1Department of Physiology, University of Adelaide, South Australia 5005, Australia; and 2Department of Physiology and Biophysics, School of Medicine, University of Washington, Seattle, Washington 98195
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ABSTRACT |
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Türker, K. S. and R. K. Powers. Effects of Large Excitatory and Inhibitory Inputs on Motoneuron Discharge Rate and Probability. J. Neurophysiol. 82: 829-840, 1999. We elicited repetitive discharge in hypoglossal motoneurons recorded in slices of rat brain stem using a combination of a suprathreshold injected current step with superimposed noise to mimic the synaptic drive likely to occur during physiological activation. The effects of repetitive en mass stimulation of afferent nerves were simulated by the further addition of trains of injected current transients of varying shapes and sizes. The effects of a given current transient on motoneuron discharge timing and discharge rate were measured by calculating a peristimulus time histogram (PSTH) and a peristimulus frequencygram (PSF). The amplitude and time course of the simulated postsynaptic potentials (PSPs) produced by the current transients were calculated by convolving the current transient with an estimate of the passive impulse response of the motoneuron. We then compared the shape of the injected current transient and the simulated PSP to the profiles of the PSTH and the PSF records. The PSTHs produced by excitatory PSPs (EPSPs) were characterized by a large, short-latency increase in firing probability that lasted slightly longer than the rising phase of the EPSP, followed by a reduced discharge probability during the falling phase of the EPSP. In contrast, the PSF analysis revealed a proportionate increase in discharge rate over the entire profile of the EPSP, even though relatively few spikes occurred during the falling phase. The PSTHs associated with inhibitory PSPs (IPSPs) indicated a reduction in discharge probability during the initial, hyperpolarizing phase of the IPSP, followed by an increase in the discharge probability during its subsequent repolarizing phase. Using the PSF analysis, the initial phase of the IPSP appeared as a large hole in the record where a very small number or no discharges occurred. The subsequent phase of the IPSP was associated with frequency values that were lower than the background values. The primary features of both PSTHs and PSFs can be used to estimate the relative amplitudes of the underlying EPSPs and IPSPs. However, PSTHs contain secondary peaks and troughs that are not directly related to the underlying PSP but instead reflect the regular recurrence of spikes following those affected by the PSP. The PSF analysis is more useful for indicating the total duration and the profile of the underlying PSP. The shape of the underlying PSP can be obtained directly from the PSF records because the discharge frequency of the spikes follow the PSPs very closely, especially for EPSPs.
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INTRODUCTION |
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The ability to record motor unit activity in human
subjects has provided a wealth of information about the neural control of motoneurons and in particular has allowed the study of how reflex
and descending control of motoneurons change as a function of task
during fatigue and after nervous system injury. Although synaptic
potentials cannot be directly recorded in human motoneurons, their
characteristics can be inferred from measurements of the effects of
activating a set of peripheral or descending fibers on the discharge
probability of one or more motoneurons. These effects often are
assessed by compiling a peristimulus time histogram (PSTH), which
measures the probability of occurrence of a motoneuron spike as a
function of time from the stimulus (e.g., Calancie and Bawa
1985; Garnett and Stephens 1980
) or by measuring
the stimulus-evoked change in the discharge of a population of
motoneurons as reflected in the mean level of rectified surface
electromyographic activity (sEMG) (e.g., Türker and Miles
1985
). The limitations of the PSTH technique were recognized at
the outset (Moore et al. 1970
), and recent workers also
have emphasized that PSTH features depend not only on the
characteristics of the underlying synaptic potentials but also on the
discharge properties of the postsynaptic cell (Awiszus et al.
1991
; Türker and Cheng 1994
;
Türker et al. 1997
). In particular, although
short-latency PSTH or average sEMG features are likely to be related to
the underlying synaptic potentials, later peaks and troughs may be
caused by synchronous discharge of the motor units at a fixed latencies
after the stimulus. In addition, a marked increase in discharge
probability associated with the rising phase of an excitatory
postsynaptic potential (EPSP) often is followed by a lower than normal
number of spike counts on its falling phase due to the postdischarge
refractory period (Ashby and Zilm 1982
; Fetz and
Gustafsson 1983
).
We and others have proposed methods that use the interspike intervals
and instantaneous discharge frequencies of single-motor-unit discharge
for estimating the synaptic potentials produced by afferent stimulation
(Awiszus et al. 1991; Poliakov et al.
1994
; Türker and Cheng 1994
;
Türker et al. 1989
, 1994
, 1997
). One of these methods, the peristimulus frequencygram (PSF), plots the instantaneous discharge frequency values against the time of the stimulus and recently has been used to examine reflex effects on motoneurons (Türker and Cheng 1994
; Türker et al.
1997
), as well as the sign of the net common input that
underlies the synchronous discharge of human motor units
(Türker et al. 1996
). The instantaneous frequency
values comprising the PSF should not necessarily be affected by
previous activity at any particular time, and hence the PSF should be
free from the synchronization and count-related errors associated with
sEMG and PSTH measurements.
Because the discharge frequency of a motoneuron reflects the net
current reaching the soma (Baldissera et al. 1982;
Kernell 1965
; Powers et al. 1992
;
Redman 1976
; Schwindt and Calvin
1973a
,b
), any significant change in the poststimulus discharge
frequency should indicate the sign and the profile of the net input
(Türker and Cheng 1994
; Türker et al.
1997
). However, PSF features have never been directly compared
with the characteristics of synaptic potentials measured in the same
cells. Recent work on both neocortical pyramidal cells (Reyes
and Fetz 1993
) and motoneurons (Poliakov et al. 1996
,
1997
) has shown that the effects of synaptic potentials on
discharge probability can be mimicked by injected current transients. The aim of the present study was to simulate large, compound synaptic potentials with injected current transients and to test the extent to
which the effects of the transients on discharge frequency (as measured
by the PSF) reflect the underlying synaptic potentials. We studied the
effects of excitatory and inhibitory current transients of varying
profiles (shapes and sizes) on the discharge properties of motoneurons.
The results indicated that both PSTH and PSF features could be used to
estimate the amplitude of the underlying synaptic potentials. However,
the PSF technique is more useful than the PSTH for indicating the total
duration and the profile of the underlying PSP.
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METHODS |
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The basic surgical and experimental procedures we used to obtain
intracellular recordings from rat hypoglossal motoneurons in vitro have
recently been described in detail (Poliakov et al. 1996,
1997
; Sawczuk et al. 1995
), so only the main
features of the protocols will be summarized here.
Rat hypoglossal motoneurons were studied in 400-µm-thick brain stem
slices obtained from 18- to 24-day-old Sprague-Dawley rats. After the
induction of anesthesia with an intramuscular injection of a mixture of
ketamine (68 mg/kg) and xylazine (4 mg/kg), a section of brain stem was
removed and glued to a Plexiglass tray filled with cooled, artificial
cerebrospinal fluid in which Na+ had been
replaced with sucrose [S-ACSF; composed of (mM) 220 sucrose, 2 KCl,
1.25 NaH2PO4, 26 NaHCO3, 2 MgCl2, 2 CaCl2, and 10 glucose]. A series of transverse slices were
cut throughout the length of the hypoglossal nucleus, transferred to a
holding chamber, and incubated at room temperature (19-21°C) in
S-ACSF for 30 min, followed by 30 min incubation in standard ACSF (the same as S-ACSF except that sucrose was replaced with 126 mM NaCl). For
the experimental recordings, the slices were submerged in a recording
chamber and perfused with ACSF at a rate of 2 ml/min. We used glass
micropipettes filled with 3 M KCl (electrode resistances of 20-60
M) to obtain intracellular recordings from hypoglossal motoneurons.
Motoneuron identity was based on location and on the similarity of cell
properties to those reported by previous investigators (Haddad
et al. 1990
; Sawczuk et al. 1995
; Viana et al. 1990
, 1993a
,b
).
Recording and current injection techniques
Motoneurons initially were accepted for study if they exhibited
resting potentials more negative than 60 mV and action potentials with positive overshoots. We performed the complete experimental protocol only on those motoneurons capable of producing sustained, repetitive discharge in response to long suprathreshold current steps.
After impalement, we used steps of injected current to measure the
motoneuron's input resistance, rheobase, and steady-state frequency-current relation (see following text). We subsequently measured the motoneuron's response to a series of injected current waveforms consisting of suprathreshold current steps with superimposed noise and synaptic-like current transients. The waveforms were stored
as sequences of digitized values and converted to a current command via
a D/A converter at a rate of 10 kHz. The membrane potential was
simultaneously sampled at the same rate and stored.
Stimulus waveforms
Long epochs of repetitive discharge were elicited by 42-s
injected current waveforms consisting of four components: a 35-s suprathreshold step, a 26.2-s zero-mean random noise waveform starting
5 s after step onset, a 26.2-s train of injected current transients (CTs) starting at the same time as the noise waveform, and
two series of eight 1-ms, 1-nA hyperpolarizing current pulses applied
before and after the current step. The random noise waveforms had a
Gaussian amplitude distribution with standard deviations ranging from
0.03-0.5 nA and power spectra that were relatively flat up to either
160 or 500 Hz. When superimposed on the current steps, this range of
noise waveforms induced similar discharge rates and variabilities as
typically observed in voluntarily-activated human motoneurons (cf. Fig.
1 of Poliakov et al. 1996). The effects of repetitive en
masse stimulation of afferent fibers were simulated by the further
addition of a train of current transients to the injected current
waveform. The current transients (CTs) were specified either by an
alpha function (cf. Poliakov et al. 1997
) or an alpha function with a modified decay phase, and the parameters of these functions were varied to produce a wide range of amplitudes (0.1-0.5 nA) and time courses (rise times of 0.1-20 ms, half-widths of 1-50
ms). The intervals between CTs were uniformly distributed between 200 and 600 ms. The voltage responses to the hyperpolarizing current pulses
that preceded and followed the suprathreshold current step were used to
estimate the passive impulse response of the motoneuron (see following text).
Experimental protocol
The rheobase and steady-state frequency-current (f-I) relation of each cell were determined before the application of the current steps with superimposed random noise and current transients. We injected 50-ms current steps of various amplitudes and determined the rheobase current as the minimum current amplitude needed to elicit a spike. The steady-state f-I relationship was estimated by delivering a series of 2-s current steps of various amplitudes and plotting the relation between current amplitude and the average frequency calculated over the last second of discharge.
The effects of the CTs on motoneuron discharge rate and probability were determined from a series of responses to the injected current waveforms described in the preceding text. The background discharge rate of the motoneuron was maintained by counting the number of spikes for each epoch of the experiment and periodically altering the size of the current step to maintain about the same mean discharge rate in all epochs in the same cell. Unless the effect of the background discharge rate was studied, the spike count in the duration of the epoch (26 s) was maintained at ~400 spikes (~15 imp/s).
Data analysis
We obtained a number of derived measures from the digitized membrane responses to the stimuli, including: the profiles of the simulated PSPs; peristimulus time histograms (PSTHs) between the times of occurrence of the CTs and motoneuron spikes; and peristimulus frequencygrams (PSFs) between the times of occurrence of the CTs and motoneuron spikes.
The recorded membrane potentials first were corrected for electrode
artifacts as described by Poliakov et al. (1997).
Although this procedure facilitated accurate measurement of the times
of spike occurrence, a significant contribution from uncompensated electrode resistance often remained in the records because of changes
in electrode resistance during the course of the trial. For this
reason, it was not possible to measure accurately the membrane
potential response to a given current transient. Instead we estimated
the membrane response to each CT (i.e., the simulated PSP) by
convolving this waveform with an estimate of the passive impulse
response of the motoneuron (Poliakov et al. 1997
). This impulse response was derived from the average responses of the motoneuron to the series of hyperpolarizing current pulses preceding and following each current step. We determined the best double exponential fit to the decay of the membrane potential following the
offset of the current pulse (curve-fitting routine of Igor Pro,
Wavemetrics, Lake Oswego, OR). The passive impulse response then was
calculated by adjusting the amplitude of each exponential component to
that expected for a response to a 1-nA current pulse with a width equal
to our sampling interval (cf. D'Aguanno et al. 1986
).
Although any errors in our estimates of the passive impulse response of
motoneurons will lead to errors in the estimated time course of the
PSPs, these errors are expected to be random rather than systematic
(e.g., the PSP amplitude will be overestimated in some cases and
underestimated in others). However, it should be emphasized that our
estimates of simulated PSP time course represent the PSPs that would be
recorded near the resting potential, assuming symmetric responses to
de- and hyperpolarizing currents. During repetitive discharge, the
membrane conductance will differ from the resting conductance as will
the impulse response of the motoneuron and the PSP time course. The
effects of changes in membrane conductance on PSP time course are
addressed in the DISCUSSION.
The responses of the motoneuron to a series of CT trains were used to compile PSTHs and PSFs. PSTHs and PSFs typically were compiled from three or six repetitions of the injected current waveform, each of which contained 66 CTs. Thus there were typically either ~198 or 396 triggers used in each PSTH and PSF. PSTHs were constructed to cover ±200 ms around the time of delivery of each CT (1-ms binwidth). PSFs were compiled by determining the frequency of each interspike interval as a function of time between the CT and the time of the spike at the end of the interval, and plotting frequency as function of time lag (see Fig. 1C).
Cumulative sums (CUSUMs) (Ellaway 1978) were
calculated from the PSTHs by subtracting the mean bin count at negative
lags (
200 to 0 ms pre-CT) from the PSTH, and integrating the result (Fig. 1B, top). The area of
the PSTH peak (or trough) was calculated from the CUSUM maximum (or
minimum). These values were converted to the probabilities of spike
occurrence by dividing by the number of CT stimuli. The duration of the
PSTH peak (or trough) was estimated from the time lag at which the
CUSUM maximum (or minimum) occurred.
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Two different procedures were used to quantify the main features of each PSF. First, a running mean of frequency values was calculated by first sorting the frequency values by time lag and then calculating the average frequency over a window of 10 consecutive values (solid thick trace in Fig. 1C). The peak (or minimum) frequency and the time to peak were determined from this running average. The running mean provided a good estimate of the mean frequency around the peak (or minimum) frequency because the individual frequency values generally were clustered tightly in time at these points but could provide a distorted view of PSF time course over regions in which the individual frequency values were widely separated in time. To determine the total duration of the effect of the CT on discharge rate, a CUSUM of frequency values was calculated in an analogous fashion to that described above for the PSTH. This frequency CUSUM was calculated by subtracting the mean prestimulus discharge rate from the PSF and integrating the remainder (Fig. 1C, top). The maximum (or minimum) of this CUSUM was taken to represent the duration of the CT's effect on discharge rate.
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RESULTS |
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We have recorded from eight rat hypoglossal motoneurons in seven
experiments. In each cell, at least three different CTs were tested for
at least three epochs each. In four of the cells, each of which
continued to discharge regularly for 4 h,
100 epochs were recorded.
In these cells, we tested several different CT profiles and amplitudes,
using one to four different noise amplitudes. In one of these cells, we
also examined the effects of excitatory and inhibitory CTs at four
different background discharge rates. Intracellular recordings were
terminated when the motoneurons started to discharge spontaneously
and/or the membrane potential depolarized to above
60 mV.
Excitatory current transients
The effects of excitatory current transients on the discharge probability and the instantaneous discharge frequency of motoneurons depended on their shape and size. Figure 1A illustrates a long-lasting excitatory CT (thin trace) and the simulated EPSP it produced (thick trace). The EPSP profile is likely to be similar to that produced by activating a set of afferents with a wide range of conduction velocities and synaptic delays (peak amplitude of 2.3 mV, time to peak of 24 ms, half-duration of 50 ms). The effects of this EPSP on discharge timing and frequency are illustrated in Fig. 1, B and C, respectively. The EPSP induced a peak and a trough in the PSTH (Fig. 1B) that then are repeated three times. The PSF plot (Fig. 1C) illustrates that during the first PSTH peak, the discharge frequency of the motoneuron increased considerably. During the first trough in the PSTH, however, the discharge rate of the cell continued to be higher than the background discharge rate even though the number of data points were low. During the second peak in the PSTH, the discharge rate of the unit was either similar or lower than the background discharge rate. During the second trough in the PSTH, the discharge rate of the cell returned back to normal discharge rate of the cell. During the next peak and trough of the PSTH, the discharge rate stayed at its average prestimulus value.
The PSF indicates an increase in discharge frequency over most of the duration of the EPSP, whereas the PSTH indicates an increase in firing probability primarily during the rising phase of the EPSP. The PSF thus provides a more accurate reflection of the entire profile of the underlying EPSP. The shape of the EPSP was approximated by the instantaneous discharge frequency of the cell in such a way that during the rising phase of the EPSP, the frequency increased very rapidly along the shape of the EPSP and during the falling phase, the discharge rate followed the EPSP profile closely even though there were relatively few discharges during this phase.
The PSTH generally contained secondary features (peaks and troughs) not related to the underlying synaptic potential. Although many of these additional features were not reflected in the PSF, the discharge frequency at the end of an EPSP was often lower than the background discharge rate. Figure 2 illustrates the source of the secondary features in both the PSTH and PSF. Figure 2A illustrates the PSTH associated with a large (10.6 mV) EPSP (A, dashed line, and B, top). The peak in the PSTH occurring on the rising phase of the EPSP is followed by a trough and two secondary peaks centered at lags of 75 and 125 ms. The associated PSF is illustrated in Fig. 2B, top and bottom three panels, represent subsets of the discharges contributing to the PSF. The three horizontal lines in each panel represent the mean background discharge rate (solid line) and ±2 SD (dotted lines). The increase in discharge frequency can be divided into three segments (labeled 1-3), corresponding to the early portion of the rising phase of the EPSP, the last portion of the rising phase to the early portion of its falling phase and the last part of the falling phase, respectively.
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Figure 2B (bottom 3 panels) show that the first
spikes in the intervals contributing to these three phases arose at
distinct times preceding the EPSP: >30 ms, 10-30 ms, and <10 ms.
When the EPSP occurred 30 ms after a preceding spike (1), spikes were evoked on the early portion of its rising phase. The next occurrences of these spikes were at longer than normal intervals, however (arrow).
The spikes marked as 2 occurred when the early part of the rising phase
of the EPSP did not reach threshold. The later spikes crossed the
threshold with the aid of noise because these spikes were very rare for
a given size of an EPSP when the discharge of the motoneuron was
achieved by current pulses without the superimposed noise (not
illustrated). The preceding occurrences of the spikes marked as 2 were
closer to the stimulus, and hence the EPSP was unsuccessful in bringing
the trajectory to the firing threshold during the rapid rising phase.
When these 2 spikes discharged again, like the 1 spikes, the discharge
rate was lower than the average background rate (arrow). However, the
frequency values for subsequent discharges were within the normal
limits of the average background discharge rate. The spikes marked as 3 (the spikes in the late falling phase of the EPSP) were still
discharging at higher rates than background rate. These spikes arose
when the onset of the EPSP occurred within 10 ms of the preceding
spike. The interspike intervals after the ones shortened by the EPSP were around the mean interval.
The source of the PSTH features can be determined from the density of
the points contributing to the three different subsets of the PSF. The
mean prestimulus discharge interval in this example was 62 ms, so about
half of the EPSPs would be expected to follow the preceding spike by
30 ms. These EPSPs triggered spikes on the first two-thirds of their
rising phase (0-7.7 ms), leading to the short-latency peak in the
PSTH. Subsequent spikes occurred at multiples of the mean interval,
contributing to the secondary PSTH peaks. When EPSPs occurred within 30 ms of the preceding spike, subsequent spikes were triggered over a wide
range of lags (4.4-65.9 ms), but the density of spikes at lags of
12-50 ms was low, leading to the trough in the PSTH.
ASSESSING THE AMPLITUDE OF AN EPSP FROM THE PSF AND PSTH. Figure 3 illustrates the relation between EPSP amplitude and PSF features. The amplitude and the time course of the poststimulus increase in discharge frequency roughly followed the EPSP time course at each EPSP amplitude. In contrast, the duration of the PSTH peak decreased with increasing EPSP amplitude (not illustrated), from 14 ms at the lowest amplitude to 8 ms at the highest. The duration of the trough after the peak became longer with increasing EPSP amplitude. This was reflected on the PSF graph as a smaller number of spikes during the falling phase of the EPSP.
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ASSESSING EPSP RISE TIME.
The current transients used in the present study were designed to
produce relatively large simulated EPSPs and inhibitory PSPs (IPSPs),
such as those likely to be evoked by the stimulation of tens to
hundreds of afferent fibers. The EPSPs ranged in amplitude from 0.8 to
13.5 mV (5.1 ± 3.2 mV), and the vast majority of EPSPs were >2
mV in amplitude. On the basis of previous comparisons of PSP and PSTH
shapes (Fetz and Gustafsson 1983), the duration of the
PSTH peaks produced by these large EPSPs would be expected to reflect
the rise time of the EPSP. Figure
4A illustrates the relation
between the duration of the PSTH peak and the time to peak of the
underlying simulated EPSP for small (<2 mV, ×), medium (2-6 mV,
), and large (>6 mV,
) EPSPs; A line of identity (
) was drawn,
shifted upward by 1 ms to account for the approximate maximum delay
between spike initiation and spike detection. For EPSPs with rise times
of <15 ms, most of the points lie above this line, suggesting that the
duration of the PSTH peak tends to overestimate rise time for these
EPSPs. In contrast, for very slowly rising EPSPs the peak duration
tends to be shorter than EPSP rise time.
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ASSESSING THE FALLING PHASE OF THE EPSP.
When mixed nerves are stimulated by large electrodes as is done in
H-reflex studies in human subjects, it is likely that a variety of
types of afferent fibers are coactivated, including those arising from
primary muscle spindles (Ia) and Golgi tendon organs (Ib), that would
be expected to produce monosynaptic EPSPs and oligosynaptic IPSPs,
respectively (Burke et al. 1983, 1984
). If that is the
case, the effect of the Ia-EPSP may be cut short by the arrival of
Ib-IPSPs in the motoneuron. We have simulated this situation using two
CTs with identical rising phases but different falling phases. Figure
5 illustrates the results of this
experiment on a single cell. Figure 5, A and B,
illustrates the PSTH and PSF produced by a current transient with a
slow exponential decline after the peak. The associated EPSP also is
included in each panel (thick trace in A, thin trace in
B). The CUSUM of the PSTH (thin trace in A)
follows the entire time course of the EPSP, consistent with the
suggestion that the spike-triggering efficacy of the EPSP is related to
the time course of its derivative provided that the rate of EPSP decay
is lower than the rate at which the membrane potential approaches
threshold (cf. Fetz and Gustafsson 1983
). However, this
match does not apply for more rapid rates of EPSP decay, as illustrated
in Fig. 5, C and D, which shows the PSTH and PSF
produced by a current transient with the same rising phase as that used
in A and B but with a rapid decline followed by
hyperpolarization. The CUSUM of the PSTH associated with this transient
is qualitatively similar to that in Fig. 5A even though the
PSP time course is quite different. Although the PSF provides no
quantitative information about the falling phase of the PSP, the
absence of points on the falling phase contrasts markedly with the
increased discharge frequency in Fig. 5B.
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Inhibitory current transients
The effects of inhibitory current transients on motoneuron discharge rate and probability were more complex than those of excitatory current transients, particularly since the largest transients typically prevented motoneuron discharge over most of their time course. Figure 6 illustrates a typical simulated IPSP and its effect on the discharge characteristics of a motoneuron. The PSTH associated with the IPSP (Fig. 6A) exhibits a short-latency trough followed by three peaks (delineated by 3 pairs of vertical lines at positive lags) and two additional troughs. The PSF (Fig. 6B) illustrates that during the first PSTH trough, the cell either did not fire at all or fired only a few times. During the first peak in the PSTH, however, the discharge rate of the cell was lower than the background discharge rate. During the second peak in the PSTH, the discharge rate of the unit increased to a slightly higher rate than the background rate. During the second trough in the PSTH, the discharge rate of the cell returned to the prestimulus discharge rate and remained at this rate at more positive time lags.
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Although the PSF provided no information about the initial phase of the IPSP, it was clear that the PSF more accurately reflected the profile of the underlying IPSP than the PSTH. The PSTH indicated the initial, hyperpolarizing phase of the inhibitory PSP as a very low number of occurrences. When the spikes did occur during the subsequent repolarizing phase of the IPSP, there was a large increase in the number of counts in the PSTH, suggesting an "excitatory" event. In contrast, the PSF showed that the instantaneous discharge frequencies associated with the large number of discharges on the repolarizing phase of the IPSP were in fact lower than the average background discharge rate, thus correctly indicating the effects of the IPSP on discharge.
The IPSP produced secondary features in the PSF that followed the
initial effects. As was the case for the effects of EPSPs, the source
of secondary features in the PSTH and the PSF could be determined by
separating the points contributing to the PSF according to the time
between the IPSP and that of the preceding spike. When the IPSP
occurred >30 ms after the preceding spike, the subsequent spikes were
delayed until the repolarizing phase of the IPSP and the discharge rate
was lower than the background rate (B1, ). The following
interspike interval was shorter than normal, as indicated by the
cluster of frequency values above the baseline (B1,
).
Qualitatively similar effects were seen when the IPSP occurred between
10 and 30 ms after the preceding spike (B2). When the IPSP
occurred <10 ms after the preceding spike it had no effect on
discharge rate (B3). The delay of spikes to the repolarizing
phase of the IPSP led to the first peak in the PSTH because a large
number of spikes occurred at this time. Subsequent peaks in the PSTH
reflected additional discharges at about the mean background discharge rate.
ASSESSING THE AMPLITUDE OF THE UNDERLYING IPSP FROM THE PSF AND
PSTH.
Figure 7 illustrates the relation between
the amplitude of the simulated IPSP and PSF features. Except for the
smallest IPSP, no spikes occurred during the initial falling phase of
the IPSP. For this reason, the PSF provided no direct information about the amplitude of the IPSP. However, lower than normal discharge rates
occurred on the subsequent rising (repolarizing) phase of the IPSP, and
the peak decrease in firing rate at this time was linearly correlated
with IPSP amplitude (slope = 0.24 imp · s1 · mV
1, r = 0.993). The decrease in firing
probability (estimated from the PSTH) was also linearly correlated with
IPSP amplitude (0.033 fewer spikes/mV, r = 0.977). In
the two other cells in which the effects of different amplitude IPSPs
were compared, the slopes of the relation between the PSF rate decrease
and IPSP amplitude were 0.40 (r = 0.999) and 0.10 (r = 0.724) imp · s
1 · mV
1. The
slopes of the linear relations between the decrease in firing probability and IPSP amplitude were 0.029 (r = 0.999)
and 0.015 (r = 0.905) fewer spikes/mV.
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EFFECT OF BACKGROUND DISCHARGE RATE ON PSF AND PSTH FEATURES. Although the background discharge rate of the motoneuron was generally kept at ~15 imp/s (see METHODS), in one cell we systematically examined the effects of altering background discharge rate. Figure 8 illustrates the relation between PSF features associated with a simulated EPSP (left) and a symmetrical IPSP (right) at different background discharge rates. The background discharge rate was increased from ~10 imp/s (top) to 17-18 imp/s (bottom). The PSF plots on the left show the effects of an 8-mV EPSP on discharge rate. The peak change in discharge rate was similar at all background discharge rates, as was the probability of an EPSP evoking an extra spike (not illustrated). However, the falling phase of the EPSP was illustrated more clearly at increasing background discharge rates.
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DISCUSSION |
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Our aim in this study was to test the hypothesis that the
stimulus-induced changes in the discharge frequency of motoneurons can
provide a better estimate of the underlying synaptic potential than the
PSTH (Türker and Cheng 1994; Türker
et al. 1997
). To test this hypothesis, we measured the effects
of injected current transients on the discharge probability and firing
rate of repetitively discharging rat hypoglossal motoneurons.
Repetitive discharge was elicited by injected current steps with
superimposed noise to mimic the noisy synaptic drive likely to occur
during physiological activation. The time course and amplitude of the
injected current transients were chosen to mimic the synaptic currents
produced by synchronous activation of large numbers of afferent fibers (simulating compound EPSPs and IPSPs). The spike times and discharge frequencies then were used to build PSTHs and PSFs, and they were compared with the underlying PSP profiles.
Comparison of PSTH and PSF techniques
Previous estimates of synaptic potentials based on motoneuron
discharge have relied almost exclusively on stimulus-evoked changes in
firing probability, indicated by peaks or troughs in the PSTH (reviewed
in Awiszus 1997; Miles 1997
). In
agreement with previous findings (Cope et al. 1987
;
Fetz and Gustafsson 1983
; Poliakov et al.
1997
), we found that for excitatory inputs the PSTH peaks were
slightly wider than the rising phase of the EPSP but narrower than the
time course of the EPSP itself. These findings are consistent with the
proposal that for large inputs the time course of the PSTH is
proportional to the PSP derivative (Fetz and Gustafsson
1983
). However, this approximation may only hold for a limited
range of PSP shapes and sizes because clear deviations from this
prediction have been observed for small PSPs (Gustafsson and
McCrea 1984
) and for both complex EPSPs and IPSPs (Fetz
and Gustafsson 1983
). Although Gustaffson and McCrea
(1984)
reported that the PSTHs associated with small PSPs were
well fit by a linear combination of the shape of the PSP derivative and that of the PSP itself, the contribution of the PSP derivative predominates for larger PSPs (Poliakov et al. 1997
). The
present results indicate that the PSTH provides little or no
information about the falling phase of large EPSPs and confirm that the
PSTH does not reflect the PSP derivative in the case of biphasic PSPs (see Fig. 5).
The PSTH is particularly unsuitable for indicating changes in membrane
potential whose duration is of the same order as the mean interspike
interval of the postsynaptic cell. In the case of a regularly
discharging postsynaptic cell, such as a motoneuron, the initial
increase or decrease in discharge probability associated with the onset
of an EPSP or IPSP also gives rise to additional peaks and troughs that
are not related to the PSPs but occur due to the regular discharge of
the spikes following those that were affected by the PSPs. These
secondary effects of PSPs on the PSTH were noted in early descriptions
of the technique (Moore et al. 1970) and are revealed in
the autocorrelation of the postsynaptic cell. Quantitative assessment
of long-latency effects from the PSTH thus requires some means of
normalizing the PSTH based on the autocorrelogram (cf. Awiszus
et al. 1991
). However, these normalization techniques can be
computationally expensive compared with plots of the instantaneous
discharge frequency (or interspike interval) as a function of time from
the stimulus (Awiszus et al. 1991
).
In spite of these limitations, the primary features of the PSTH can be
used to predict the relative amplitude of EPSPs and IPSPs. When the
area of the PSTH peak associated with EPSPs was normalized to the
number of stimuli, in our data, the probability that an EPSP would
evoke an extra spike was linearly related to the peak amplitude of the
underlying EPSP. The average slope of this relation was 0.07 extra
spikes per millivolt of EPSP, which is comparable to a slope of 0.11 extra spikes per millivolt found for single fiber Ia EPSPs in cat
motoneurons (Cope et al. 1987). The slightly lower slope
found in the present results could result both from differences in the
motoneuron properties in the two preparations as well as from the
larger EPSPs used here. The area of the PSTH trough was also linearly
related to IPSP amplitude, although the slope values (0.015-0.033
fewer spikes/mV) were much lower than those found for EPSPs. This is
consistent with previous analysis of the effects of small EPSPs and
IPSPs (see Fig. 2 of Poliakov et al. 1997
).
Our results indicate that some of the limitations of PSTHs can be
avoided when the effects of synaptic potentials are analyzed in terms
of stimulus-linked changes in spike frequency rather than changes in
the probability of spike occurrence. The PSF used here is similar to
the interspike-interval superposition plot (IISP) originally introduced
by Awiszus (1988) except that each point on the display
is the reciprocal of the affected interspike interval (i.e., the
instantaneous frequency) rather than the value of the interspike
interval itself. Both techniques avoid the count and
synchronization-related errors associated with the PSTH because it is
the value of the affected interspike interval or its reciprocal that is
used to estimate the underlying synaptic potential instead of the
number of discharges that occur at a particular time lag. The PSF has
the additional advantage that the sign of the synaptic input is
directly reflected in the stimulus-evoked changes in frequency. In
fact, our result show that for excitatory inputs the PSF followed the
entire PSP profile during the first interspike interval. These findings
support the conclusions of Türker and co-workers that the
prolonged increase in discharge frequency after an H reflex
(Türker and Cheng 1994
) and following a tendon jerk (Türker et al. 1997
) is evidence of prolonged
synaptic excitation of the parent motoneuron, rather than an artifact
of the technique as has been claimed (Miles 1997
).
Furthermore we found that the peak change in frequency was linearly
related to EPSP amplitude over a wide range of amplitudes.
The PSF provided less information on the time course of IPSPs because
the large IPSPs used in the present study generally prevented discharge
until their rising (repolarization) phase. Nonetheless the PSF
correctly indicated a decrease in discharge frequency during the rising
phase of the IPSP, rather than a period of excitation, as indicated by
the peak in the PSTH at this time. The size of the drop in frequency
was linearly related to IPSP amplitude, although as in the case of the
PSTH, the slope of this relation was lower than that for EPSPs. Thus as
far as the total duration and the profile of the underlying IPSP is
concerned, the PSF avoids many of the errors associated with
interpretation of PSTH features. The PSTH does not indicate the
duration of the inhibitory event because when the delayed spikes
finally occur, they induce a large increase in the discharge
probability in the PSTH that has been wrongly interpreted as an
excitatory event. This point has been discussed widely in the human
reflex literature (Miles and Türker 1987;
Miles et al. 1987
; van der Glas and van Steenberghe 1989
). Unlike the PSTH, the PSF does indicate the rising phase of the IPSP and hence indicate the total duration of the
IPSP for slower IPSPs. The PSF also can trace the profile of the
falling phase of the IPSP quite well, especially when the stimulus
intensity is small and/or background discharge rate is high. However,
at very high background rates (Fig. 8, at 18.3 Hz), this fit can become
distorted with some higher than expected frequency events occurring at
the peak of the IPSP. The reasons underlying this phenomenon need to be
investigated further.
The early time course of the PSF reflects the primary effects of PSPs
on discharge rate, i.e., changes in the interspike interval in which
the PSP occurs. In the case of large PSPs, the following interspike
interval was also affected. The discharge rate of the following
interval was reduced after EPSPs and increased after IPSPs. These
secondary effects are most easily explained by summation of the
conductance underlying the postspike afterhyperpolarization (Baldissera and Gustafsson 1974; Baldissera et
al. 1978
). During repetitive discharge at rates above the
minimum steady discharge rate, the AHP conductance does not decay to
zero during the interspike interval, so that the conductance after a
given spike is summed on top of the residual conductance left from the
previous discharge. For intervals shortened by EPSPs, this residual
conductance is likely to be higher than that remaining at the end of
unaffected intervals so that the peak AHP conductance is increased in
the subsequent interval and that interval is longer than normal.
Similarly, intervals after IPSP-lengthened intervals will be shortened
due to a decrease in the amount of AHP conductance left at the end of
the affected interval. These history-dependent effects limit the
usefulness of the PSF as a quantitative measure of long-lasting or
complex synaptic potentials because secondary effects evoked by the
early portion of the synaptic potential are likely to add to the
primary effects of the later portion of the PSP.
Estimating synaptic potential amplitude from PSTH and PSF features
Our results indicate that both the PSTH and the PSF can be used to
estimate the relative amplitude of a synaptic potential. A model or
estimate of the interspike membrane potential trajectory is needed to
obtain an absolute estimate of PSP amplitude. A number of investigators
have modeled the interspike trajectory as an initial postspike drop in
potential followed by a linear rise to threshold to derive quantitative
estimates of PSP amplitude from PSTH features (Ashby and Zilm
1982; Fetz and Gustafsson 1983
; Miles et
al. 1989
) or from stimulus-evoked changes in discharge frequency (Türker and Cheng 1994
) or interspike
interval (Poliakov et al. 1994
). These models are based
on the observation that during repetitive discharge, the interspike
voltage trajectories of cat lumbar motoneurons are fairly stereotyped
particularly over the latter portion of the interspike interval in
which the membrane rises linearly toward threshold (Calvin and
Stevens 1968
; Schwindt and Calvin 1972
). Spikes
are advanced in these models whenever the rising phase of an EPSP
exceeds the gap between membrane potential and threshold.
Errors in estimates based on these models may arise from the omission
of certain important biophysical features of real motoneurons, such as
interspike variations in membrane conductance and in the voltage
threshold for spike initiation (Powers and Binder 1996). Although interspike variations in spike threshold have been
demonstrated experimentally (Calvin 1974
; Calvin
and Stevens 1968
; Powers and Binder 1996
) and
also acknowledged in the application of motoneuron models (Ashby
and Zilm 1982
; Fetz and Gustafsson 1983
), spike threshold often is assumed to be fixed. Similarly, although interspike variations in membrane conductance are well documented
(Baldissera and Gustafsson 1974
; Mauritz et al.
1974
; Schwindt and Calvin 1973a
,b
),
threshold-crossing models typically assume that membrane conductance
remains fixed at its resting value.
The interspike trajectory of membrane potential is therefore only one
factor affecting the ability of EPSPs and IPSPs to alter the interspike
interval. It is the combined effect of changes in membrane potential,
conductance, and spike threshold that determine the effective distance
to threshold at a particular point in the interspike interval and hence
limit the usefulness of all indirect techniques of assessing synaptic
potential including the PSF. This point is illustrated in Fig.
9A, which shows the average membrane trajectory of a rat hypoglossal motoneuron with simulated EPSPs superimposed on it. The average membrane trajectory was obtained
from a response to current alone that produced a background firing rate
of ~16 imp/s. The EPSPs are the same as those illustrated in Fig. 3,
and their placement on the average trajectory was determined from the
peak firing rate that each EPSP produced. For example, the largest EPSP
produced a peak firing rate of 36.3 imp/s, which occurred at the peak
of the EPSP. The reciprocal of this rate gives a mean interval of 27.5 ms, so the EPSP was aligned so that its peak occurred 27.5 ms after the
preceding spike. The other EPSPs were aligned in a similar fashion. A
rough estimate of the voltage threshold for spike initiation in the
absence of an EPSP based on the assumption of a fixed spike threshold
is shown in Fig. 9 (- - -). The fact that the different size EPSPs
peak at different distances from this line indicates that the effective distance to threshold is determined by factors other than the average
membrane trajectory. Early in the interspike interval, the membrane
conductance is much greater than at rest (Baldissera and
Gustafsson 1974; Mauritz et al. 1974
;
Schwindt and Calvin 1973a
,b
) so that the EPSP amplitude
will be less than that estimated at the resting potential, and as a
result, the effective distance to threshold is greater than the
distance from the average membrane trajectory to the dashed line.
Toward the end of the interspike interval, membrane conductance is
closer to its resting value and the spike threshold is lower than its
value at the end of the interspike interval (cf. Fig. 5 of
Powers and Binder 1996
), so that the effective distance
to threshold is less than the distance from the average trajectory to
the dashed line (cf. Türker 1995
).
|
The same factors that produce errors in estimates of EPSP amplitude are likely to affect estimates of IPSP amplitude. Figure 9, A and B, shows triangular approximations ( · · · to the average interspike voltage trajectory. Figure 9B shows the expected effects of superimposing IPSPs of different amplitude on this trajectory. The largest increases in interspike interval would be expected to result when the IPSPs occur late in the interspike interval. When IPSPs of different amplitude are added to the model trajectory, threshold-crossing is delayed for almost the entire duration of the IPSP. This simple approximation predicts that even the smallest IPSPs will lead to a decrease in discharge rate from 16 to ~8 imp/s, whereas the experimental results indicated a maximum decrease in rate of only about half this amount. The approximation of Fig. 9 does not consider the effect of noise, which will tend to produce earlier spike triggering and thus decrease the discrepancy between the predicted and experimental results. However, at least part of this discrepancy is likely to result from the fact that the membrane hyperpolarization produced by the IPSP leads to a decrease in the voltage threshold for spike initiation because hyperpolarizing current pulses can decrease spike threshold (R. K. Powers and M. D. Binder, unpublished observations).
The complex interaction between synaptic potentials and the membrane
conductances underlying repetitive discharge underscores the fact that
both the PSTH and PSF methods are indirect techniques for estimating
synaptic potentials, and investigators should be aware of their
limitations. For example, even though the PSF records do not contain
synchronization and count related errors, secondary effects related to
the length of the preceding interspike interval imply that increases or
decreases in the instantaneous discharge rate at long latencies cannot
necessarily be attributed to long latency excitatory or inhibitory
connections (cf. Awiszus et al. 1991;
Türker et al. 1997
). Because the PSF can only
indicate the time course of a PSP for durations shorter than the mean
background interspike interval, estimates of PSP time course will be
affected by the mean discharge rate of the motoneuron. Although we
systematically varied background discharge rate in only one case, our
limited results are consistent with other evidence that an increase in discharge rate allows a more accurate description of the falling phase
of PSPs. In particular for predicting the properties of the IPSP, the
background discharge rate is of utmost importance because the
proportion of the IPSP over which discharge occurs increases with
increasing discharge rate. This is very similar to the finding on the
effect of inhibitory reflex on human motoneurons (Miles and
Türker 1986
).
In summary, the present results indicate that the time course of synaptic potentials can be estimated more accurately from stimulus-related changes in discharge frequency than from changes in discharge probability. Although both types of measurements can be used to estimate the relative amplitude of synaptic potentials, estimates of absolute magnitude and profile depend critically on an accurate representation of the how the "effective distance to threshold" varies during the interspike interval. This effective distance represents a combination of membrane potential, membrane conductance and spike threshold changes. In addition, PSP-evoked changes in an interspike interval are likely to affect the length of the following interval due to changes in AHP summation. As a result, the changes in discharge rate associated with PSPs lasting longer than a typical interspike interval reflect both the PSP time course and the recent discharge history. By measuring PSPs, membrane properties and discharge characteristics in the same cells, we hope to develop a motoneuron model that can provide a more accurate estimate of the relation between PSP properties and their effects on discharge.
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ACKNOWLEDGMENTS |
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We thank C. Madore for assistance with the surgery. We are grateful to Prof. Marc Binder for encouragement and support during this study and valuable comments and contributions to the manuscript. We thank Prof. Eb Fetz for scrutinizing the manuscript.
This study was supported by National Institute of Neurological Disorders and Stroke Grants NS-26840 and NS-31925 and the National Health and Medical Research Council of Australia.
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FOOTNOTES |
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Address reprint requests to Kemal S. Türker.
The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
Received 11 January 1999; accepted in final form 22 April 1999.
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REFERENCES |
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