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The Journal of Neuroscience, December 15, 2001, 21(24):9608-9618
Random Response Fluctuations Lead to Spurious Paired-Pulse
Facilitation
Jimok
Kim1 and
Bradley
E.
Alger1, 2
1 Program in Neuroscience and 2 Department
of Physiology, University of Maryland School of Medicine, Baltimore,
Maryland 21201
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ABSTRACT |
We studied paired-pulse depression (PPD) of GABAAergic
IPSCs under conditions of reduced transmitter release (caused
by Cd2+, baclofen, or reduced stimulus intensity)
with whole-cell voltage clamp in CA1 pyramidal cells in
vitro. The use-dependent model of paired-pulse responsiveness
holds that a decrease in the probability of neurotransmitter release
during the first stimulus will cause predictable changes in the
paired-pulse ratio (PPR, the amplitude of the second IPSC divided by
that of the first). However, the applicability of the use-dependent
model to inhibitory synapses is controversial. Our results are
inconsistent with this model, but are consistent with the hypothesis
that random fluctuations in response size significantly influence PPR.
PPR was sensitive to the extracellular stimulus intensity in all
conditions. Changes in PPR were not correlated with changes in the
first IPSC, but were correlated with changes in variability of the PPRs
of individual traces. We show that spurious paired-pulse facilitation
(PPF) can result from averaging randomly fluctuating PPRs because the method of calculating PPR as the mean of individual PPRs is biased in
favor of high values of PPR. Spurious PPF can mask the intrinsic paired-pulse property of the synapses. Calculating PPR as the mean of
the second response divided by the mean of the first avoids the error.
We discuss a simple model that shows that spurious PPF depends on both
the number of synapses recruited for release and the probability of
release at each release site. The random factor can reconcile some
conflicting published conclusions.
Key words:
short-term plasticity; neurotransmitter release; use
dependency; release probability; hippocampus; GABAergic IPSC
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INTRODUCTION |
The small size and inaccessibility
of most nerve terminals in the CNS make direct functional studies of
synapses difficult or impossible, and indirect methods are used to
study the control of neurotransmitter release. One method involves
paired-pulse stimulation of presynaptic cells (for review, see Zucker,
1989 ; Thomson, 2000). Two stimuli are delivered at a short interval (<5 sec), and a difference between the amplitudes of the first (A1)
and second (A2) responses, expressed as the paired-pulse ratio (PPR),
is taken to reflect a transient change in the probability of release.
Often there is an inverse relationship: the larger the A1, the smaller
the A2 and vice versa. This is the basis of the use-dependent model of
PPR. Neuromodulators or physiological processes that affect transmitter
release probability (Pr) affect PPR.
Conversely, changes in PPR often are assumed to reflect changes in the probability of neurotransmitter release. Use dependence describes paired-pulse responsiveness at many excitatory synapses (e.g., in dissociated hippocampal cell culture) [Dobrunz and Stevens (1997), although cf. Brody and Yue (2000)].
When inhibitory synapses are activated by paired stimulation, A2 is
normally smaller than A1 [i.e., paired-pulse depression (PPD)
occurs]. Less transmitter is released by the second stimulus because
of activation of GABAB autoreceptors in the CA1
(Davies et al., 1990) and dentate gyrus regions in the hippocampal
slice (Mott and Lewis, 1991) or because of transmitter depletion
resulting from the first release, as in CA3 cells in the slice
preparation (Lambert and Wilson, 1993, 1994) and at inhibitory synapses
in tissue culture (Wilcox and Dichter, 1994). Both are use-dependent processes. Nevertheless, the applicability of the use-dependent model
to changes in PPD at inhibitory synapses is not clear: decreasing the
probability of release by the first stimulus (e.g., with low [Ca2+]o) may not
increase PPR, as in synaptically coupled dentate granule cell-interneuron pairs (Kraushaar and Jonas, 2000). Within pairs, A2 and A1 may be uncorrelated, as also found by Kraushaar and Jonas
(2000) and by Waldeck et al. (2000) at the axo-axonic connections between Mauthner cells and cranial relay interneuron pairs.
GABAAergic inhibition plays vital roles in the
regulation of CNS excitability and is affected by numerous presynaptic
modulatory effects (for review, see Thompson, 1994; Alger and Le Beau,
2001); hence it is very important to understand the plasticity of
inhibitory synaptic transmission. We have reexamined the PPR of
monosynaptic GABAAergic IPSCs in the hippocampal
slice to resolve the apparent discrepancies between the use-dependent
model of PPR and the findings referred to. The use-dependent model
makes several predictions concerning the effects of an experimental
treatment on PPR. (1) There should be a direct relationship between the
change in A1 and the change in PPR. (2) Decreasing the probability of
release should cause a consistent increase in PPR. (3) The change in
PPR should be independent of the number of synapses that have been
activated. We tested these predictions by analyzing the changes in PPR
that occur when IPSCs are decreased by
Cd2+, baclofen, or reduction of the
stimulus intensity. Our results are inconsistent with the use-dependent
model and imply instead that random response variation can play a
significant role in apparent shifts from PPD to paired-pulse
facilitation (PPF) when "mean PPR" is calculated as the mean of the
individual PPRs. Unless otherwise stated, mean PPR refers to this
method of calculation. The findings have practical and theoretical
importance and raise questions concerning some previous conclusions
based on PPR.
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MATERIALS AND METHODS |
Preparation of slices. Hippocampal slices were
obtained, using conventional techniques, primarily from 4- to
6-week-old male Sprague Dawley rats, although ~20% of the
experiments were done on 16- to 20-d-old rats. There was no obvious
difference between the results with animals from these different age
groups, and all of the results have been combined. All experiments were
performed in accordance with the guidelines set forth by the
Institutional Animal Care and Use Committee of the University of
Maryland School of Medicine. After the animals were anesthetized deeply
with halothane and decapitated, the hippocampi were removed and
sectioned into slices 400 µm thick in ice-cold saline, using a
Vibratome (Technical Products International, St. Louis, MO). The slices
were maintained at room temperature in an interface holding chamber in
a humidified atmosphere saturated with 95%
O2/5% CO2. The slices were
used at least 1 hr after sectioning. The recording chamber warmed the submerged slice, and experiments were performed at 30 ± 1°C
(Nicoll and Alger, 1981).
Electrophysiology. Whole-cell voltage-clamp recordings of
CA1 pyramidal cells were performed via the "blind" patch method (Blanton et al., 1989) with patch electrodes (2-5 M in the bath). Recordings with series resistance <30 M were accepted. During the
experiments series resistance was checked by  1 mV hyperpolarizing voltage steps, and data associated with obvious changes of series resistance or unstable current baseline were discarded. Holding potential was 70 mV in all experiments. Monosynaptic IPSCs were elicited by 100 µsec extracellular stimuli delivered with concentric bipolar stimulating electrodes (David Kopf Instruments, Tujunga, CA)
placed in stratum pyramidale 0.5-1 mm apart from the recording site,
with the tip of the electrode lowered ~250 µm into the
slice. Evoked IPSC data were collected with an Axopatch 1C or Axoclamp 2B amplifier (Axon Instruments, Union City, CA), filtered at 2 kHz, and
digitized at 5 kHz with a Digidata 1200 and Clampex7 software (Axon
Instruments).
The intracellular recording solution contained (in mM): 90 or 85 CsCH3SO3, 50 CsCl2, 0.2 CaCl2, 1 MgCl2, 2 Mg-ATP, 2 Cs4-BAPTA, 10 HEPES, and 5 QX-314, pH 7.20 with
CsOH (295 mOsm). The extracellular solution included (in
mM): 120 NaCl, 3 KCl, 25 NaHCO3, 1 NaH2PO4, 2.5 CaCl2, 2 MgSO4, and 15 glucose (300 mOsm). The extracellular solution was oxygenated with 95%
O2/5% CO2 gas and flowed
continuously through the recording chamber at a rate of ~1
ml/min.
The local anesthetic QX-314 (Sigma, St. Louis, MO) was included in the
recording pipette to block sodium-dependent action potentials (Connors
and Prince, 1982) as well as postsynaptic GABAB
responses in the pyramidal cell (Nathan et al., 1990; Andrade, 1991).
To isolate monosynaptic IPSCs, we included ionotropic glutamate receptor blockers 10 µM
1,2,3,4-tetrahydro-6-nitro-2,3-dioxo-benzo[f]quinoxaline-7-sulfonamide (NBQX; Sigma) and 50 µM
DL-2-amino-5-phosphonopentanoic acid (DL-AP-5; Sigma) (Davies et al., 1990) in the bath solution throughout the experiments. Water-based stock solutions of CdCl2
(Sigma) or (±)baclofen (Research Biochemicals, Natick, MA or Sigma)
were added to the bath solution and perfused into the recording chamber
when needed.
Data analysis. Except where discussed in the text, PPR was
calculated by dividing A2 by A1. A1 and A2 were determined by measuring the difference between baseline amplitude immediately before the first
or the second stimulus and peak amplitude. To calculate a mean PPR in a
given condition, we recorded 20-50 individual traces,
calculated PPRs of individual traces, and averaged them. We called
these 20-50 traces in a given condition a "trace group." The
stimulus intensity was adjusted so that failures of evoked IPSC almost
never occurred. Only a few trace groups contained any failures, and
when a failure did occur, it was excluded from the trace group.
Data analysis was done with Clampfit 6.0.5 (Axon Instruments) and Excel
97 (Microsoft, Redmund, WA), and graphs were drawn in SigmaPlot 2000 (SPSS, Chicago, IL). Statistical tests were done in Excel 97 and
SigmaStat10 (SPSS), and the regression tests were performed in
SigmaPlot 2000 and Origin 6.0 (Microcal Software, Northampton, MA). All
t tests were two-tailed tests; the p value for
significance was < 0.05. Random number generation in Figure 1 was
done with Microsoft Excel 97 or SigmaPlot 2000. The neuronal network
stimulation program, Stella Research Software 5.1.1 (High Performance
Systems, Hanover, NH), was used for the simulations in Figures 1 and
7.
Simulation. Pairs of random integers were generated
initially by the random number generators in Excel 97 by using
"randbetween" or in SigmaPlot 2000 by using the "rand"
commands. The ratio of the second number divided by the first simulated
a PPR, and one trace group contained 50 PPRs. The results obtained with
both programs were indistinguishable, demonstrating that our
conclusions do not depend on the use of one particular random number
generator. The Excel random number generator was used for the
experimental results that are shown. Because each number has an equal
chance of occurrence, this type of model simulates a uniform spatial distribution of Pr. We obtained
virtually identical results (data not shown) by using the Gaussian
random number generator in SigmaPlot 2000, suggesting that a uniform
Pr distribution is also inessential to
the main conclusions.
To simulate physiological random PPRs more realistically, we generated
pairs of random numbers by assuming that Pr is
distributed in a spatially nonuniform manner and can be modeled by
nonuniform Pr distributions by  density functions (Martin, 1973) of the form:
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(1)
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where
Distributions have been used to describe the
Pr distributions of synapses in
tissue-cultured hippocampal neurons (Murthy et al., 1997). p
and f(p; , ) in Equation 1
represent Pr and the number of
synapses that have the release probability of p,
respectively. Two methods were used to evaluate the value of Equation 1. First, the integral value of () was calculated in SigmaPlot
2000 in the range from 0 to 5000 with increments of 0.05. Then the
integral value was plugged into Equation 1. With the second method the value of Equation 1 was calculated with the built-in function of Excel
97, "gammadist." In the range of 0.5-2, the difference in
Equation 1 values between the two methods was from 24 to 0.02%, respectively, whereas the difference between them was
<10 5% when was >2. When the
values of Equation 1 were multiplied by scaling factors consistent with
the total number of synapses being 200 (see below) or other numbers as
appropriate (see Fig. 7), the distributions were identical. We fixed
at 1/11 (cf. Murthy et al., 1997) and varied to obtain
Pr distributions with various mean
Pr values. When the mean
Pr is low, the shape of the
Pr distributions is skewed negatively,
and when the mean Pr is high, the
distributions are skewed positively. These distributions closely
resemble density functions used in modeling climbing fiber-Purkinje cell synapses (Silver et al., 1998).
Pr was binned by 0.05 from 0 to 1. For
each Pr the number of synapses was
calculated with Equation 1. Equation 1 was multiplied by a scale factor
so that the total number of synapses for a distribution was 200, except
for Figure 7, in which the total number of synapses was varied. We
chose to model 200 synapses because this approximated the number
expected to generate a typical IPSC amplitude in our experiments
(~1 nA) assuming a quantal IPSC amplitude of ~20 pA (Morishita and Alger, 1997), the release of a single quantum per action
potential per synapse, and the estimated
Pr of individual release sites ~0.4
(based on data in Miles and Wong, 1984; Buhl et al., 1995; Vida et al.,
1998). If the true Pr differs from 0.4, then the number of synapses could be too high or too low, but in
general these numbers represent reasonable estimates of the actual
physiological conditions. To simulate a probabilistic release event
from this nonuniform distribution, we compared the Pr at each synapse with a random
number generated between 0 and 1; if
Pr was greater than the random number,
the synapse was considered to have released a quantum, and if
Pr was less than the random number, a
failure of release was counted. The response size (i.e., amplitude) was
taken as the sum of releases across the population of synapses for a
given trial, with each response of a pair being simulated by generating
a new random number distribution. Simulated PPR was obtained from the
ratio of two response sizes simulated in this way. A trace group
consisted of 50 simulated PPRs.
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RESULTS |
Computer simulations
A widely used method of calculating the PPR is to take the mean of
the ratios of responses to pairs of stimuli, A2/A1 [i.e., mean(A2/A1)]. If PPR > 1, an increase in the probability of
transmitter release is said to have occurred. However, the mean(A2/A1)
method of calculating PPR is biased systematically in favor of
detecting PPF. Consider two numbers (representing IPSC amplitudes)
a and b (where a, b > 0 and a  b); if a/b
is >1.0, then b/a will be <1. Moreover, because
a/b can be arbitrarily large (between 1 and
infinity) but b/a must be between 0 and 1, then
|a/b 1| > |b/a 1|. The mean of a set of such
a, b ratios will be >1 (i.e., it will appear
that PPF has occurred) even if the values a and b
occur randomly and are equally likely to occur as A2 or A1.
To show this graphically, we first simulated a paired-pulse experiment
by using a random number generator and assuming a uniform distribution
of random numbers (see Materials and Methods). We took pairs of random
numbers (ranging between 10 and 100 to simulate the process of
normalizing across experiments) and calculated the ratios of the pairs,
simulated PPRs, with 50 PPRs in each experimental trace group. We then
plotted the PPR against the corresponding value of simulated A1. An
inverse relationship between PPR and A1 has been considered to reflect
a use-dependent mechanism, because a small A1 should cause a large
increase in PPR. Nevertheless, Figure
1A shows that, when
individual PPRs of a simulated trace group are plotted against A1, an
inverse relationship is generated. In Figure 1A, the
largest values of simulated PPR were associated with the smallest
values of A1 simply because a small value of A1 is statistically likely
to be followed by a larger value for A2 (PPF); conversely, a larger
first number is likely to be followed by a smaller second number (PPD).
Thus, the inverse relationship does not imply a physiological,
use-dependent mechanism. The mean PPR of all of the simulated data in
Figure 1A is 1.51 (i.e., it shows the bias toward PPF
introduced by random variability).
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Figure 1.
Simulation of paired-pulse ratios (PPRs)
by means of randomly generated numbers. Simulated PPRs were generated
assuming that the distribution of Pr across
the simulated population is either uniform (A,
B) or nonuniform (C, D).
A, To test whether spurious PPF can be obtained by the
simple occurrence of random numbers, we generated 50 pairs of random
numbers between 10 and 100 and took the ratio (simulated PPR) of the
second (A2) to the first (A1). When PPR is plotted against A1, the
result resembles the output of a use-dependent process. The mean of the
PPRs of this trace group is 1.51. B, Spurious PPF is
related to the CV of the distribution of sampled random numbers. We
varied the CV by restricting the range of random numbers that were
sampled and plotted the means of trace groups generated as in
A; one dot represents the mean PPR of one
trace group. The least variable numbers were generated between 90 and
100, and the most variable numbers were generated between 5 and 100. Spurious PPF increased monotonically as the CV of the population of
sampled numbers increased. In all figures CV is given as its absolute
value and is plotted as descending to the right to
emphasize that large values of CV are associated with small response
sizes. C, D, The analysis is the same as
in A and B except that a nonuniform
Pr distribution of a population of simulated
synapses was modeled with a density function (see Materials and
Methods). Simulation of probabilistic release was accomplished by
comparing an assigned Pr at a synapse with a
randomly generated number between 0 and 1; if
Pr was greater than a random number, then a
release was counted. C, Fifty pairs of random responses
were generated from a distribution of
Pr, with a mean of 0.033 (to simulate
low Pr conditions) and individual
Pr values distributed across 200 synapses.
Note again the inverse relationship between simulated PPR and A1. The
mean PPR of this simulated trace group is 1.32. D, CVs
of the nonuniform Pr distributions were
varied by varying the mean Pr of the distributions (from 0.013 to 0.645). Again, spurious PPF increases with
increasing the CV of simulated responses.
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The important factor leading to spurious PPF is not the small size of
A1 per se, but rather the coefficient of variation (CV) of the
populations of A1 and A2. This can be seen in Figure
1B, in which each dot represents the mean PPR of an
entire simulated trace group, such as the one seen in Figure
1A. To vary CV systematically, we varied the ranges
of the populations from which A1 and A2 were drawn randomly. Groups
with the lowest CV had random numbers between 90 and 100, and groups
with the highest CV ranged between 5 and 100. The mean PPR of randomly
generated pairs calculated with the mean(A2/A1) method was plotted
against the CV (Fig. 1B). The plot shows that PPF is
largest when CV is largest. Note that the values of PPR approach 1.0 as
the CV decreases toward 0. The CV for the simulated trace group in
Figure 1A is 0.48.
In these initial simulations we used simple random models to
demonstrate the generality of the result. Implicitly, these models resemble the physiological case in which uniform distributions of
release probabilities exist for populations of synapses. Yet uniform
distributions of Pr do not
characterize populations of synapses in the brain. Nevertheless,
spurious PPR can occur if we assume nonuniform
Pr distributions. To show this, we
used the program Stella and made a model based on data from the
population of glutamatergic synapses in tissue culture, which shows a
nonuniform Pr distribution that is
well described by the distribution (Murthy et al., 1997). This is a
realistic and convenient model that bears a close resemblance to the
distribution that also has been used to characterize possible
nonuniform Pr distributions (Silver et al., 1998). As can be seen in Figure 1C, the resulting plot
of PPR versus A1 for this simulated trace group resembles the
simulation in Figure 1A. To test the prediction that
spurious PPF would be correlated with the CV of the response
amplitudes, we produced six different distributions (by fixing and varying ) that had mean Pr
values that varied from 0.013 to 0.645. The
Pr distributions determined from
physiological experiments that characterize single release sites at
GABAergic synapses are generally thought to lie within this range (see
Materials and Methods). In Figure 1D each dot
represents the mean of a simulated trace group of 50 PPRs generated
randomly from these distributions, plotted against the CV of the trace
group. As in Figure 1B, the magnitude of spurious PPF
increases smoothly with increases in CV. Thus the conclusion that
spurious PPF can be produced readily by the mean(A2/A1) method does not
depend on the assumption of a uniform
Pr distribution.
These considerations do not prove that PPF calculated by the
mean(A2/A1) method is spurious (genuine, use-dependent PPF would be
detected with this method as well), but they do raise the concern that
PPF calculated in this way might be spurious. To determine whether the
presence of spurious PPF contributes to experimental paired-pulse
response data as well as to these computer simulations, we tested
several predictions of the use-dependent model.
Experimental tests of the use-dependent model of PPF
Evoked monosynaptic GABAA receptor-mediated
IPSCs were recorded from pyramidal cells in the rat hippocampal CA1
region by stimulating extracellularly in stratum pyramidale in the
presence of 50 µM DL-AP-5 and 10 µM NBQX (Davies et al., 1990). The paired-pulse interval
was 100 msec, and the interval between consecutive pairs of stimuli was
usually 5 sec, although in different cells it was between 4 and 9 sec
to permit full recovery of the IPSCs between pairs. To examine the
effects of decreasing the initial IPSC amplitude on PPR, we treated the
slices with 10- 60 µM
Cd2+ or 2-3 µM baclofen or
reduced the stimulus intensity. The first two manipulations should
change Pr, and hence PPR, under the
use-dependent model. The last will change the number of terminals
activated with less, if any, effect on
Pr. In normal saline, pairs of IPSCs were recorded at a few different stimulus intensities and then recorded
again in the presence of Cd2+ or baclofen
at the same intensities. Data were recorded from a total of 36 cells;
of these 14 were treated with Cd2+ and 13 with baclofen. For the remaining nine cells the data were recorded only
in normal saline at different stimulus intensities.
Inconsistent change of PPR and deviation from the
use-dependent model
The use-dependent model suggests that PPR should increase
consistently when the probability of release is reduced (i.e., less release on the first response will lead to greater release during the
second). However, we did not observe a consistent change in PPR in any
of the treatments, although they all produced significant decreases in
A1. Rather, the effects were mixed: PPR was increased or did not change
when Cd2+ or baclofen was applied or when
stimulus intensity was reduced (Fig.
2A,B). It was
surprising that both kinds of effects (increase or no change) could be
seen even in a single cell (Fig. 2A,C). In general,
Cd2+ or baclofen had no effect on PPR of
IPSCs evoked by higher stimulus intensities, but increased PPR when
lower intensities were used. This observation is shown graphically in
Figure 2C, in which we plotted the change in PPR, expressed
as a percentage of control PPR, for a given cell and treatment
condition obtained at two levels of stimulus intensity: weak and
strong. To compare the effects of reduced stimulation at two different
stimulus intensities (Fig. 2C, circles), we
recorded PPR at three intensities from a cell: strong, medium, and
weak. The variability in recording conditions from slice to slice
precludes general, precise definitions of these terms. A strong
stimulus was in the range 140-600 µA, and the responses that were
produced were very stable from trial to trial; the weak stimulus was in
the range of 50-130 µA, and the responses varied considerably, but
there were no, or few, response failures. The medium stimulus intensity
was between the other two. The PPR change from strong to medium
stimulus intensities is considered an effect at stronger intensity
(y-axis in Fig. 2C), and the PPR change
from medium to weak is an effect at weaker intensity (x-axis
in Fig. 2C). If the same degree of PPR change had been
produced at both stimulus intensities, the data points would fall on
the dotted line. In fact, they mostly fall to the right of the line,
meaning that there was a greater tendency toward PPF, or PPR increase,
when weak stimulation was used than when strong stimulation was used,
although both levels of stimulation were given to the same cell in the
same treatment condition. GABAB-dependent PPD
increases with increasing stimulus intensity (Davies et al., 1990;
Lambert and Wilson, 1994); therefore, differences in
GABAB-mediated autoinhibition cannot account for
this result. Because increases in stimulus intensity should increase
the numbers of fibers and synapses that have been activated without
changing the Pr, these data are not
predicted by a use-dependent model.
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Figure 2.
Effects of experimental treatments on measured
PPR. Cd2+ (10-60 µM), baclofen (2-3
µM), or reduced stimulus intensity had inconsistent
effects on PPR change. A, Whole-cell voltage-clamp
recordings of IPSCs evoked by paired-pulse stimuli at a holding
potential of 70 mV. Stimulus artifacts were removed graphically. The
PPR in control solution with strong stimulation was 0.75; with weak
stimulation it was 0.63 in the same cell. Baclofen (2 µM)
did not change the PPR significantly when the strong (140 µA)
stimulus was used (PPR was 0.83; i.e., 110% of control PPR) but
increased it in the same cell when weak (103 µA) stimulation was used
(PPR was 0.90; i.e., 143% of control PPR). Although the mean PPR was
averaged from 30 individual PPR traces, only five traces per condition
are shown for clarity. PPR was not altered by reduced stimulus
intensity in the control saline before adding baclofen in this example.
B, Histogram of PPR change after Cd2+
(n = 14 cells; 29 trace groups), baclofen
(n = 13 cells; 34 trace groups), or reduced
stimulus intensity (n = 15 cells; 30 trace groups)
compared with control PPR. Note the skew of distribution toward higher
values of PPR. The distributions of PPR change for individual treatment
are shown as a horizontal dot plot on the top of the
histogram; each dot represents mean PPR from one trace
group. The patterns of PPR change are similar in all treatments.
C, When data were obtained from a given cell at two or
more stimulus intensities, PPR changes at two intensities were
analyzed. One dot represents PPR changes in one cell at
two different stimulus intensities. Deviation of a
symbol from the dotted line means a
different change of PPR was recorded in the cell at different stimulus
intensities. In general, PPR increases at the lower intensity and does
not change at the higher intensity. D, The degree of PPR
change was not correlated with the degree of IPSC amplitude change. One
dot represents one trace group; PPR changes vary
independently of IPSC amplitude changes. The same conclusion can be
reached if the Cd2+, baclofen, and stimulus
intensity groups are plotted separately, as can be seen from inspection
of the individual symbols.
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According to the use-dependent model, decreases in
Pr should cause increases in PPR, and
there should be an inverse relationship between the degree of
depression of A1 and the change in PPR. The cell-to-cell variation of
IPSC reduction induced by the experimental treatments was very large
and ranged from 5 to 90% of control amplitude. However, there was no
correlation between the PPR change and IPSC amplitude changes that were
observed (Fig. 2D). We analyzed the
Cd2+, baclofen, and stimulus intensity
groups separately and found no correlation between PPR and degree of
depression of A1 within these groups (data not shown); therefore, the
data were combined in Figure 2D.
Another commonly used method of assessing use dependence is to
plot A2 versus A1 for each pair of responses (Kraushaar and Jonas,
2000; Waldeck et al., 2000); the use-dependent model predicts an
inverse relationship between them. Accordingly, we plotted A2 against
A1 for every trace group from 25 cells [57 trace groups in normal
saline, 20 trace groups in Cd2+, and 22 trace groups in baclofen (data not shown)]. Of 99 trace groups the
great majority (92 of 99) had an
r2 value of <0.1 (i.e., no
correlation), and only seven showed a significant negative relationship
(p < 0.05;
r2 = 0.33; slope, 0.53)
between A2 and A1. Therefore, in agreement with previous reports
(Kraushaar and Jonas, 2000; Waldeck et al., 2000), we conclude that use
dependence may not be the main underlying mechanism of PPR of IPSCs.
Both larger and smaller values of PPR are associated with increases
in mean PPR
We find that the variability of individual PPRs increases along
with the increase in the mean PPR of the trace group, as might be
expected from the increased variance of individual responses predicted
by the variance-mean analysis of transmission (Silver et al., 1998).
However, there is also a greatly increased occurrence of individual
PPRs that are smaller than the PPRs in control, which would not be
expected in a simple use-dependent model. Examples of traces from a
single cell are shown in Figure
3A. Both the first and second
IPSCs in the pairs were relatively constant over several trials in
control solution. After Cd2+ (30 µM for this cell) was added to the bathing
solution, both responses (A1 and A2) became much more variable, with
some individual PPRs being higher and many others lower than those in
control. The complete set of data from this cell is shown in the graph below the traces.
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Figure 3.
When variability of individual PPRs increases,
mean PPRs also increase. A, The individual traces at the
top are representative samples from a single cell before
and after Cd2+ (30 µM) application.
The mean PPR increased from 0.78 to 1.16 (dotted lines)
as in the graph of the complete set of data from this cell. One
dot represents one individual PPR. Individual PPRs range
from very low to very high. B, Trace groups with larger
mean PPRs have higher variability of individual PPRs. SD values of PPR
(SDPPR) within a trace group were plotted against
the mean PPR of the trace group. One dot represents one
trace group. The variability is fairly constant below a PPR of ~0.85
in contrast to the variability when the PPR > 1.0 (the PPF
region), in which variability increases proportionally with PPR. In the
PPR region between 0.85 and 1.0 there is an intermediate pattern of
variability. C, When mean PPR increased, the largest
individual PPRs increased, and the smallest PPRs decreased. The means
of the three largest PPRs (open circles) and of the
three smallest PPRs (filled circles) in a trace
group were calculated from trace groups that showed a mean PPR increase
after the treatments. Data were divided into three groups according to
the PPR after treatment (PPRtreat). In the group of
PPRtreat < 0.85 (n = 15 trace
groups), the largest and the smallest PPRs did not change (paired
t tests, p > 0.1). In the other two
groups (n = 23 trace groups each), however, the
largest PPRs increased and the smallest PPRs decreased when mean PPR
increased. Data from all treatments were pooled because they showed
similar patterns individually. The left dot in each pair
represents the control value, and the right dot
represents the value after treatment. The error bars are SEM. The
numbers of trace groups treated by reduced stimulation,
Cd2+, or baclofen, respectively, included the
following: for PPR < 0.85: 3, 4, and 8; for PPR between 0.85 and
1: 6, 9, and 8; for PPR > 1: 11, 8, and 4. *Paired
t test, p < 0.01. D,
The largest and smallest PPRs are related inversely in groups showing
mean PPF. Each symbol represents the mean of the three
largest PPRs of a trace group plotted against the mean of three
smallest PPRs of the given trace group. Data are from trace groups for
which the mean PPRs were >1.0. The solid lines in
D-F are the y = 1/x
curves, which describe a perfect inverse relationship.
E, The same plot as in D made for groups
with mean PPRs below 0.85. F, The same plot as in
D and E for simulated data. Filled
circles are trace groups with a CV of A1 > 0.3;
open circles are trace groups with a CV of A1 < 0.3.
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In all treatments we found that the trace groups with higher mean PPRs
had higher variability of individual PPRs than those groups with lower
mean PPRs. This relationship is shown in Figure 3B, in which
we plotted the variability (SD) of PPR within a group against the mean
PPR of that group in all conditions. Data in Figure 3B were
from all 36 cells (178 trace groups). The relative variability was
fairly low and constant when PPR was below 1 (i.e., PPD was present)
but then began to rise and was very large in the region when PPR was
>1 (PPF).
To determine whether it is generally true that when individual PPRs
became variable the mean PPR increases, we took the largest three
individual values of PPR for a given trace group and the smallest three
values of that group as a measure of the range of values in the group.
We then compared these values for control and experimental conditions
in cases in which the mean PPR increased in the experimental treatment,
because this was the direction of change predicted by the use-dependent
model. Because the changes in variability of PPR were clearly dependent
on the value of the mean PPR in a given condition (Fig. 3B),
we analyzed the data in three groups: final value of PPR below 0.85, PPR between 0.85 and 1.0, and PPR >1.0. These data are summarized in
Figure 3C. When the final PPR was low, there was hardly any
change in the distribution of values of the PPR (paired t
test between control group and treatment group, p > 0.1). In the other two groups the lowest values of PPR were
significantly lower than control, and the highest values were
significantly higher than control (paired t test,
p < 0.01).
The changes in variability of PPR are consistent with the random
fluctuation model, but may not exclude use-dependent models, because
increases in absolute response variance associated with decreases in
Pr can be seen in variance-mean plots
(Silver et al., 1998). To determine whether the variability in PPR that
we recorded actually reflected random response fluctuations, we applied several tests.
Highly variable PPRs might arise from random A1 and A2
One prediction of the random model is that there will be an
inverse relationship between the largest PPR and the smallest PPR
within a trace group. Consider two of the possible values for A1 and
A2, say a and b. If a and b
occur randomly within an experiment, then the value of PPR
a/b should occur as frequently as the value
b/a. The occurrence of a/b
and b/a will be related inversely (i.e., within a
given trace group the largest values of PPR will be related inversely
to the smallest values of PPR). To test this prediction, in Figure
3D we plotted the mean of the three largest PPRs,
y, in a trace group against the mean of the three smallest
PPRs, x, of the same trace group for the
Cd2+, baclofen, and low-stimulus-intensity
data. When the mean of the PPRs was >1.0, the relationship between the
largest and smallest PPRs within the group was close to the inverse
relationship, y = 1/x, predicted by the
random model (Fig. 3D, solid line). However, such
a relationship was not found when PPR was <0.85 (Fig. 3E) or when 0.85 < PPR < 1.0 (data not shown). Finally, Figure
3F shows the fit of y = 1/x to
simulated PPR data generated by the random model, using either functions having different CVs (which was necessary to obtain the full
range of PPR ratios to make the comparison) or a uniform
Pr model.
Additional tests of the random model
If the pattern of individual PPRs reflects random variability, it
would be the same with long interstimulus intervals at which there is
no short-term plasticity as with the 100 msec interval. If the pattern
of individual PPRs at the 100 msec interstimulus interval reflects a
genuine physiological property, it should change with long
interstimulus intervals because of recovery from short-term plasticity
at these intervals. In these experiments the long interstimulus
intervals were between 4 and 9 sec for different trace groups, although
within a trace group the interval was fixed. To calculate PPRs with
4-9 sec interstimulus intervals, we divided a given A1 by the previous
A1 within the same trace group (Fig. 4).
Although A2 was evoked between A1 and the next A1, the interval between
A2 and the next A1 was long enough to eliminate any use dependence.
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Figure 4.
Comparison between PPR at short and long
interstimulus intervals. The short interval was 100 msec; the long
interval varied between different cells between 4 and 9 sec (but was
constant for a given cell). PPR at long intervals was calculated by
dividing A1 from one pair by the A1 of the immediately preceding pair.
Because the interpair interval was 4-9 sec, "A1/previous A1" is a
good approximation to long intervals.
A1, Representative cell with PPR < 0.85. At the 100 msec interval this cell showed PPD
(filled circles), but the mean PPR changed to
~1.0 at the long interval (open circles). One
dot is one PPR. A2,
Group data (n = 87 trace groups) in which PPR < 0.85 shows significant changes in mean PPR and in the distribution
of individual PPRs. The histogram compares the mean PPRs, the three
largest PPRs, the three smallest PPRs, and the SDPPR of the
trace groups at the 100 msec (filled bar) and
long (open bar) intervals. The asterisks
indicate significant differences (paired t tests,
p < 0.01). B1,
Representative trace groups from a cell with PPR > 1.0 both at
the 100 msec and at the long intervals.
B2, Group data for 40 groups
that showed PPF at the 100 msec and at the 4-9 sec intervals. The
histogram shows that the mean PPR and the PPR distribution patterns at
these two intervals did not differ (paired t test,
p > 0.05).
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In the trace groups with mean PPR < 0.85 (i.e., PPD), the mean
PPR increased to ~1 at the 4-9 sec interstimulus intervals (Fig.
4A). Of 178 trace groups gathered from all cells, 87 had mean PPR < 0.85, and these changed from 0.74 ± 0.010 to
1.01 ± 0.0035 (paired t test, p < 0.01; Fig. 4A2) with the change of interval from 100 msec to 4-9 sec. This suggests that PPD was a
genuine property of the responses. In contrast, when the mean of the
PPRs was >1.0 (i.e., PPF) at 100 msec (40 of 178 trace groups), then
PPR did not change with the interval change from 100 msec to 4-9 sec
(Fig. 4B); the mean PPR was 1.23 ± 0.031 at the
100 msec interval and was 1.29 ± 0.052 at the 4-9 sec interval (paired t test, p > 0.05; Fig.
4B2). We
again compared the three largest PPRs, the three smallest PPRs, and SD
of PPRs within a trace group. In addition to the lack of change in the
mean PPR, the pattern or distribution of individual PPRs within a trace group was not significantly different at the two intervals (paired t test, p > 0.05; Fig.
4B2). The lack of change in PPR
between the 100 msec and the 4-9 sec PPR intervals strongly implied
that apparent PPF was caused by random fluctuations of A1 and A2.
Spurious PPF is eliminated by the meanA2/meanA1 method
If A1 and A2 differ simply because of random variation, then
within a trace group mean A1 should be the same as mean A2. If PPR were
calculated by dividing mean A2 by mean A1, spurious PPF would be
eliminated because the random fluctuations that give rise to it would
average out. To test this, we recalculated mean PPR for each trace
group by the meanA2/meanA1 method and plotted these values against the
mean PPR calculated by mean(A2/A1) (Fig. 5). PPRs > 1 calculated with
mean(A2/A1) changed to ~1 with the meanA2/meanA1 method, as predicted
by the random model. Interestingly, many of the PPRs that were <1 also
shifted toward smaller values (Fig. 5B), implying that the
effects of random fluctuations also bias the mean PPR in this region,
even when overt PPF is not calculated.
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Figure 5.
Spurious PPF disappears when PPR is calculated by
meanA2/meanA1. A, For each trace group the PPR was
calculated by dividing the mean of all of the A2 values for a given
group by the mean of the A1 values for that group (meanA2/meanA1); this
PPR value was plotted against the PPR calculated by mean(A2/A1). Note
that PPF calculated as the mean(A2/A1) (i.e., values >1.0 on the
x-axis) disappeared with the meanA2/meanA1 method.
B, The region between 0.65 and 1.0 of the plot in
A is expanded. Deviation of PPR values from the
dotted line also can be seen in the PPD region (values
<1.0), indicating that random fluctuations also influence PPD values
calculated by mean(A2/A1) even when spurious PPF is not apparent.
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Because the spurious PPF is dependent on the CV of the data points as
well as on the method of calculation, the random model predicts that
spurious PPF in the experimental data should depend on the CV of A1, as
was true in the simulated data in Figure 1. We therefore replotted our
experimental PPR data, using mean(A2/A1), against the CV of A1 for each
experimental trace group. PPF clearly was associated with the higher
values of CV (Fig. 6A).
If PPF in this case is spurious, then replotting the experimental PPR data by using meanA2/meanA1 against the CV of A1 should remove it.
Figure 6B confirms this expectation: virtually all of
the points fall below the value 1.0, revealing the consistent
occurrence of PPD throughout the range of experiments. Figure
6C presents a similar plot of meanA2/meanA1 versus CV of A1
for data simulated by using functions, showing, as expected, that
the points scatter about 1.0 (i.e., there is no tendency for PPF or PPD
in the random data when meanA2/meanA1 is used).
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Figure 6.
Spurious PPF as a function of CV in experimental
and simulated data. A, Experimental data were plotted as
the mean PPRs of a trace group versus a CV of the same trace group, as
in Figure 1, B and D. PPF increases as CV
increases as in the simulated pattern in Figure 1, B and
D. B, Recalculation of the data in
A by meanA2/meanA1 and plotting it against a CV of A1
removes spurious PPF without altering PPD. C, The
simulated PPR data in Figure 1D were recalculated
with meanA2/meanA1 and plotted against CV. Spurious PPF in large part
disappeared; the symbols vary ~1.0.
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Sources of random fluctuations
For simplicity, we assume that the random variability that
dominates experiments such as these arises principally from variability in the numbers of synapses that have been activated and in the probability of transmitter release from each synapse. We manipulated these factors experimentally by changing the stimulus intensity or by
the addition of either Cd2+ or baclofen
and found that both kinds of manipulations appear to be equivalent in
their tendency to produce spurious PPF. To verify that the resulting
changes in CV alone were sufficient to cause spurious PPF, we simulated
PPR calculated by mean(A2/A1) and varied both the numbers of synapses
that had been activated and the mean
Pr of nonuniform distributions of
Pr, as in Figure 1. The results, shown
in Figure 7, make two points: decreasing Pr and decreasing the number of
activated synapses dramatically increase spurious PPF. Conversely,
increasing the number of synapses that have been activated (analogous
to increasing stimulus intensity) decreases spurious PPF for any given
Pr. This latter result explains the
observation in Figure 2 that varying the stimulus intensity in a given
condition alters the PPR.
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Figure 7.
Theoretical model of dependence of spurious PPF on
Pr and stimulus strength when mean(A2/A1) is
used. Random PPRs were simulated by a nonuniform
Pr distribution ( density function) as in
Figure 1, C and D. The total number of
activated synapses (n) was varied from 10 to
4000. [The bin size for the Pr distribution
(see Materials and Methods) was 0.05 except when n was
<100 and Pr = 0.645; then it was
0.1.] This simulation was done with three mean
Pr values of the functions (indicated by
different symbols). Each symbol
represents the mean of 6-15 trace groups ± SEM, and each trace
group comprised 50 individual PPRs. Note that PPR is dependent both on
the mean Pr of the population and on the
number of activated synapses. Moving along the y-axis at
a particular x point simulates the addition of
Cd2+ or baclofen application (i.e., decreasing
Pr) at a fixed stimulus intensity. As
Pr decreases, spurious PPF increases. Moving
along the x-axis simulates increasing the stimulus
intensity (increasing the number of activated synapses). For every
value of Pr, increasing the number of
activated synapses decreases spurious PPF; decreasing this number
increases PPF. Therefore, spurious PPF will increase as stimulus
intensity is decreased.
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DISCUSSION |
We conclude that changes in PPR do not necessarily reflect changes
in the probability of neurotransmitter release. The unrecognized influence of random fluctuations in response amplitudes can lead to
erroneous interpretations of experiments that use the PPR calculated by
mean(A2/A1). When A1 and A2 are small and vary randomly, then mean PPR
will tend to be high by chance alone, and the intrinsic paired-pulse
property of the synapse can be masked. This is a particular problem
because the effect of the random error is in the direction of the
changes predicted by use-dependent models. In these experiments we used
Cd2+ and baclofen to reduce IPSCs by
reducing transmitter output at individual synapses, and we used a
decrease in stimulus intensity to reduce IPSCs without reducing the
amount of transmitter released by an individual synapse. Both
GABAB-dependent and
GABAB-independent mechanisms for PPD exist
(Davies et al., 1990; Mott and Lewis, 1991; Lambert and Wilson,
1993, 1994). Reductions in GABA release by
Cd2+ should reduce both forms of PPD at
all GABAA synapses, and baclofen will reduce PPD
at all GABAA synapses with presynaptic
GABAB receptors. Cd2+ and baclofen therefore should have
qualitatively similar effects on PPD under the use-dependent model.
Reduced stimulus intensity could decrease
GABAB-dependent PPD disproportionately (Lambert and Wilson, 1994), but because it accounts for a lesser fraction of
total PPD, even the loss of GABAB-dependent PPD
could not explain our results. Our finding that the same results on PPD
were obtained with each method of reducing IPSCs illustrates the
problem in using PPR to probe mechanisms of release from an individual
synapse. The dependence of PPR on stimulus intensity might suggest that the different populations of interneurons with different inherent PPR
properties were activated by different stimulus intensities (i.e.,
interneurons may vary in their tendency to show PPF or PPD). Although
we cannot rule out a small contribution by this factor, our data cannot
be explained by such differences. If, for example, low stimulus
intensities selected for interneurons that tended to show real PPF,
then PPF should have been apparent in the meanA2/meanA1 plots and
should have disappeared at the 4-9 sec interstimulus intervals.
Figure 7 illustrates that spurious PPF can arise when few synapses are
activated either because of decreased
Pr or because of other factors that
prevent transmitter release. Although nonlinearities in the efficacy of
the extracellular stimulation that often is used in experiments like
ours can lead to spurious PPF, spurious PPF also will arise from
simultaneous recordings from synaptically coupled pairs of cells, as
implied by Figure 7. This is because the CV of the responses grows as
the number of synapses that have been activated decreases, an effect
that is made clear by Silver et al. (1998), who used distributions
to model spatial nonuniformity of Pr
and to demonstrate the monotonic increase in CV even down to quantal
responses. Evidence that spurious PPR may be observed in paired-cell
recordings can be inferred from an investigation of unitary IPSCs in
CA1 pyramidal cells (Ouardouz and Lacaille, 1997). Analysis of unitary
IPSC PPR data by mean(A2/A1) suggested that use-dependent PPF occurred,
whereas analysis of the same data with meanA2/meanA1 revealed no PPF. A
possible interpretation was that the averaging involved in the
calculation of meanA2/meanA1 had masked a true use-dependent PPF that
was obvious only when A1 was small. Our results would suggest that the
PPF was spurious and that there was no use-dependent plasticity at
these synapses.
As shown in Figures 5 and 6, spurious PPF can be avoided if PPR is
calculated by meanA2/meanA1, because random fluctuations in the two
responses are averaged out before PPR is determined. However, even
without averaging, the appearance of high values of PPR during an
experimental treatment that dramatically suppresses the basal level of
transmitter release also has been interpreted to mean that a
presynaptic effect on the probability of release occurred (Luscher et
al., 1997). We suggest that the influence of the random effect may be
suspected when the variability of the PPRs increases and especially
when the variability clearly extends to values much smaller, as well as
larger, than control values of PPR (Fig. 3). The variance of the PPR
has been suggested to be a more sensitive index of the locus of
synaptic modification (Saitow et al., 2000) than the PPR itself, but
the role of variability in spurious PPF has not been discussed.
An important issue is how much the use of the mean(A2/A1) method has
affected previous work. To estimate this, we examined 32 peer-reviewed
papers published between 1990 and 2001 that investigated synaptic
function with the use of PPR. In 10 of these the mean(A2/A1) method was
used, in six the meanA2/meanA1 (or a variant) was used, in four papers
both methods were used, and in 12 papers we were unable to determine
which method was used. All experiments involved measurements of
synaptic responses with whole-cell or intracellular recording
techniques, 12 involved recordings from synaptically coupled pairs, and
24 were studies of inhibitory responses. In many cases the response
amplitudes after a manipulation were very small and were comparable in
amplitude to the variable responses we have observed. Generally, the
data that were reported did not permit reanalysis, so we could not test
for the influence of random fluctuations in detail. Nevertheless, the
widespread use of the mean(A2/A1) method, together with the example
discussed above, suggests that the influence of the random effect may
be greater than generally appreciated. We note that protocols that use
a brief train of pulses instead of just two also are subject to the
random error effect, if a ratio [A(n)/A1, where
A(n) is the amplitude of the nth response]
ultimately is used to characterize the results.
Because spurious PPF is nonphysiological, it is independent of the
intrinsic plasticity properties of a synapse. We suggest that the
inhibitory synapses that we have studied are characterized primarily by
PPD but that when the IPSCs are small and variable the spurious PPF
masks the PPD. The similarity of our experimental data in Figure 6 with
the simulated data in Figure 1 supports this conclusion. When
variability was low, PPD was prominent in the experimental data; when
variability increased, so did the occurrence of spurious PPF. Other
evidence for the masking of PPD by random fluctuations is found in
Figure 5. Data points in the PPF region fall into the PPD region when
recalculated by meanA2/meanA1. In addition, in the region of PPR < 1 many data points are below the dotted line; that is, the PPRs
calculated by meanA2/meanA1 are significantly less than the PPRs by
mean(A2/A1) (paired t test, p < 0.01). Thus
random fluctuations contributed to the mean PPR in this region, and to
some extent the degree of PPD was masked by spurious PPF. Of course, we
do not suggest that genuine, physiological PPF does not exist at many
synapses; it clearly does (for review, see Thomson, 2000). The
possibility of spurious PPF is an insidious and
underappreciated factor in the determination of PPR by the mean(A2/A1)
method, however.
The PPR traditionally has been used for two main reasons: to determine
whether a presynaptic or a postsynaptic effect occurred or to
investigate the mechanism of a particular presynaptic effect. Our
experiments show that spurious PPF can be produced by manipulations that affect presynaptic function. However, a nonuniform postsynaptic effect, one that altered the synaptic strength of a subset of synapses
by affecting the probability of activation of receptor patches, for
example, also could alter PPR by random effect. Thus changes in PPR
probably cannot be used reliably to distinguish presynaptic from
postsynaptic factors in cases in which CV is large and the mean(A2/A1)
method is used. Finally, although we have focused on the spurious PPF
that can occur when synaptic depression occurs, errors of
interpretation in the opposite direction could occur as well. Consider
an initial small response pair in which spurious PPF contributes to
measured PPR. If an experimental treatment leads to larger initial
responses and a decrease in relative response variability (CV), then a
decrease in PPR will occur because of a decrease in spurious PPF.
Because a decrease in PPR also is predicted by a use-dependent model of
synapse strengthening, an erroneous conclusion concerning the mechanism
of the effect could be drawn.
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FOOTNOTES |
Received June 21, 2001; revised Sept. 27, 2001; accepted Sept. 27, 2001.
This work was supported by National Institutes of Health Grants RO1
NS36612 and RO1 NS30219 to B.E.A. J.K. was supported by the
Training Program in Neuroscience T32 DE1474. We thank Scott Thompson
and Darrin Brager for help with Stella in the modeling studies and for
their comments on this manuscript. We also thank Greg Carlson and
Namita Varma for reading and commenting on this manuscript.
Correspondence should be addressed to Dr. Bradley E. Alger, Department
of Physiology, University of Maryland School of Medicine, 655 West
Baltimore Street, Baltimore, MD 21201. E-mail: balger{at}umaryland.edu.
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TOP
ABSTRACT
INTRODUCTION
