Random response fluctuations lead to spurious paired-pulse facilitation - PubMed (original) (raw)

Random response fluctuations lead to spurious paired-pulse facilitation

J Kim et al. J Neurosci. 2001.

Abstract

We studied paired-pulse depression (PPD) of GABA(A)ergic IPSCs under conditions of reduced transmitter release (caused by Cd(2+), 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.

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Figures

Fig. 1.

Fig. 1.

Simulation of paired-pulse ratios (PPRs) by means of randomly generated numbers. Simulated PPRs were generated assuming that the distribution of P_r 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_P_r distribution of a population of simulated synapses was modeled with a Γ density function (see Materials and Methods). Simulation of probabilistic release was accomplished by comparing an assigned _P_r at a synapse with a randomly generated number between 0 and 1; if_P_r was greater than a random number, then a release was counted. C, Fifty pairs of random responses were generated from a Γ distribution of_P_r, with a mean of 0.033 (to simulate low _P_r conditions) and individual_P_r 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 _P_r distributions were varied by varying the mean _P_r of the Γ distributions (from 0.013 to 0.645). Again, spurious PPF increases with increasing the CV of simulated responses.

Fig. 2.

Fig. 2.

Effects of experimental treatments on measured PPR. Cd2+ (10–60 μ

m

), baclofen (2–3 μ

m

), 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 μ

m

) 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.

Fig. 3.

Fig. 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 μ

m

) 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.

Fig. 4.

Fig. 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.A 1, 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).

Fig. 5.

Fig. 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.

Fig. 6.

Fig. 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 1_D_ were recalculated with meanA2/meanA1 and plotted against CV. Spurious PPF in large part disappeared; the symbols vary ∼1.0.

Fig. 7.

Fig. 7.

Theoretical model of dependence of spurious PPF on_P_r and stimulus strength when mean(A2/A1) is used. Random PPRs were simulated by a nonuniform_P_r distribution (Γ 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 _P_r distribution (see Materials and Methods) was 0.05 except when n was <100 and _P_r = 0.645; then it was 0.1.] This simulation was done with three mean_P_r values of the Γ 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 _P_r 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_P_r) at a fixed stimulus intensity. As_P_r decreases, spurious PPF increases. Moving along the _x_-axis simulates increasing the stimulus intensity (increasing the number of activated synapses). For every value of _P_r, 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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