functions that are shifted versions of a single intrinsic recovery function (John- son et al., 1986; Zacksenhouse et al., 1992).

l Shifting the intrinsic recovery function into the abso- lute deadtime results in activation of a suppress- and-rebound process. This phenomenon reflects the fact that no spike is generated during the absolute deadtime and describes the rebound in firing rate immediately after the absolute deadtime (Zack- senhouse et al., 1992). The results presented in this paper suggest that the

effect of the excitatory stimulus level can also be de- scribed by applying simple operations, shifting and amplifying, to the intrinsic recovery function. Thus, the intrinsic recovery function is history and stimulus inde- pendent. For clarity, we will focus for now on modeling the conditional intensity function when the magnitude of the shift is positive: The shift is away from the absolute deadtime and the conditional intensity func- tion does not interact with the absolute deadtime. In this case, the shifting and amplifying operations can be formulated as

,+,,+I; T,,> =P@)+,+I -d-s(Tn; E)]

X4T,,+ I - cl>

where kJE> is the amplitude of the intensity, E is the excitatory stimulus level, 4. ) is the intrinsic recovery function, d is the absolute deadtime, s( .; E) is the shifting function, and the unit step z.4. > assures that the intensity function is zero during the absolute dead- time.

This formulation clearly restricts the effect of the excitatory stimulus level to shifting and amplifying the intrinsic recovery function. Furthermore, the effect of the excitatory stimulus level on the shifting operation can be easily characterized. It has been shown (John- son et al., 1986) that the shifting function equals, up to an additive constant, the conditional mean function (for positive shifts). Because the shape of the condi- tional mean function is independent of the excitatory stimulus level (Figs. 1-2, also (Johnson et al., 1986)), we must conclude that the effect of the excitatory stimulus level on the shifting function is to change the baseline shift. For linear shifting functions, which de- scribe well the measured conditional mean functions (Fig. l), we have

s(T~; E) =a(E) -be,

The effect of the excitatory stimulus level E is explic- itly restricted to the baseline shift a and is linearly separable from the effect of the preceding interval T,,

on the magnitude of the shift. This expression for the shifting function permits

negative shifts, which correspond to shifts into the absolute deadtime. Such negative shifts will trigger the interaction between the conditional intensity function

210

and the absolute deadtime according to the suppress- and-rebound process Gacksenhouse et al., 1992). It is only when this interaction is triggered that we can observe the effect of the absolute deadtime directly; otherwise its effect cannot be distinguished from the effect of the baseline shift a. Detailed modeling work indicated that the duration of the absolute deadtime may vary slightly (by less than 10%) as the excitatory stimulus level is varied. Thus, the complete model for the conditional intensity function, which explicitly de-

Decreasing excitation Increasing i~ibition

scribes the effects of both the excitatory stimulus levcf and the absolute deadtime, is

where dr, + 1; 7,) is the rebound function, and the absolute deadtime d(E) may depend on the excitatory stimulus level. An exponential function has been shown

increased

Interval (msec)

Intefvai (msec)

Intensity - baseline stimulus

Intensity - reduced excitation level Intensity - increased inhibition level

Fig. 5. Illustration comparing the main effects of excitation and inhibition on the intrinsic recovery function (upper panels) and on the intensity function (central and lower panels). Reducing excitatory stimulus level results in both a shift toward longer intervals and a scaiing effect (upper left) while increasing inb~bito~ stimulus level affects only the scafe of the intrinsic recovery function (upper right). The three ~mens~nai plots describe the intensity as a function of the current interval T,,+ 1 and the previous interval 7,. The intensity describing the response to a monaural control stimulus (central panel) provides a baseline. The effect of decreasing excitation on the intensity description (lower left) is contrasted with the effect of increasing inhibition (lower right). To facilitate comparison, all the 3-dimensional illustrations are plotted on the same scales. Also, the minor effect on the duration of the absolute deadtime is not included. The solid lines in the three-dimensional plots mark the condi~onal intensity functions following a specific conditioning interval duration, and correspond to the dashed (baseline) and solid lines (reduced excitation,

left; increased inhibition, right) in the upper panels.

21 I

to well approximate the rebound function (Zack- suppressed probability of firing due to the absolute

senhouse et al., 1992). deadtime process.

7 WE) II + I

Here T is the time constant of the rebound process. The area g&T,,) of the rebound is set equal to the

/ d(E)

max(.s(r,)+d(E),O) +,,+, -4E) -~h,~E)l~~,,+,.

S( Tn) < 0.

Slow chopper

(+3(l) Ad = 0.0 Aa = -2.1 cx = I .3 I

(+4(l) Ad = 0.0 Aa = -3.0 CI = 1.4 2000

I

Interval (ms) I.5

I I I

t+3()) Ad = 0.0 Aa = -2.1 o!= I.1

I I

(+4()) Ad = 0.0 Aa = -3.0 Cx= 1.4

0 lntcrval T,, (ms) 15

Fig. 6. The recovery functions (left column) and conditional mean functions (right column) derived from discharges of a slow-chopper unit (thick

lines) compared with those derived from simulations (thin lines). The stimulus conditions are described in the Fig. 3 caption for the unit

illustrated in the left column. Three of the parameters defining the intensity function used to generate the simulation for the lowest stimulus

level-the baseline shift, the amplitude of the intensity function, and the absolute deadtime-have been modified to generate the simulations for

the higher stimulus levels. The excitatory stimulus level above threshold (in dB), the change in the duration of the absolute deadtime Ad (in

milliseconds), the change in the baseline shift Aa (in milliseconds), and the amplification of the magnitude cy = kc, (higher level)/p,, (lowest level) are indicated above each graph.

The last four equations completely describe the conditional intensity function of LSO units discharges under different excitatory stimulus levels in terms of the shifting function, the intrinsic recovery function, the rebound function, and the relation of the rebound area to the portion of the conditional recovery function shifted into the absolute deadtime interval. These equations are used to generate streams of ‘noise-free’ intervals. A Gaussian white noise (with standard devia- tion P of 60-120 cl.s) is then added to each of these intervals to simulate possible measurement noise (Johnson, 1978) and temporal fluctuations in spike generation (Verveen and Derksen, 1948). The effect of adding noise is to smooth the step-like increase in the

discharge probability imnlediately after the absolute deadtime when rebound occurs. Adding noise is moti- vated by the fact that aithough the rebound in dis- charge probability appears to rise very sharply, it does not rise instantly (Figs. 4, 7. 8).

As before, the intrinsic recovery function is re- stricted to be a non-decreasing function of the time elapsed since last discharge (Johnson et al., MS). Furthermore, we have found that the intrinsic recovery function can be restricted to be a saturating linear function of the shape shown in Fig, 5,

T<R

T>R

Fast chopper

0 Interval (ms) 10

(+3(j) Ad = -0.1 Aa = -0.8 a = 4.3

(+40) Ad = -0.15 Aa = -0.9 a = 8.2

0 i I I 1 I 1

0 Interval i, (ms) 10

Fig. 7. The recovery functions (left column) and conditional mean functions (right column) derived from discharges of a fast-chopper unit (thick lines) compared with those derived from simulations (thin lines). The stimulus conditions are described in the Fig. 4 caption. Three of-the parameters defining the intensity function used to generate the simulation for the lowest stimulus level-the basefine shift, the ~pljtude of the intensity function, and the absolute deadtime- have been modified to generate the simulations for the higher stimulus levels. The excitatory stimuhs level above threshold (in dB), the change in the duration of the absolute deadtime Ad (in miiIis~~), the change in the baseiiine Shift

Aa (in ms), and the amplification of the amplitude a = pa (higher level)/&, (lowest level) are indicated above each graph.

where at intervals longer than R, the intrinsic recovery function is constant.

Excitatory IS. inhibitory effects Recent studies comparing the LSO unit discharges

to monaural and binaural stimuli (Tsuchitani, 1988a,b) indicate that the effect of increasing the contralateral inhibitory stimulus is not equivalent to that of reducing the ipsilateral excitatory stimulus. In a previous paper, we showed that inhibition scales the intrinsic recovery function (Zacksenhouse et al., 1992). In contrast, exci- tation both scales and shifts the intrinsic recovery func- tion. Hence, the data analysis and the model clearly distinguish between excitatory and inhibitory mecha- nisms: Their effects are not symmetrically opposite.

213

The excitatory and inhibitory effects-described as op- erators applied on the intrinsic recovery functions-are schematically illustrated and contrasted in Fig. 5 (up- per panels). Three-dimensional plots of the intensity as a function of the current interval T,+, (time elapsed since last discharge), and the previous interval T,, are illustrated in the lower three panels of Fig. 5 to con- trast the effects of decreasing excitation and increasing inhibition on the intensity function. The minor effect of the excitatory stimulus level on the duration of the absolute deadtime is not included. Increasing inhibi- tion affects only the scale of the intensity function (lower right and central panels); decreasing excitation produces more complicated effects, including a dra- matic change in the form of the intensity (no rebound)

Bimodal unit

(+4) (+4)

I I I I

(+I4) Ad=O.O Aa=+]. cr=2.7

(+24) Ad = +. I5 Aa = -0.3 cx = 1 I

0 1 I I

0 Interval T,, (Ins) 1s

Fig. 8. The recovery functions (left column) and conditional mean functions (right column) derived from discharges of a bimodal unit (thick lines)

compared with those derived from simulations (thin lines). The stimulus conditions are described in the Fig. 4 caption. Three of the parameters

defining the intensity function used to generate the simulation for the lowest stimulus level-the baseline shift, the amplitude of the intensity

function, and the absolute deadtime-have been modified to generate the simulations for the higher stimulus levels. The excitatory stimulus level

above threshold (in dB), the change in the duration of the absolute deadtime Ad (in milliseconds), the change in the baseline shift Aa (in ms),

and the amplification of the amplitude (Y = pLg (higher level)/p(, (lowest level) are indicated above each graph.

TABLE I

Parameters defining the conditional intensity functions used in the presented simulations

Slow chopper Fast chopper Bimodal unit

Intensity amplitude pa (Spikes/s) Absolute deadtime d (ms) Rebound time constant 7’ (ms) Shifting function:

baseline shift a (ms) slope h

Intrinsic recovery function: Linearity interval R (ms)

Additive Gaussian noise: Standard deviation cr (ms)

I750 2 745 930 1.4 1.7 1.45 0.4 0.4 0.2

7.4 0.7 0.25 0.2 0.22 0.9

14.0 18.0 27.0

0.06 0.1 0.1

(0.16 @ intermediate level)

The values of the parameters used to simulate the discharges of a slow chopper, a fast chopper and a bimodal unit under the corresponding lowest stimulus levels are specified . The values of the intensity amplitude pa, the baseline shift a, and the duration of the absolute deadtime d have been changed when simulating the responses of these units to higher stimulus levels. The values of the other parameters were held constant in simulating the responses of each neuron. The intrinsic recovery functions are all saturating linear functions which saturate at interval R. The standard deviation c of the additive white Gaussian noise is also indicated.

and increased apparent deadtime (lower left and cen- tral panels). The overall effects on the recovery func- tion computed from regular (unconditional) interval histogram are further complicated in either case by the corresponding effects on the relative distribution of interval durations.

Simulation results To confirm that the effect of excitation is restricted

to scaling and shifting the intrinsic recovery function, we performed computer s~uiations of various units’ responses to monaural stimulation at different excita- tory stimulus levels. The invariant parameters of the conditional intensity function-the interval R at which the linear intrinsic recovery function reaches the satu- ration level, the strength of the serial dependency b, and the rebound time constant T-were determined by inspecting the shape of the measured recovery func- tion, the slope of the measured conditional mean, and the shape of the rebound, respectively. The stimulus dependent parameters-the intensity magnitude ~&2), the baseline shift a(E), and the absolute dead- time d(E) were then adjusted to simulate the response of the same neuron to different excitatory stimulus levels. The ability of the model to generate spike trains with statistics similar to those generated by I.30 neu- rons is demonstrated in Fig. 6 for a slow chopper, in Fig. 7 for a fast chopper, and in Fig. 8 for a bimodai unit. The values of the parameters defining the condi- tional intensity functions-including the stimulus de- pendent parameters used to simulate the response to the lowest stimulus level-are summarized in Table I. Changes in the stimulus dependent parameters, i.e. the change in the absolute deadtime Ad, the change in the

baseline shift Aa, and the ~piification applied to the magnitude of the intensity, denoted by a?, are indicated above the corresponding graphs in Figs. 6-8.

The measured and simulated statistics of the siow- chopper discharges, shown in Fig. 6, demonstrate the excitatory effects-shifting and scaling-with no inter- ference from interactions with the absolute deadtime. The simulation of the fast chopper discharges (Fig. 7) demonstrates that the excitatory effects and their inter- actions with the absolute deadtime process do indeed combine to produce the complex effects of excitatory stimulus level on the recovery function (compare to Fig. 4, left column, where shifting and scaling do not seem to account for the complex excitatory effects). The simulation of the bimodal unit discharges (Fig. 8) further demonstrate that a negatively sloped section in the recovery function can be produced by the suppress- and-rebound process even when the underlying intrin- sic recovery function is a non-decreasing function. Here again, the observed complex excitatory effects are fully accounted by the model (compare to Fig. 4, right column).

The general trend is for the baseline shift a to decrease, and for the intensity magnitude @0 to in- crease as the excitatory stimulus level is increased (Figs. 6-8). An exception have occurred in simulating the response of the bimodal unit to the intermediate stimulus level: the baseline shift had to be increased. The intermediate stimulus level was presented toward the end of the experiment with this bimodal unit-after the lowest and the highest stimulus levels among others were presented. Hence, the above anomaly may reflect some change in the neuron or its environment which obscured the effect of the stimulus level.

Conclusions

The sustained discharges of LSO units under differ- ent stimulus conditions are described by a single point process model wherein the underlying intensity process

is related to stimulus levels at the two ears. The model clearly factors the cell recovery characteristics from the

effects of the stimulus conditions and the timing of previous spikes. Each unit is characterized by an intrin-

sic recovery function that is stimulus and history inde- pendent. The stimulus and history effects are described

by shifting and scaling operators applied to the intrin-

sic recovery function: The serial dependency is de-

scribed by a shift that is proportional to the length of

the previous interval (Johnson et al., 1986). The excita- tory stimulus effect is described by a baseline shift and by an amplification factor while the inhibitory stimulus

effect is described by a scaling factor (Zacksenhouse et al., 1992). The model provides a unifying point process

representation of the discharges produced by all three

LSO unit types. Variations observed in the response patterns of the different LSO unit types are attributed

to the interaction of the unit’s post-spike recovery

process with the absolute deadtime process.

Description of LSO units response patterns to

time-varying stimuli is thereby simplified to specifying

the temporal variations in the baseline shift, in the

magnitude of the intensity process, and in the absolute deadtime. Other parameters of the model, including

the strength of the serial dependency and the shape of the intrinsic recovery function, are invariant character- istics of the unit. These parameters do not vary with

stimulus conditions and can be estimated from station- ary portions of the response. Furthermore, the model-

ing work presented here suggests that LSO neurons may all have the same intrinsic recovery function-a

saturating linear function. Decreasing the excitatory stimulus level reduces the

discharge rate due to two mechanisms: The recovery function is both shifted toward longer intervals and scaled. In contrast, when the same reduction in dis-

charge rate is achieved by increasing the inhibitory stimulus level, only the scale of the intrinsic recovery function is affected. Consequently, the response to the second stimulus condition (increased inhibition) can be differentiated from the response to the first stimulus

condition (decreased excitation) by comparing the number of relatively short intervals. Comparing a

monaural discharge with a binaural discharge of similar mean rate, the binaural discharge should exhibit the

relatively frequent occurrence of very short intervals accompanied by relatively frequent occurrence of long

intervals. Thus, the discharge microstructure-the tim- ing of the discharges in an individual spike train, or alternatively the shape of the interspike interval distri- bution-can be used to differentiate between re-

sponses elicited under different stimulus conditions

producing the same mean sustained discharge rate. We

thus pose the question: To what extent is this informa-

tion, rather than just the average rate, extracted by higher centers receiving inputs from the LSO? Are the

differences in the characteristics of LSO unit responses to different stimulus conditions, which produce the

same mean discharge rate, accidental or are they rele-

vant for further information processing’? Physiological considerations support the observed

shifting and scaling effects of the ipsilateral input on

the intrinsic recovery function of LSO units. Excitatory

terminals, containing round synaptic vesicles, are lo-

cated on the distal dendrites (Cant and Casseday, 1986;

Glendenning et al., 1985). Presumably, within the LSO unit’s dendrites the ipsilateral stimulus has the ulti-

mate effect of producing excitatory post synaptic po- tentials (EPSPs) that sum and spread passively toward

the cell body. According to a simplified spike initiation

model, the cell produces a spike when the effect of the

accumulated EPSPs on the membrane potential at the spike generator crosses a threshold voltage level.

Moreover, the negative serial dependency exhibited by

LSO unit discharges suggest that the timing of repeti-

tive discharges of LSO units is governed by an afterhy- perpolarization (AHP) (Smith and Chen, 1986; Zack-

senhouse et al., 1992). The afterhyperpolarization arises

from an increase in potassium conductance that decays slowly with a time constant of about 2-7 ms (Smith and

Goldberg, 1986). Consequently, the effect of the accu-

mulated EPSPs on the membrane potential depends on the level of the afterhyperpolarization. When the

conductance of the AHP potassium channels is large, immediately after spike initiation, the distally gener- ated EPSPs produce a relatively small change in the

membrane potential, which is superimposed on the

AHP potential. As the conductance of the potassium channels decays, the effect of the same EPSPs on the membrane potential increases and, if the membrane

potential increases above the threshold level, may lead to a new discharge. Accordingly, the probability of a discharge increases with the time elapsed since the last

spike in a characteristic way that mirrors the decay of the conductance of the AHP potassium channels. This phenomenon may be the underlying mechanism cap- tured by the intrinsic recovery function and its non-de- creasing nature.

The effects of varying stimulus conditions may also be interpreted in a similar vein. As the excitatory stimulus level increases, the effect of the accumulated EPSPs on the membrane potential increases and may result in a new discharge even when superimposed on increasingly larger AHP potentials. Hence, increasing the excitatory stimulus level results in a nonzero proba- bility of firing at shorter intervals, which corresponds to the shifting operation. Since the AHP potassium

channels are located near the spike generation site, they have also a divisive (shunting) effect on the EP- SPs. Hence, as the conductance of the AHP potassium channels decay, a constant increase in the magnitude of the EPSPs will produce an increased effect on the membrane potential, which corresponds to the amplify- ing operation.

We interpret the negative serial dependency exhib- ited by LSO units as an evidence of a cumulative AHP effect. The point process analyses and modeling work presented here suggest two additional correlates with the characteristics of the AHP: The intrinsic recovery function may reflect the decay profile of conductance of the AHP potassium channels following spike genera- tion, and the shifting and amplifying operators may reflect the interaction of the accumulated EPSPs with the decaying potassium conductance.

Acknowledgements

The work was supported by NIDCD grant 8 DC00258 to Rice University and NIDCD grant 8 DC00261 to The University of Texas at Houston.

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