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The Journal of Neuroscience, November 1, 2001, 21(21):8362-8369
Paired-Pulse Plasticity at the Single Release Site Level: An Experimental and Computational Study
Eric Hanse and Bengt Gustafsson Institute of Physiology and Pharmacology, Göteborg University, SE-405 30 Göteborg, Sweden
ABSTRACT
TOP
ABSTRACT
INTRODUCTION
CA3-CA1 glutamatergic synapses in the hippocampus exhibit a large heterogeneity in release probability (p) and paired-pulse (PP) plasticity, established already in the early neonatal period when the CA3-CA1 connections consist of only a single release site. At such a site two factors decide initial release probability: the number of immediately releasable vesicles (preprimed pool) and the vesicle release probability (Pves1). Depletion and replenishment of this pool, an alteration in Pves, and desensitization of postsynaptic receptors may contribute to PP plasticity. A model based on data from single neonatal CA3-CA1 synapses has been used to address the relative importance of these factors for the heterogeneity in PP plasticity. At a 20 msec PP interval, the PP ratio (P2/P1) varied from 0.1 to 4.5 among the synapses. At this interval desensitization and replenishment were of little importance. The heterogeneity was explained mostly by the variation in Pves1, whereas the preprimed pool size was of minor importance. Pves altered from the first to the second stimulus such that Pves2 was rather uniform among the synapses. Its variation thus contributed little to the heterogeneity in PP ratio. The model also shows that the relationship between alterations in release probability and PP ratio is complex. Thus, an increase in release probability can be associated with an increase, a decrease, or no change at all in PP ratio, depending on the original values of Pves1 and the preprimed pool and on which one of these factors is altered to produce the increase in release probability.
Key words: paired pulse; release probability; hippocampus; CA1; synaptic plasticity; development
INTRODUCTION
A ubiquitous feature of synapses is that synaptic activity modifies synaptic action. In its simplest form this plasticity can be seen as paired-pulse (PP) facilitation (PPF)/paired-pulse depression (PPD), in which the second afferent stimulation produces more/less synaptic action than the first one (Katz and Miledi, 1968
; Zucker, 1989
To properly understand what underlies variations in paired-pulse plasticity among synapses, as well as to use it as a tool, one would have to know what factors determine release probability and how these factors may be altered after a first stimulus. For the Schaffer collateral synapses on CA1 pyramidal cells, release probability to the first (initial) stimulus and paired-pulse plasticity vary considerably among the synapses in a correlated manner (Dobrunz and Stevens, 1997
In the present article, we have modeled the paired-pulse behavior of single release sites exhibiting the above features. The aim has not been to give a full account of all aspects of paired-pulse behavior. Rather, by explaining a specific instance of paired-pulse behavior our aim is that some general insights into how paired-pulse plasticity is molded and how it can be used as a tool may emerge.
MATERIALS AND METHODS
Hippocampal slice preparation. The experimental data used in the present study were obtained as described in detail previously (Hanse and Gustafsson, 2001a
Afferents in the stratum radiatum were activated with 10 impulse, 50 Hz trains at 0.2 Hz using minimal extracellular stimulation. Several findings suggested that this minimal stimulation consistently resulted in the activation of a single axon contributing a single synapse to the cell recorded from this synapse containing a single release site (Hanse and Gustafsson, 2001a
Determination of vesicle release probability and size/variation of preprimed pool. The release probability (p) of a single release site is thought to be determined by the number of release-ready, or primed, vesicles (npool) and by the Pves, such that
Pves varies among the release sites but is considered to be the same within a release site (Hanse and Gustafsson, 2001b
(1) This analysis also allows for an estimation of Pves1, because the trials in which the preprimed pool consisted of only one vesicle are the trials in which only one release event occurred before the refilling point. Thus, Pves1 was determined as the release probability in the first stimulus position for those single release trials. This method for determining Pves1 is thus based on a subset of the trials (~100) to which each synapse was subjected. To estimate the sampling error in the estimation of Pves1 we performed a Monte Carlo simulation of release from a preprimed pool according to Equation 1 and a binomial distribution of the pool size (see Fig. 2B). These simulations, each with 100 trials, gave an estimated Pves1 that on average was equal to the predefined one with a SD of ~0.06. This can be compared with the SD of 0.28 for the variation between synapses (Hanse and Gustafsson, 2001b
0.7), the error with respect to the calculated P1 (for a given simulation or experiment) will thus only be approximately one-half the above estimated error in Pves1. The Pves value at the second stimulus position (Pves2) was calculated as follows:
where P2 is the release probability at position 2 (using all trials) and npool is the average size of the preprimed pool.
(2) If release events occurring up to the refilling point were considered, any given synapse displayed a substantial trial-to-trial variation in the number of such events. This variation was used to estimate the size distribution of the preprimed pool across all trials (see Fig. 2). Although a fixed refilling point provides for an accurate estimation of the average preprimed pool (Hanse and Gustafsson, 2001b
Model computations. Based on the range of the experimentally estimated values of Pves1 and Pves2 and the size and variation of the preprimed pool, release probabilities in response to a first (P1) and a second (P2) stimulus were calculated using Equation 1. Pves1 was varied between 0.1 and 1.0 and the (average) preprimed pool was varied between 0.6 and 1.8. Pves2 was set to a fixed value of 0.35. The trial-to-trial variation in the preprimed pool size was simulated by a binomial distribution. The paired-pulse ratio was calculated as P2/P1. The analysis and the calculations were performed using custom software written in Igor Pro (Wavemetrics, Lake Oswego, OR).
Unless otherwise indicated, data are presented as mean ± SEM. Student's t test was used to determine statistical significance.
RESULTS
Figure 1A illustrates unitary quantal release from a single terminal of a Schaffer collateral axon onto a CA1 pyramidal cell in response to train activation (20 msec interval). Such activation of synapses in 1- to 7-d-old rats resulted in release that varied considerably among the synapses with respect to initial release probability (P1), and facilitation/depression behavior (Hanse and Gustafsson, 2001b
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Figure 1. Release probabilities and paired-pulse (20 msec) ratio among synapses. A, Ten consecutive sweeps (0.2 Hz) from one synapse in response to paired stimuli. EPSCs are indicated by asterisks. B, Relationship between P1 and P2 among synapses (n = 42). The solid line is a linear regression line (r = 0.14; p > 0.05), and the dashed line indicates equality between P1 and P2. Nine synapses with no first-release probability (low-frequency mute synapses) are not included in the graph. C, Relationship between the paired-pulse ratio (P2/P1) and P1 among the synapses (n = 42). The dashed line indicates equality between P1 and P2. D, Relationship between paired-pulse ratios measured using release probabilities and EPSC areas. The solid line is a linear regression line (r = 0.96; p < 0.001).
Paired-pulse plasticity was also evaluated as EPSC2/EPSC1, where EPSC1 and EPSC2 are the average EPSC magnitudes (including failures). Discrepancies between this ratio and that of P2/P1 would indicate the influence of changes in quantal size on paired-pulse plasticity. On average, both the magnitude and probability ratio were 0.84 ± 0.12 (n = 43), and the two ratios correlated well (slope = 0.98) throughout the range of paired-pulse plasticity (Fig. 1D). That is, postsynaptic factors such as desensitization do not participate in paired-pulse plasticity under these conditions.
To analyze what may explain the above paired-pulse behavior, P1 and P2 were calculated using Equation 1 as described in Materials and Methods.
Binomial trial-to-trial distribution of preprimed vesicles
As described in Materials and Methods, the size of the preprimed pool at a given release site varies from trial to trial. To account in the model for this variation, the nature of this variation was examined. For each synapse the number of preprimed vesicles at each stimulus trial was determined (see Materials and Methods), and a distribution of these values was obtained. Synapses were then subdivided arbitrarily into four groups with respect to their average pool size, and the distributions within each of these groups were pooled together (Fig. 2, left column). In the group with the lowest average size of preprimed pool (Fig. 2, left, uppermost graph), the pool was zero in more than one-half of the trials, and trials with two preprimed vesicles were rare. However, in the group with the largest average pool (Fig. 2, left, lowermost graph) preprimed vesicles were absent in <10% of the trials, and up to four preprimed vesicles could occur.
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Figure 2. Distribution of the trial-to-trial variation in the preprimed pool size. The left column shows the trial-to-trial variability in the number of preprimed vesicles. Results from different synapses were pooled together in four groups according to the average size of their preprimed pool. The average pool size within each group is indicated in the graphs together with the number of synapses included. The right column shows binomial distributions using two, three, four, and five sites, respectively; each site had an occupancy probability of 0.3.
The fact that on some trials preprimed vesicles were absent suggests that priming is reversible. Otherwise, it seems difficult to understand why during some of the 5 sec intertrial intervals two to three vesicles have entered a primed state whereas during many other such intervals no vesicle has entered such a state. It may then be conceived that docked vesicles are in equilibrium between a primed and a nonprimed state. The simplest model is to assume that each synapse has a number of docking/priming sites equal to the largest number of preprimed vesicles observed for that synapse. We thus computed the binomial distribution of site occupancy by varying the number of sites from two to five and keeping the probability of site occupancy (at each site) constant. The right column of Figure 2 shows that for matching average preprimed pool sizes, a p value of 0.3 gave distributions closely resembling the experimental ones.
Such a value can then used to model the trial-to-trial variability of the preprimed pool.
Computed paired-pulse ratio: Pves1 and preprimed pool
The experimentally determined values of Pves for the first stimulus (Pves1) vary among the synapses from close to 0 up to almost 1 (Fig. 3) (Hanse and Gustafsson, 2001b
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Figure 3. Experimentally obtained relationship between Pves2 and Pves1 among the synapses (n = 42). The dashed line is the regression line for these data (r = 0.09; p > 0.05). Pves2 was calculated using Equation 2, where P2 is the release probability at stimulus position 2, npool is the average size of the preprimed pool, and P1 is the release probability at stimulus position 1.
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Figure 4. Calculated relationships between P1, P2, and the PP ratio at different magnitudes of Pves1 and the preprimed pool. The release probabilities in response to the first (P1) and second (P2) stimulus were calculated using Equation 1 as described in Materials and Methods. Pves1 was varied between 0.1 and 1 in steps of 0.1. The average preprimed pool was varied between 0.6 and 1.8 vesicles in steps of 0.3. Pves2 was set to a fixed value of 0.35. A, Relationship between P1 and P2. The dashed line indicates equality between P1 and P2. B, Relationship between the paired-pulse ratio (P2/P1) and P1. The dashed line indicates a PP ratio of 1. C, Same as in B, but each PP-Pves1 curve is normalized with respect to the paired-pulse ratio value obtained at a pool of 1.2.
Figure 4A shows that most calculated values fall below the "P1 = P2 line" (dashed line), indicating a predominance of PPD over PPF. When the P2/P1 ratio is plotted against P1 (Fig. 4B), there is an overall but broad relationship between the paired-pulse ratio and P1, in agreement with the experimentally observed relationship (Fig. 1C). The broadness is again related to the contrasting actions of Pves and preprimed pool variations, respectively. When P1 increases because of an increase in Pves1, the paired-pulse ratio decreases, in line with the common notion that an increase in release probability should be associated with a substantial decrease in paired-pulse ratio. However, the horizontal nature of the lines drawn through the iso-Pves values in Figure 4B shows that when P1 increases because of an increase in the pool size, the paired-pulse ratio changes little or, for large Pves1 values, actually increases. To better illustrate the relative change in the paired-pulse ratio introduced by preprimed pool variations, the same values have been replotted in Figure 4C after normalization to the PP ratio calculated for the median (average) preprimed pool (1.2). It can be noted that for Pves1 values of >0.5, an increase in the preprimed pool causes an increase in P1 associated with a substantial relative increase in the paired-pulse ratio.
Nevertheless, the above calculations suggest that the variation in paired-pulse ratio is dominated by the variation in Pves1. This effect of Pves1 depends on two factors. The first factor is that a change in Pves1 alters the Pves2/Pves1 ratio, thereby changing the P2/P1 ratio. The second factor is that a larger Pves1 will lead to a larger depletion after the first stimulus. In Figure 5A, the calculated values of P2/P1 (solid lines) are plotted against the Pves1 value for the five different pool sizes. It can be noted that when Pves1 is small (0.1-0.2), there is a large PPF of 100-200%. When Pves1 is large (>0.7) there is a large PPD, with the second response being only some 10-30% of the first one. To separate the above two effects of Pves1, the depletion factor was annulled by using the same pool size for the calculation of P2 as for P1. These P2/P1 ratios are shown in the same graph (Fig. 5A, dashed lines). Comparison between the two sets of P2/P1 calculations indicates that most of the variation in paired-pulse ratio depends on changes in the Pves2/Pves1 ratio. That is, depletion does not cause large changes in the absolute values of the paired-pulse ratio. Nevertheless, depletion appears to cause considerable changes in the normalized paired-pulse ratio, in particular for larger values of Pves1. To illustrate that effect more directly, the calculated values (Fig. 5A, solid lines) were, for each size of (average) preprimed pool, normalized with respect to those calculated using the same pool size for P2 as for P1 (Fig. 5A, dashed lines). This procedure demonstrates (Fig. 5B) that depletion causes a decrease in the normalized paired-pulse ratio that depends strongly on the value of Pves1 as well as on the preprimed pool size.
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Figure 5. Paired-pulse ratio (P2/P1) against Pves1: effects of Pves2 variations and of depletion. These calculations were performed as described in the legend to Figure 4. A, Relationship between Pves1 and the paired-pulse ratio. Solid lines represent the relationship for five different pool sizes (0.6, 0.9, 1.2, 1.5, and 1.8, respectively). The dashed line represents calculations using the same five pool sizes, but in this case the pool size was the same for the first and second stimulus (i.e., there was no depletion of vesicles). B, Relative effect of vesicle depletion for paired-pulse ratio for different pool sizes (0.6-1.8) and for different Pves1 values. The plot is derived from A such that for each pool size, the ratio between the curves with (solid line in A) and without (dashed line in A) depletion was constructed. C, Effect of different Pves2 values on the relationship between the paired-pulse ratio and first-release probability. The white area, corresponding to a Pves2 value of 0.35, is the same as the plot shown in Figure 4B. The gray and black areas correspond to Pves2 values of 0.25 and 0.45, respectively. These Pves2 values correspond approximately to the mean ± SD of the experimentally obtained Pves2 (0.33 ± 0.11).
Computed paired-pulse ratio: Pves2
Figure 3 shows that the experimentally estimated values of Pves2 varied from ~0.2-0.5 independently of Pves1. The variation in Pves2 will then not be expected to affect the paired-pulse ratio in a manner that is correlated with initial release probability but rather to introduce scatter in the PPF/PPD-P1 relationship. The influence of Pves1 (and of preprimed pool) variations on paired-pulse ratio was thus examined using a fixed Pves2 value of 0.35. However, to indicate the effect of Pves2 on the paired-pulse ratio, the calculations of P2 and P1 illustrated in Figure 4B were also performed using Pves2 values of 0.25 and 0.45. Figure 5C shows that this variation of Pves2 introduces some shift of the relationship between paired-pulse ratio and initial release probability without altering its overall shape.
Paired-pulse ratio versus Pves1 and preprimed pool size
Heterogeneity in P1 among the synapses is explained about equally by variations in Pves1 and in preprimed pool size (Hanse and Gustafsson, 2001b
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Figure 6. Pves1, but not the preprimed pool, determines the paired-pulse ratio. A, Relationship between P2/P1 and Pves1. Filled circles are experimental data obtained from 42 synapses. Filled squares represent binned averages (bin size is 0.2 Pves units) of the experimental data. Error bars are ±SEM and are only seen outside the symbol for the lowest Pves1 value. Lines are connecting calculated values using the parameter values given in the legend to Figure 4. B, Relationship between P2/P1 and the preprimed pool. Filled circles are experimental data obtained from 42 synapses. The dashed line is the regression line for these data (r = 0.14; p > 0.05). Solid lines are connecting calculated values using the parameter values given in the legend to Figure 4.
DISCUSSION
The present experimental results and calculations suggest that heterogeneity in paired-pulse plasticity among the Schaffer collateral synapses in the neonatal rat is primarily explained by a variation in Pves1. Variations in Pves2 and in the size of the release-ready vesicle pool were found to be of secondary importance, and desensitization was of no importance. The present model also suggests that an increase in initial release probability is not necessarily associated with a decrease in paired-pulse ratio but can also be associated with no significant alteration or even with a substantial increase.
Paired-pulse plasticity: Pves changes, pool changes, and desensitization
Paired-pulse plasticity is commonly seen as resulting from the interaction of three factors: two presynaptic ones and a postsynaptic one. Facilitation results from an increase in Pves, based for example on "residual" calcium from the first stimulus. Depression can result from a decrease in Pves, a decrease in vesicle pool size (depletion), and desensitization of postsynaptic receptors. In the present calculations, desensitization was not taken into account because, at least with the paired-pulse intervals used (20 msec), paired-pulse plasticity was found experimentally to be the same regardless of whether it was evaluated by EPSC magnitude or by release probability. That is, postsynaptic factors such as desensitization do not play any role (Hjelmstad et al., 1999
The importance of vesicle depletion was evaluated using model calculations. Depletion was found to have an effect on paired-pulse plasticity that was strongly dependent on Pves1 and on the preprimed pool. For lower Pves1 values, depletion gave ~20% lower values of paired-pulse plasticity that were independent of preprimed pool size. For large Pves1 values, corresponding values were 40-80%, with the effect being more accentuated for the smaller preprimed pool sizes. Vesicle depletion can thus be a significant factor in the generation of PPD under certain conditions. These calculations did not take into account possible recruitment of newly primed vesicles. Approximately one-sixth of the hippocampal neonatal synapses lack initial release but display a low release probability (0-0.1) to the second stimulus ("low-frequency mute" synapses) (Hanse and Gustafsson, 2001b
Our model calculations suggest that the variation in Pves1 among the synapses creates the large heterogeneity in paired-pulse plasticity. This effect of Pves1 depends on two factors. The first is that a change in Pves1 alters the Pves2/Pves1 ratio, thereby changing the P2/P1 ratio. The second is that a larger Pves1 will lead to a larger depletion effect. A key model factor is that Pves2 is kept constant at an intermediate value (0.35). At synapses with higher/lower Pves1 values, Pves is thus supposed to decrease/increase during the paired activation and lead to PPD/PPF (see also Matveev and Wang, 2000
Temporal aspects of paired-pulse plasticity
Experimental data have been limited to a single paired-pulse interval (20 msec). This is an interval at which the initial release-dependent release inhibition should have vanished (Stevens and Wang, 1995
Dissociation between initial release probability and paired-pulse plasticity
It is commonly assumed that an increase in initial release probability is associated with a decrease in paired-pulse ratio. However, the calculations show that when P1 increases because of an increase in preprimed pool size there is either little change, or, for larger values of Pves1, a substantial increase in the paired-pulse ratio. Because of the small size of the preprimed pool, its average size had a large effect on release probability. For example, a doubling of pool size could cause an ~50% increase in P1 associated with anything from no change to a 100% increase in paired-pulse ratio. In the model, a pool-size change can be achieved by an increase either in the probability for a docked vesicle to be in a primed state or in the number of docking/priming sites. The observation of a phorbol ester-induced change in release probability unaccompanied by changes in paired-pulse ratio (Honda et al., 2000
Preprimed pool distribution
The experimental analysis suggested that the preprimed pool of vesicles fluctuated in size from trial to trial. A binomial model for this fluctuation was constructed for usage in the paired-pulse calculations. This binomial model was based on the assumption that the final release-ready stage is reversible, with docked vesicles being in equilibrium between a nonprimed and a primed state. Such reversibility in the final release-ready stage appears compatible with current molecular models of the release process (Murthy and Stevens, 1999
Dependence on age
The experimentally observed paired-pulse ratio did not correlate with the age of the animal (within the first postnatal week), indicating that its variability among the synapses was not a developmental feature. The presently found relationship between paired-pulse ratio and initial release probability also agrees in its overall variability and shape with that obtained from putative single release sites of the same hippocampal connections from older animals (Dobrunz and Stevens, 1997
Paired-pulse plasticity within a synapse
Can the present calculations also explain what happens to the paired-pulse ratio when Pves1 and the preprimed pool change within a given synapse? With respect to changes in pool size, there seems no reason to believe otherwise. However, with respect to Pves1, the situation is more complicated. Recent studies, albeit in neocortical axons (Koester and Sakmann, 2000
FOOTNOTES Received April 6, 2001; revised Aug. 10, 2001; accepted Aug. 21, 2001.
This study was supported by grants from the Swedish Medical Research Council (project numbers 12600 and 05180), the Swedish Society of Medicine, and Harald Jeanson's Foundation. We thank F. Asztely, J. Eilers, L. Groc, and P. Wasling for critically reading this manuscript.
Correspondence should be addressed to Eric Hanse, Institute of Physiology and Pharmacology, Göteborg University, Box 432, SE-405 30 Göteborg, Sweden. E-mail: eric.hanse{at}physiol.gu.se.
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