The concept of Ca²⁺-dependent quantal vesicular release was introduced to synaptic physiology in the 1950s by Bernhard Katz et al. based on electrophysiological findings (Fatt and Katz, 1952; Del Castillo and Katz, 1954). The idea of quantal transmitter release received further support by the invention of rapid-freezing combined with timed synaptic stimulation and electron microscopy. Heuser and Reese succeeded in catching synaptic vesicles (SVs) in the act of fusion (Heuser et al., 1979). The concept of quantal release has since been confirmed in several studies and further extended (Neher, 2015). In this view, the amplitude of a postsynaptic current (PSC) is given by PSC = p n q, where p is the average probability that a vesicle (or “unit” as it was called initially) fuses, n is the number of fusion-competent SVs and q the amplitude of the postsynaptic response resulting from the fusion of a single vesicle. The latter is referred to as the “quantal size” and the product of p and n is referred to as the “quantal content (QC).” Hence, the amplitude of a PSC is the product of quantal content and quantal size and the overall rate of synaptic failures (F) or successes (S) strictly depends on the quantal parameters, being given by F = (1−p) ⁿ and S = 1 – F.

The total number of fusion-competent vesicles constitutes the readily releasable pool (RRP) of SVs. Fusion occurs at specific presynaptic release sites (N) or docking sites as a synonym. However, quantitative estimates of RRP and N frequently deviate from each other and their relationship is not fully clear (Neher, 2015). The relationship between RRP and N and the reasons underlying discrepancies between estimates of RRP and N are one of the topics of this article.

During synaptic activity, the RRP needs to be replenished by a continuous supply of SVs in order to maintain synaptic function. This supply comes from additional SV pools that have been postulated in recent years (Neher, 2015). SVs run through different Ca²⁺-dependent and Ca²⁺-independent steps that include docking and priming to become fully fusion-competent SVs of the RRP (Neher and Brose, 2018; Silva et al., 2021). Furthermore, the size of the RRP or the N can change during activity, which according to recent findings is a major determinant of synaptic short-term plasticity (reviewed, e.g., in Neher and Brose, 2018; Miki, 2019; Schmidt, 2019; Neher, 2023). Models with sequential pools of SVs have been proposed that accounted for several experimental findings on transmitter release and short-term plasticity at different synapses in the cerebellum (Miki et al., 2016; Doussau et al., 2017), the neocortex (Bornschein et al., 2019b), the brainstem (Lin et al., 2022), and the hippocampus (Aldahabi et al., 2024).

We will distinguish three types of sequential models here. In the first type, presynaptic release sites are at rest fully occupied by SVs forming the RRP. During synaptic activity, the RRP gets replenished from SVs that occupy replenishment sites and form a replenishment pool (RP) with a finite size that is intermediate between the reserve pool (RSP) and the RRP. While we use “replenishment” throughout the manuscript, there are other frequently used synonyms including “replacement” or “recruitment.” The number of release sites itself can increase during high-frequency activity, thereby giving rise to synaptic facilitation (Doussau et al., 2017). We refer to this model as the sequential occupied sites (SOS) model (Figure 1A). The second type is similar to the first type, but at rest, part of the release sites are considered to be not occupied by SVs. During high-frequency activity, the occupancy but not the number of release sites increases, thereby again accounting for synaptic facilitation (Miki et al., 2016). While this model has been referred to as the replacement site/docking site model previously, we refer to it as the sequential empty sites model here for clarity (SES; Figure 1B). The third model also has a fixed number of release sites and includes empty sites. In this model, SVs are first in a loosely docked and primed state (LS) and reversibly pass through a tightly docked and primed state (TS) prior to fusion. An increase in TS accounts for facilitation here. This model is referred to as the LS/TS model (Figure 1C) (Neher and Brose, 2018; Neher, 2023). While SVs in the TS correspond to the RRP in the narrower sense, SVs in the LS are not identical to the RP vesicles (see Discussion).

Therefore, in order to account for short-term plasticity, in these sequential models, either it is assumed that the occupancy of a fixed number of N is incomplete at rest and increases during activity, i.e., the RRP increases but not the N (SES and LS/TS) (Trigo et al., 2012; Miki et al., 2016; Neher and Brose, 2018; Neher, 2023), or it is assumed that the number of N itself (= RRP) increases (SOS) (Valera et al., 2012; Brachtendorf et al., 2015; Doussau et al., 2017). Both phenomena are sometimes referred to as ‘overfilling’. In all models, the increase in the size of the RRP is viewed as activity-dependent and reversibly. In any case, the result is paired-pulse facilitation (PPF) as observed, e.g., at cerebellar parallel-fiber (PF) synapses. The results obtained with rapid-freezing electron microscopy methods showed a reversible increase in the number of docked SVs shortly after timed synaptic stimulation (Kusick et al., 2020; Kusick et al., 2022), which is consistent with the sequential models and reversible overfilling. However, it does not differentiate between the three types of models.

An alternative and earlier model proposes a subdivision of the RRP into two parallel pools, differing in their vesicular release probabilities (p_v) (Wölfel et al., 2007; Hallermann et al., 2010; Mahfooz et al., 2016). In traditional parallel models, the intermediate RP is not implemented (Wölfel et al., 2007; Mahfooz et al., 2016). We refer to the traditional parallel model as the PP model here (Figure 1D). In a recent study, it was found that sequential and parallel models may almost equally well describe different aspects of experimental data (Eshra et al., 2021; Weichard et al., 2023). Therefore, it is difficult to distinguish not only between the different sequential models but also between the sequential and parallel models.

Two standard electrophysiological methods are frequently used for the quantitative estimation of synaptic parameters, including SV pools: the analysis of cumulative PSC amplitude plots (CumAna) (Schneggenburger et al., 1999) and variance–mean analysis or multiple probability fluctuation analysis (MPFA) as a synonym (Clements and Silver, 2000). In CumAna, trains of action potentials (APs) are applied under recording conditions suitable to drive synapses into equilibrium between release and replenishment. This is typically given if the vesicular release probability (p_v) is sufficiently high to achieve a steady-state depression of ~60% during the train. At synapses with moderate p_v, this may require performing recordings in an elevated extracellular Ca²⁺ concentration ([Ca²⁺]_e). Additional methodological requirements for the successful application of CumAna have been described in detail elsewhere (Neher, 2015). The result is a linear relationship between cumulative PSC amplitudes late in the train and the corresponding stimulus numbers or times. Fitting a line to this linear phase and extrapolating it to the y-intercept removes the contribution of SVs added via replenishment in the steady-state phase. Hence, the y-intercept is thought to report the initial size of the RRP. More precisely, it reports a value close to the decrement of the RRP during the train and the “real” size of the RRP can be obtained with a correction calculation as long as the RRP gets strongly depleted during the train (Thanawala and Regehr, 2013; Neher, 2015). Dividing the first PSC or quantal content by the y-intercept then gives the average p_v.

For MPFA, PSCs are recorded under conditions of several different p-values, which are typically obtained by changing the [Ca²⁺]_e. Alternative approaches to change p include broadening the presynaptic AP, e.g., by application of blockers of voltage-gated potassium channels such as TEA or 4-AP. The variance and the mean of the PSCs are calculated during stable recording periods after the wash-in of each different Ca²⁺ solution or alternative treatment and the variance is plotted against the mean. A parabolic fit to these data yields N and the average release probability per release site (p_N) (Clements and Silver, 2000).

In our experiments at cortical synapses, we typically found that the estimates of RRP from the y-intercept were larger than the estimates of N from MPFA for the same synapses. Accordingly, the estimates of the p-values showed the opposite behavior (Schmidt et al., 2013; Baur et al., 2015; Bornschein et al., 2019a; Bornschein et al., 2019b). Deviations between y-intercept and N were observed also at many other synapses (Table 1) (Neher, 2015). However, the cause of these deviations is not fully clear.

CumAna and MPFA were established before the development of sequential or parallel pool models. Here, we used computer simulations to systematically investigate which entities are actually reported by the two experimental methods in light of different pool models and considering incompletely populated release sites. The systematic approach starts with basic simulations of simple arrangements of SV pools, which become increasingly complex. This article aimed to investigate how much information about the organization of SVs can be obtained based on the experimental results alone, without the need to fit complex models to the data. We suggest that a combination of CumAna with MPFA provides complementary insights into the functional organization of SV pools and their dynamics that cannot be achieved with either method alone.

In this paper, we theoretically explored the insights that can be gained into the organization and dynamics of SV pools by combining the experimental methods CumAna and MPFA, including phenomena such as overfilling and the replenishment of new release sites. We used computer simulations to guide our theoretical considerations and focused on two recent sequential vesicle pool models, the SOS (Doussau et al., 2017; Bornschein et al., 2019b) and the SES (Miki et al., 2016). We further covered a traditional PP model that does not harbor a series-connected RP (Wölfel et al., 2007; Mahfooz et al., 2016). In the following, we will summarize our main conclusions and discuss them in a broader context:

In summary, based on points (ii), (iii), and (v), we suggest that the y-intercept is greater than N_MPFA if presynaptic boutons harbor an RP and replenishment sites in series with the RRP (y(0) > N_MPFA), while both are equal for parallel RRPs without RP (y₀ = N_MPFA). Biexponential decay of synaptic responses during AP trains thus indicates sequential or parallel pools (i), and the combined use of CumAna and MPFA offers the possibility to distinguish between SOS and SES on the one hand and PP on the other. Finally, MPFA with paired pulses provides a means to identify a factual increase in N as opposed to a mere increase in the occupancy of N; i.e., it provides a means to distinguish between SOS and SES models (Table 2).

The basis of CumAna is the assumption that late during the train the synapse is in a steady state between SVs being released and newly replenished and that the rate of replenishment is constant during the train. Furthermore, for studying changes in pool size, it is important to aim at keeping p_v constant, e.g., by adjusting the [Ca²⁺]_e in experiments (Neher, 2015). Therefore, in our simulations, we kept both p_v and the replenishment rates constant. p_v was set to 0.6 to meet the additional requirement of depression and no increase in p_v was assumed during the train.

A recent variant of MPFA used trains of APs at ‘simple synapses’ that harbor only a single active zone, in combination with counting of individual release events by deconvolution (Miki et al., 2016; Miki, 2019). Variance mean analysis was extended there to cover also cumulative values, somewhat reminiscent of a combination of MPFA with CumAna. The quantification of the data relied on more complex modeling and provided evidence for sequential pools with incomplete initial release site occupancy (SES model). The aim of the present study was to probe if the classical and more simple versions of MPFA (Clements and Silver, 2000) and CumAna (Schneggenburger et al., 1999) can provide similarly deep insights into the organization of release sites and vesicle pools in the absence of complex modeling. Our results suggest that a combination of the two methods with canonical parabolic or linear analysis can indeed provide detailed information about the organization of release at the active zone.

The results for the SOS and SES model will not be identical to another recent sequential model in which SVs reversibly shift their state from LS to TS before they can fuse (Neher and Brose, 2018; Neher, 2023). As in the SES model, empty sites occur in the LS/TS model and increasing occupancy of the TS is a major mechanism of facilitation. Similar to the RP in the SOS and SES models, SVs in LS will show up in the y-intercept as the empty sites will do. However, different from vesicles in the RP, LS vesicles will also appear in the N of the MPFA. This means that in the LS/TS model, y(0) and N_MPFA could be quite similar, just as in the PP model. Thus, while there are several similarities between the sequential models, there are also crucial differences between the SOS, SES, and LS/TS models. In particular, vesicles of the RP or in LS are not identical (Figure 9). However, the three sequential models need not be mutually exclusive, and, while there is so far no experimental evidence for this, it is well conceivable that at a given synapse more than one type of overfilling mechanism is operational to produce synaptic facilitation.

In our simulations, released quanta were assumed to be perfectly synchronized, which is a simplification compared to real synaptic release as investigated in experiments. In the SOS and SES models, it was further assumed that SVs from the RP do not contribute to the first release. In experiments, CumAna and MPFA are typically based on the analysis of PSC amplitudes. Even with ultra-rapid replenishment (Miki et al., 2016; Doussau et al., 2017) in which SVs from the RP may even contribute to the first PSC, it is more likely that these SVs contribute to the decay of the PSC rather than to its peak amplitude. In addition, in rapid-freezing electron microscopy studies the transient increase in the number of docked SVs was observed only after the stimulation (Kusick et al., 2022). Hence, we think that a non-perfectly synchronized release will not affect the general conclusion of y(0) > N_MPFA for the SOS and SES models.

For our theoretical considerations, individual release sites were modeled with linear summation of released quanta and direct “read out” of the number of successes. However, in experiments, the degree of saturation of postsynaptic receptors has to be considered carefully for quantitative estimations of N. In particular, multivesicular release, which appears to be frequent in the brain (Rudolph et al., 2015), may result in receptor saturation and underestimation of N. Fortunately, methods exist to alleviate receptor saturation by the use of competitive antagonists such as γ-DGG at glutamatergic synapses. For a comprehensive discussion of univesicular versus multivesicular release in MPFA, we refer to Silver (2003).

In the PP model also the low p_v pool got fully depleted in our simulations. As the amplitude of the Ca²⁺ signal and the corresponding release rates rapidly drop with increasing distance from the Ca²⁺ channels (Bucurenciu et al., 2008; Bornschein et al., 2013; Schmidt et al., 2013; Nakamura et al., 2015; Bornschein et al., 2019b; Chen et al., 2024), this may not always be possible to achieve in experiments. In this case, the y-intercept will not report the sum of both RRPs but rather an intermediate value between the size of the high p_v pool and the sum of both pools, i.e., RRP_{high p} < y(0) < RRP_{high p} + RRP_{low p}. Then, SVs from RRP_{low p} can contribute to the slope of the steady-state phase. In particular, this may arise if p_v is strongly heterogeneous between SVs and/or if SV pools are very large, harboring thousands of SVs such as in the calyx of Held (Neher, 2015). Considering this possibility, the comparison of y-intercept and N_MPFA yields y(0) ≤ N_MPFA for the PP model. However, y(0) > N_MPFA as in the SOS and SES models will not occur.

Footprints of our conclusions can be found in experiments on different CNS synapses, including cerebellar, neocortical, or brainstem synapses. At different synapses, changes in the functional presynaptic nanotopography were found during postnatal development. In particular, the coupling distance between voltage-gated Ca²⁺ channels and the synaptic vesicles was found to switch from loose to a tight coupling during development, e.g., at the Calyx of Held (Fedchyshyn and Wang, 2005; Nakamura et al., 2015), PF–PC synapses (Baur et al., 2015) and L5PN–L5PN synapses (Bornschein et al., 2019b). At the latter synapse, evidence was provided that the switch in coupling was accompanied by the maturation of a rapid replenishment pool that transformed the decay time course of EPSC amplitudes during trains of action potentials from mono- to biexponential (Bornschein et al., 2019a).

Cerebellar granule cells (GCs) typically form only a single PF synaptic contact that harbors only a single active zone (Xu-Friedman et al., 2001) with their postsynaptic targets, including PCs and molecular layer interneurons (MLI). These ‘simple synapses’ are an intensively investigated model for a typical small cortical synapse (Pulido and Marty, 2017; Schmidt, 2019; Silva et al., 2021). MPFA in paired GC–PC recordings quantified N_MPFA and p_N to be ~3 and 0.25, respectively (Schmidt et al., 2013). Strikingly, with this very limited immediate resource for transmitter release, PF synapses show long-lasting high-frequency facilitation over up to 30 APs with initially paired-pulse ratios of up to ~3 (Valera et al., 2012; Brachtendorf et al., 2015; Doussau et al., 2017). MPFA with paired pulses at this synapse showed that the parabola in the second pulse got wider than in the first pulse, which was interpreted as a use-dependent factual increase in N as a major source of PPF at these synapses (Valera et al., 2012; Brachtendorf et al., 2015). Furthermore, the long-lasting high-frequency facilitation of this synapse was explained by a sequential pool model with ultra-rapid, reversible increases in N (Doussau et al., 2017). The current considerations and simulations support this interpretation by ruling out the possibility that an increasing width of the parabola results solely from a mere increase in the occupancy of a fixed number of release sites. However, they do not rule out the possibility that, in addition to the increase in N, there is also incomplete initial occupancy. Incomplete initial occupancy has been detected at MLI–MLI synapses (Trigo et al., 2012) and increasing occupancy of release sites during successive synaptic activations has been suggested at PF–MLI synapses as a mechanism of PPF, using the SES model (Miki et al., 2016). As PF–PC and PF–MLI synapses are formed by the same presynaptic GC, it appears plausible that at PF terminals both mechanisms, increasing N and incomplete initial occupancy, are operational synergistically. For the interesting question of what constitutes an empty release site and more generally how the view of the release site has been changing in recent years, we refer to recent comprehensive reviews (Pulido and Marty, 2017; Neher and Brose, 2018; Silva et al., 2021; Kusick et al., 2022; Neher, 2023).

The prioritization of the sequential over the parallel model was not explicitly justified at PF synapses (but see Doussau et al., 2017). However, the data from CumAna and MPFA show y(0) > N_MPFA at PF–PC synapses (Schmidt et al., 2013; Baur et al., 2015), which argues in favor of the sequential model. Similar findings come from an inhibitory cerebellar synapse (Chen et al., 2024) and a neocortical synapse formed between L5PNs (Bornschein et al., 2019a,b). Interestingly, at the latter synapse evidence was found that the RP develops only during synaptic maturation between the first and third postnatal week in mice, thereby changing the short-term plasticity properties (Bornschein et al., 2019a).

Two recent studies explained longer lasting forms of synaptic facilitation, augmentation (Shin et al., 2024), and LTP (Weichard et al., 2023) by overfilling, using sequential pool models. Synaptotagmin 7 (Syt7) was identified earlier as a presynaptic facilitation sensor (Jackman et al., 2016), and it was tempting to speculate that Syt7 might be involved in driving overfilling (Bornschein and Schmidt, 2019). Indeed, Shin et al. (2024) currently provided evidence that Syt7 drives overfilling.

The PP model was used to simulate the biphasic time course of release at another important model synapse, the calyx of Held (Wölfel et al., 2007). However, a biphasic time course of release can also arise from sequential pools of SVs [see point (i)] and it has recently been shown that the LS/TS model describes release and short-term plasticity at the calyx very well (Lin et al., 2022).

Results on differences in short-term plasticity and also presynaptic forms of LTP are frequently considered to reflect differences in p_v. The sequential pool models suggest an alternative interpretation (Neher, 2023). The dynamics of reversible vesicle priming, varying occupancy of release sites, and the replenishment of new release sites make major contributions to short-term plasticity. The simple theoretical framework proposed here provides a means to identify signatures of the RP without the need for complex computer simulations. It is based on the combination of two standard physiological methods, cumulative analysis of PSC amplitudes, and multiple probability fluctuation analysis.