The purpose of the present work is to measure the maximum RRP size per docking site at PF–MLI synapses and to compare that maximum with the predictions of the RS/DS model (Miki et al., 2016).

The basic features of the RS/DS model are pictured in Figure 1A. Here, a single docking/replacement unit is shown for simplicity. Incoming SVs first bind to a distal ‘replacement site’ (upper position in Figure 1A), then to an associated proximal ‘docking site’ (lower position in Figure 1A) before being released. The distal replacement site is considered to be ~40 nm away from the plasma membrane, allowing simultaneous occupancy of both distal and proximal docking sites by SVs.

Figure 1

Download asset Open asset

The progression of SVs along the replacement site/docking site assembly during an AP train is driven by the conditional transition probabilities s, r, and p_r (Figure 1A). Each of these probabilities refers to one AP interval during the train. Conditions for an effective transition are: for s, that the replacement site is empty; for r, that the replacement site is occupied, and that the docking site is empty; for p_r, that the docking site is occupied. Thus, if the probability of docking site occupancy before stimulation is δ, the probability that the site releases an SV after the first AP of the train is P = δp_r (Scheuss and Neher, 2001).

Calcium elevation in presynaptic terminals promotes the replenishment of SVs to emptied docking sites (Chang et al., 2018; Kobbersmed et al., 2020; Kusick et al., 2020; Neher and Sakaba, 2008; Sakaba, 2008; Wang and Kaczmarek, 1998; Wu et al., 2022). Accordingly, we assume that calcium increases not only p_r, but also r and s. As the probability of transition r increases after an AP, SVs can move from the distal to proximal site within a few ms. In the framework of the RS/DS model, due to the high speed of this transition, both replacement and docked SVs are regarded as belonging to the RRP (Miki et al., 2018; Miki et al., 2016). Likewise, in the related LS/TS model, the RRP comprises the sum of SVs occupying a distal and a proximal SV-binding site, which are called in this model the loosely and tightly docked state (Lin et al., 2022; Neher and Brose, 2018; Neher and Taschenberger, 2021). A key difference between these two models is that the sites in the RS/DS model can be simultaneously occupied while in the LS/TS model a docking site can only accommodate one SV in either state at a time. Thus, the RS/DS model predicts a maximum RRP size per docking site of 2, whereas the LS/TS model predicts a maximum RRP size per docking site of 1.

We used previously developed methods to record from simple synapses between cerebellar granule cells (GCs) and MLIs (Figure 1C). At these synapses, it is possible to count the release of individual SVs with an effective time separation of 0.2 ms between consecutive release events (Malagon et al., 2016). It is also possible to count the number of docking sites precisely, giving an opportunity to evaluate the maximum number of released SVs per site.

To determine the maximum number of SVs that a docking site can accommodate, it was essential to maximize the RRP size and its release during an AP train, that is, to maximize δ, p_r, and r. In the extreme case where p_r and r are both equal to 1, a first AP should release all SVs that were initially in the docking site, and a second AP should release all SVs that were initially in the replacement site (Figure 1B; Tran et al., 2022). The RRP size is then given by the sum of the number of released SVs for the two APs.

Recordings from simple synapses between cerebellar GCs and MLIs (Figure 1C) were initiated in an elevated external calcium concentration (3 mM), a condition that has been shown to elevate δ, p_r, and r (Miki et al., 2018; Malagon et al., 2020). In this condition and for the example shown in Figure 2A, responses to the first two stimuli of an 8-AP (8-action potentials) train (100 Hz within each train, 10 s intervals between trains) were mostly comprised between 0 SV (failure) and 2 SVs (Figure 2A, left). While keeping 3 mM Ca_o, we next performed two modifications aiming at further enhancing release probability and docking site occupancy: we applied the potassium channel blocker 4-amidopyridine (4-AP), which increases p_r, and we performed a post-tetanic potentiation (PTP) protocol, keeping 4-AP in the perfusion (see Methods). For the example shown, responses to the first two stimuli were clearly enhanced by 4-AP (now comprised between 2 and 4 SVs, with no failure: Figure 2A, center). In contrast, responses to stimuli 6–8 were reduced with respect to the control. We then applied a series of 60 AP trains, each with 8 APs evoked at 100 Hz, with an inter-train interval of 2 s. This protocol (called ‘PTP’hereafter) results in an increase in docking site occupancy lasting several minutes (Tran et al., 2023). After PTP induction, the responses to the first stimuli increased, or remained similar to those in 4-AP (as in the experiment shown), while responses to later stimuli displayed more synaptic depression. Group results indicate a marked enhancement in the mean released SV numbers after the first two stimuli, and somewhat reduced responses for stimuli 5–8, when comparing results in 4-AP or after PTP with control (n = 8; Figure 2B, C showing the number of SVs released per AZ and per docking site, respectively).

Figure 2

Download asset Open asset

Figure 2—source data 1

Released synaptic vesicle (SV) counts for individual experiments in various experimental conditions.

This Excel Table lists s_i results in control, after 4-amidopyridine (4-AP) infusion, and after post-tetanic potentiation (PTP) induction, for the 14 individual experiments used in the present work (group results shown in Figure 2B). It also shows P_i results in the same conditions (group results shown in Figures 2C and 6), as well as P₁ + P₂ results (group results displayed in Figure 4). Finally, it shows 200 Hz results for a subset of experiments (group results shown in Figure 5).

https://cdn.elifesciences.org/articles/91087/elife-91087-fig2-data1-v1.xlsx

Download elife-91087-fig2-data1-v1.xlsx

Following stimulus number i, the number of released SVs, s_i (Figure 2B), is the product of the number of docking sites, N, and of the release probability at each docking site, P_i (see SV release normalized to N, Figure 2C). As our conclusions rested on the values of P_i, not s_i, we made a special effort to verify that our estimates of N did not include any systematic error.

One method to determine N is to perform a variance–mean analysis on s_i, plotted as a function of i in a given experimental condition (Malagon et al., 2016). In the case illustrated in Figure 3A, left (in the presence of 4-AP; same experiment as in Figure 2A), the fit indicated a value N = 3.8 ± 0.2, close to the whole number N = 4. We compared this result with that of an alternative method where the distribution of observed SV numbers at individual i values is fitted with a binomial distribution, leaving N as a free parameter (Malagon et al., 2016). When applying this method to the responses to the first two stimuli, the best fit was obtained with N = 4 (Figure 3A, center and right). Therefore, the two methods give the same estimate for N (N = 4 in the present case). Inverting the relation s_i = NP_i with the value N = 4 gives P₁ = 0.86 and P₂ = 0.66 in this example.

Figure 3 with 1 supplement see all

Download asset Open asset

Across experiments, N values returned by variance–mean curves did not change when adding 4-AP or after PTP induction (Figure 3B). Common N values across experimental conditions were consistent not only with variance–mean estimates, but also with binomial analysis of s₁, as illustrated in Figure 3C for an example experiment, and in Figure 3D for a group of 4 experiments with N = 4. Therefore, a single N value was adopted for each experiment. Because N is better constrained when P values are high, N was taken as the best whole value obtained from binomial analysis of s₁ and s₂ in 4-AP (see Methods). The invariable N values indicate that the addition of 4-AP and the PTP protocol do not increase the number of docking sites in the time frame of the experiments. N values determined with the binomial method in 4-AP varied among experiments from 2 to 6, with a mean value of 3.6 ± 0.3 (n = 14 experiments). In the subset of experiments illustrated in Figure 3B, the corresponding mean number was 4.2 ± 0.4 (range, 3–6), close to the mean value obtained by variance–mean analysis (4.3 ± 0.2, Figure 3B center; n = 8 experiments).

Figure 4 shows average values of P₁, P₂, and P₁ + P₂, across experimental conditions (in control, in 4-AP, and after PTP). P₁ significantly increased in 4-AP compared to control, and after PTP compared to the previous data in 4-AP (control: 0.39 ± 0.04; 4-AP: 0.69 ± 0.03, paired t-test p_pt < 0.01 compared to control; PTP: 0.88 ± 0.04, p_pt < 0.01 compared to 4-AP; n = 14 for control and 4-AP, n = 8 for comparison after and before PTP protocol; p_pt calculated for paired results; Figure 4, left). P₂ significantly increased in 4-AP compared to control, and it remained stable after PTP (control: 0.46 ± 0.04; 4-AP: 0.64 ± 0.03, p_pt < 0.01 compared to control; PTP: 0.67 ± 0.07, p_pt > 0.05 compared to before protocol; Figure 4, middle).

Figure 4

Download asset Open asset

As p_r and the docking site occupancy before stimulus i (δ_i) are probabilities, they are smaller than 1. Therefore, the relation P_i = δ_ip_r implies that both δ_i and p_r are larger than P_i. Since P₁ is 0.69 in 4-AP, and 0.88 in PTP, both δ1 (noted as δ) and p_r are ≥0.69 in 4-AP, and ≥0.88 in PTP. These results indicate that we did reach the conditions of elevated release probability and docking site occupancy that are required for a meaningful evaluation of RRP size.

During PTP, virtually all SVs initially bound to the proximal docking site are released by the first AP, making replenishment of this site necessary for release in response to the second AP. P₂ then reflects the number of SVs that have moved from the distal (replacement) site to the proximal (docking) site during the time interval separating the first and the second AP (10 ms). In the RS/DS model, this number is determined by r, the probability of transition from replacement site to docking site. As this transition is known to occur within a few milliseconds after a strong calcium entry (Miki et al., 2018; Miki et al., 2016), r is likely elevated (possibly close to 1) during the 10-ms interval separating the first two APs. Apart from the r transition, obtaining a release event in response to the second AP also depends on the initial occupancy of the replacement site, ρ, as well on p_r. Altogether, in this condition, P₂ can be approximated by the product of ρ, r, and p_r. As the experimental value of P₂ in PTP is 0.67, by the same reasoning as above, it follows that both ρ and r are ≥0.67.

The above argument assumes that SV replenishment through the combined s and r pathway (SVs upstream of the RRP) does not significantly contribute to P₂. Consistent with this assumption, the steady-state response at the end of a train is low, indicating that the probability of entry into the replacement site, s, is low. Furthermore, the recruitment of upstream SVs requires an empty replacement site and will therefore be delayed until the replacement site is free. Because ρ is close to 1 initially, the combined s and r pathway is unlikely to contribute significantly to P₂ (see numerical assessment of the potential error in Methods).

Altogether, our results show that in 4-AP and after PTP, the sum P₁ + P₂ can serve as an estimate of the maximal RRP size per docking site.

As shown in the right plot of Figure 4, the sum P₁ + P₂ was significantly larger than 1 both in 4-AP (1.34 ± 0.05; p_t < 0.01; n = 14) and during PTP (1.54 ± 0.05; p_t < 0.01; n = 8). This indicates that the initial RRP size was larger than 1 SV per docking site in both of these experimental conditions.

When examining the time course of release in our control conditions (3 mM Ca₀), we found that peak release rates decreased as a function of stimulus number at the end of AP trains, reflecting synaptic depression (Figure 5A). The extent of this depression grew markedly in the presence of 4-AP (second row) compared to control (first row). Depression became even more prominent after PTP (third row). In several experiments, after inducing PTP in the presence of 4-AP, we changed the frequency of stimulation to 200 Hz (n = 5). Under these conditions, synaptic depression was further enhanced to such an extent that individual peak release responses could not be distinguished at the end of the train (fourth row).

Figure 5

Download asset Open asset

Previous work suggests that while synchronous release (calculated over a period of 5 ms following each AP: dashed traces in Figure 5B) is largely due to the fusion of docked SVs upon AP arrival, asynchronous release (yellow traces in Figure 5A, B) primarily originates from SVs that did not belong to the RRP at the time of the AP (Miki et al., 2018; Miki et al., 2016; Sakaba, 2006; Tran et al., 2022). Such SVs can be released at a low rate within the following inter-AP interval after moving through distal and proximal docking sites, provided that these sites are empty. Therefore, the proportion of asynchronous release gives an indication on the degree of filling of the RRP. In control, only synchronous release was observed at the beginning of AP trains, but a significant share of asynchronous release was observed near the end of the train (top panel of Figure 5B). In 4-AP and during PTP, the proportion of asynchronous release was initially as low as in control, but this proportion increased more rapidly as a function of stimulus number (second and third panels of Figure 5B). Strikingly, when increasing the stimulation frequency to 200 Hz during PTP, most release events near the end of the trains were asynchronous, and synchronous release was not detectable for i > 5 (bottom right panel in Figure 5B). Differences in release time courses between experimental conditions can be appreciated by examining superimposed cumulative release curves (Figure 5C). Altogether, the evolution of the synchronous component of release during trains (Figure 5A) and that of the proportion of synchronous vs. asynchronous release (Figure 5B) both indicate that RRP depletion during trains increases markedly from one condition to the next and becomes close to complete for 200 Hz stimulation during PTP.

According to the scheme of Figure 1B, in the extreme case where the RRP is full and p_r = r = 1, the RRP should be equally distributed between s₁ and s₂, with values close to 1 per docking site in both cases, while s_i should be small for i > 2. The bottom right panel in Figure 5B depicts the evolution of synchronous release in the 200 Hz condition (recorded under 4-AP and after PTP induction). Here, s₂ is only slightly smaller than s₁, and s_i falls off abruptly as a function of i for i > 2. This fall-off can be fitted by an exponential function with an asymptote at 0 ordinate value, and a time constant of 1.66 inter-AP intervals (corresponding to 8.3 ms). These data indicate that synaptic depression is weak for i = 2, but very rapid and complete thereafter, thus approaching the predictions of the scheme of Figure 1B. To quantify the extent of synaptic depression in the various experimental conditions, we calculated the amount of synchronous release per AP at the end of the trains from the slopes of regression lines fitted to the cumulative synchronous release during the steady state of each condition (gray lines in Figure 5B). We then divided this number by the number of SVs released by the first AP. The resulting curve steeply decreased from 0.83 in control conditions to 0.23, 0.14, and 0.10 in 4-AP, PTP, and 200 Hz, respectively (red curve in Figure 5D, bottom). This confirms the increasing effectiveness of the various conditions chosen in the present study to enhance synaptic depression. In contrast, the paired-pulse ratio, calculated as s₂/s₁, changed much less steeply across experimental conditions, and it remained close to 1 even when s₈/s₁ had reached very low values (green curve in Figure 5D, bottom). This indicates that the second response in a train is largely immune to synaptic depression, as predicted by the scheme in Figure 1B.

To obtain a more accurate estimate of the RRP size, we adapted the classical Schneggenburger–Meyer–Neher (SMN) method of back-extrapolation of cumulative excitatory postsynaptic potential (EPSC) amplitudes (Schneggenburger et al., 1999), using SV numbers in place of EPSC amplitudes. The SMN method is accurate only under conditions where the synapse is strongly depressing (Neher, 2015). As described above, synaptic depression and RRP depletion were marked under our experimental conditions. Therefore, we applied the SMN method to the synchronous release points obtained 5 ms after each AP (Neher, 2015; Schneggenburger et al., 1999; Thanawala and Regehr, 2013). Summed numbers of synchronously released SVs for stimuli 6–8 (in control conditions) or 5–8 (other conditions) were fitted to straight lines that were back-extrapolated to the time of stimulus number 1, giving a value P_back (Figure 5B, gray lines and open circles). The estimated RRP was 0.85 SV per docking site in control, 1.66 SVs per docking site in 4-AP, and 1.87 SVs per docking site in PTP. Thus, both in 4-AP and during PTP, the SMN method indicates an RRP size that exceeds 1 SV per docking site. This confirms the earlier findings on the sum of P₁ + P₂ in the same conditions (Figure 4). Finally, when using 200 Hz stimulation, the SMN method gave an RRP estimate of 2.09 SVs per docking site (Figure 5B, bottom). The higher extrapolated value obtained for 200 Hz stimulation compared to 100 Hz was attributable to a more profound extent of synaptic depression, as discussed earlier. Notably, the values after PTP, both at 100 Hz and at 200 Hz, are close to the maximum value of 2 predicted by the RS/DS model (Figure 5D, top).

To test the ability of the RS/DS model to account for the effects of 4-AP and PTP, we next performed Monte Carlo simulations of synaptic output during trains following established procedures (Miki et al., 2016; Figure 6). With each AP, the replacement site/docking site assembly, as shown in Figure 6A, evolved with transition probabilities of s (filling of empty replacement site), r (filling of empty docking site), and p_r (release probability of an occupied docking site). The values of s, r, and p_r were assumed constant throughout the AP train. The initial occupancy of the docking site, δ, was treated as a free parameter and the initial occupancy of the replacement site, ρ, was set to 1. The parameters s, r, p_r, and δ were determined in each experimental condition (control, 4-AP, and PTP) by fitting to the mean number of released SVs after the first five APs. Near the end of the train, additional phenomena introduced significant deviations from the model, as discussed later.

Figure 6 with 2 supplements see all

Download asset Open asset

In Figure 6, simulation and experimental results are compared in two different plots: the s_i plot, showing the mean number of released SVs during a train (top row), and the cov(S_i, s_i+1) plot, showing the covariance between the total number of released SVs up to stimulus i and the number of released SVs after the following stimulus (bottom row; Miki et al., 2016).

In control conditions, the model returned an initial docking site occupancy δ = 0.65. The release probability of docked SVs, p_r, was 0.6. The probability to fill an empty replacement site during one inter-stimulus interval, s, was 0.35. Finally, the transition probability from replacement site to docking site during one inter-stimulus interval, r, was 0.7. With these control values, the model was able to capture many features of the evolution of mean numbers and covariance as a function of stimulus number (Figure 6A).

As expected, the model indicated a markedly increased probability of release of a docked SV in the presence of 4-AP, from 0.6 to 0.9. δ increased moderately (from 0.65 to 0.8), possibly because the Ca²⁺ concentration increased in the presynaptic terminals (Malagon et al., 2020). The other two kinetic parameters r and s retained their control values (Figure 6B). During PTP, model parameters were kept as before, except that the docking site occupancy increased from 0.8 to 0.9 (Figure 6C).

The model derived from the fit of s_i curves was used without further parameter adjustment to fit covariance curves. As may be seen in the lower panels of Figure 6, the model correctly predicted the general amplitude and the shape of the cov(S_i, s_i+1) plot as a function of i in the three experimental conditions of Figure 3. Covariance results and simulations were rather shapeless as a function of i in control, but they displayed a marked peak for i = 2 in 4-AP and in PTP.

The initial low covariance value in 4-AP and PTP (cov(S₁, s₂) = cov(s₁, s₂)) can be explained as follows. As p_r is very high (p_r = 0.9 according to the simulation shown in Figure 6, upper panels), successful release in response to the first AP mainly depends on the docking site being occupied prior to that AP. Following release elicited by this AP, almost all docking sites are empty. They refill during the first inter-AP interval with a probability r, independently of the initial state of occupancy prior to the first AP. Therefore, the variations in s₂ primarily originate in variations in the docking site occupancy prior to the second AP, and they are almost entirely independent of the variations in s₁. This results in a low-amplitude negative value for the first entry in the covariance plot.

Let us now consider the second point of the covariance plot, cov(S₂, s₃) = cov((s₁ + s₂), s₃). Following the second AP, some sites have released their entire RRP during the first two APs, following a successful r transition during the first inter-AP interval. These sites tend to have a high (s₁ + s₂) value and a low s₃ value. Other sites have retained their original SV on the replacement site up to the second AP, as the r transition has failed to occur during the first inter-AP interval. These other sites tend to have a low (s₁ + s₂) value and a high s₃ value. This compensatory effect between (s₁ + s₂) and s₃ results in a high-amplitude negative value for the second entry in the covariance plot.

We have found recently that replacement SVs are fed by an upstream vesicular pool of small size, the intermediate pool (IP: Tran et al., 2022). Near the end of a train, as the IP is depleted, RRP replenishment is reduced, so that the synaptic output is also reduced. Accordingly, the deficit of synaptic output observed for i = 6–8 in Figure 6 is likely explained by a depletion of the IP. To explore this possibility further, we performed additional simulations assuming an IP with an initial pool size of 10–15 SVs for an AZ of four docking sites, corresponding to 2.50–3.25 SVs per docking site. The IP was replenished by an infinite recycling pool with a transition probability of r_IP. Coupling between IP size and RRP was introduced by making the transition probability s proportional to the filling state of the IP. This resulted in an improvement of the fit near the end of the train (Figure 6—figure supplement 1).

After performing the IP correction, a residual discrepancy remained between simulated and experimental data near the end of AP trains. To explain this discrepancy, we note that our model does not include a provision accounting for asynchronous release. At the end of AP trains, asynchronous release reflects the movement of replenishment SVs across the RRP without stopping at RS or DS sites, due to persistent elevation of the presynaptic calcium concentration (Miki et al., 2018). Our model artificially forces these SVs to stop at RS and/or DS sites and to be counted as synchronous release. This causes synchronous release to appear larger in the model than in experimental data near the end of trains, even after IP correction.

We next compared the predictions between the RS/DS model (without consideration of the IP) and the LS/TS model (Figure 6—figure supplement 2). In the LS/TS model, as in the RS/DS model, we optimized parameters to fit the first five s_i values. In control conditions, both RS/DS and LS/TS models gave reasonably close representations of the data (Figure 6—figure supplement 2B). Note that the LS/TS model used very high values of r (0.95) and s (0.8).

In 4-AP, the LS/TS model could account for P₁ by increasing δ and p_r, but it displayed a value of P₂ below experimental observations (Figure 6—figure supplement 2C, upper panel). A variation on the LS/TS model adds a transitory state, the tight labile state, which is present only at high frequencies (Lin et al., 2022). It consists of LS vesicles that tightly dock for a short time after an AP. This can be understood as a short-lived increase in r. In our model such a modification cannot increase synaptic output significantly, as r = 0.95. Introducing an IP with a size of 10 improved the fitting only marginally (upper panel in Figure 6—figure supplement 2C ).

The LS/TS model could account for cov(S_i, s_i+1) data in control conditions (Figure 6—figure supplement 2B, lower panel), but it failed to do so in 4-AP (Figure 6—figure supplement 2C, lower panel). In 4-AP, whereas data and RS/DS simulations display a peak amplitude for i = 2, the LS/TS simulation displays a peak amplitude for i = 1. In the LS/TS model, release events following the first AP come from sites initially in the TS. Such release events are unlikely to be followed by an immediate TS refilling from the LS, since LS occupancy is incompatible with TS occupancy. Conversely, most release events following the second AP are due to sites that were in the LS state before the first AP, and were therefore unable to release in response to the first AP. This results in a large amplitude negative covariance point for i = 1. The covariance then decreases for higher i values as the RRP is depleted and release increasingly relies on replenishment through the s pathway.

These simulations suggest that the LS/TS model, which is simpler than the RS/DS model and contains less free parameters, can be considered as a good approximation for synapses where release probability and/or docking site occupancy are moderate.

Previous studies have led to the proposal of the RS/DS model at PF–MLI synapses based on (1) variance–mean analysis of SV counts in response to AP trains; (2) variance–mean analysis of cumulative SV counts; (3) covariance analysis of SV counts for successive AP stimulations in a train; and (4) two-step release during trains (Miki et al., 2016; Miki et al., 2018). The present study adds to this evidence by extending covariance data to conditions of very high docking site occupancy and release probability, as discussed above, and by showing that the ratio of RRP size to number of docking site reaches a maximum of 2 under the same conditions. Taken together these studies build a strong case in favor of the RS/DS model in the present preparation from a functional point of view.

However, uncertainties remain concerning the molecular composition and the morphological arrangement of docking sites. This is particularly true for PF–MLI synapses. Disrupting actin filaments by latrunculin B or inhibiting myosin II by blebbistatin results in an uncoupling between RS and DS (Miki et al., 2016). Activating synapsins following PKA activation increases the RRP size without changing p_r (Vaden et al., 2019). Apart from these findings, the effects of specific molecular modifications on the RS/DS system of PF–MLI synapses remain to be explored. Likewise, morphological data indicating SV movement between RS and DS are lacking in this preparation, although such data have been found in other preparations (Chang et al., 2018; Kusick et al., 2020; Miki et al., 2020; Martín et al., 2020; Vandael et al., 2020; Fukaya et al., 2023). Further molecular and morphological studies are needed to ascertain the applicability of the RS/DS model to the PF–MLI synapse.

Our analysis and conclusions rest on several critical assumptions that are examined in turn below.

A first assumption of our RS/DS model is that within an AZ, all RS/DS assemblies operate in a similar manner. Alternative models would hold that release sites are not equivalent, and that some sites release SVs with much higher p_r values than others (parallel models: Eshra et al., 2021; Hallermann et al., 2010; Ritzau-Jost et al., 2014; Ritzau-Jost et al., 2018). In general, distinguishing between parallel and sequential models is a difficult task that cannot be solved with absolute certainty. A study of mean and variance results at the synapse between PFs and Purkinje cells (PF–PC synapses) suggested at first a parallel model for this synapse (Valera et al., 2012), but additional results from the same group examining the behavior of PF–PC synapses in response to long trains at various stimulation frequencies favored a sequential model instead (Doussau et al., 2017). At PF–MLI synapses, our previous study of variance–mean data indicated a sequential model (Miki et al., 2016). Based on this previous work, we framed the interpretation of the present results on sequential models (RS/DS or LS/TS) with homogeneous docking/release properties; but alternative parallel models cannot be ruled out entirely.

A second assumption is that p_r does not change during a train, that is, p_r is independent of i. In other synapses, a moderate increase of calcium entry occurs as a function of i, accounting for part of facilitation (e.g., in the calyx of Held: Borst and Sakmann, 1998; Lin et al., 2022). In contrast, at synaptic boutons of cerebellar GCs, AP-driven calcium entry is independent of i (Miki et al., 2016; Kawaguchi and Sakaba, 2017). In addition, since our results and analysis indicate that p_r is high in the present work (with an estimated value of 0.9 in 4-AP), any potential further increase of p_r during trains is bound to be small.

A third assumption is that RRP release is kinetically separate from RRP replenishment from upstream pools (recycling pool and IP). In the SMN analysis, RRP replenishment is assumed to be linear as a function of time, and to correspond to the late linear part of the plot of cumulative release as a function of time. The initial rate of SV release calculated for the first two stimuli in the cumulative plot of Figure 5C in 200 Hz conditions is markedly higher than that calculated for the corresponding late period asymptotic line (with ratios of 2.6 in 4-AP, 3.3 in PTP, and 4.3 in 200 Hz), suggesting a good separation between release and replenishment. The actual ratio is likely larger than suggested by these numbers, since the rate of RRP replenishment is slower at the onset of the stimulation train (due to the cumulative calcium rise driving replenishment yet to reach its peak and the initial high filling state of the RRP inhibiting replenishment: Ruiz et al., 2011; Thanawala and Regehr, 2013; Neher, 2015). We calculated the contribution of replenishment to s₁ and s₂ release and found that it is negligible even under high p_r conditions (see Methods). The large extent of synaptic depression of synchronous release obtained in 4-AP, after PTP and when using 200 Hz stimulation (Figure 5D), is consistent with a good separation between RRP release and replenishment.

Altogether, departures from the above assumptions (homogeneous release site properties inside an AZ; constant p_r during a train; kinetic separation between RRP release and replenishment) cannot be ruled out, but such departures, if they occurred, are unlikely to have affected the main conclusions of our study.

While the RS/DS model had been previously proposed in this preparation (Miki et al., 2016; Miki et al., 2018), a key model prediction that the RRP size per docking site could reach a value close to 2 SVs had not been tested until the present work. An early estimate based on the SMN method gave a value close to 1 SV per docking site (Miki et al., 2016); this value was obtained in rats in a 3-mM external calcium concentration without K⁺ channel blocker, leaving open the possibility for alternative models such as the LS/TS model. Likewise, in the present study the SMN method gives an estimate of 0.85 SV per docking site for mice in the same solution (Figure 5B, top). The question remained open as to whether larger values could be obtained under certain experimental conditions.

Importantly, the SMN method actually measures the difference between the original size of the RRP and the size reached at steady state (Neher, 2015). Because RRP depletion is incomplete during sustained AP stimulation, the extrapolation measurement yields an underestimate of the RRP size (Neher, 2015). In addition, the original RRP size does not necessarily correspond to the number of available SV-binding sites because at rest, a fraction of these sites is not occupied (Miki et al., 2016; Neher and Brose, 2018; Trigo et al., 2012). Altogether, because of incomplete RRP depletion and because of incomplete site filling, traditional RRP measurements return values that can be markedly smaller than the number of available binding sites in the RRP. In order to perform a meaningful RRP size measurement for the purpose of the present work, it appeared important to maximize release probability (and consequently, synaptic depression) and to maximize site occupancy.

No special step was taken to increase ρ since earlier studies in rats suggested high ρ values (0.9: Miki et al., 2018; Miki et al., 2016). Consistent with these previous studies, high ρ values were needed in the present work to explain high P₂ values under conditions of very high release probability (in 4-AP after PTP). Our simulations indicate ρ values indistinguishable from 1 in all experimental conditions (control, 4-AP, and PTP). In all three cases, ρ estimates were larger than δ estimates. These results indicate that in basal conditions, the rate constant of the undocking transition (from docking site to replacement site) is larger than that of the docking transition (from replacement site to docking site).

Previous work indicates that elevating the external calcium concentration enhances the RRP size (Thanawala and Regehr, 2013) and more specifically, increases δ (Blanchard et al., 2020; Kobbersmed et al., 2020; Malagon et al., 2020; Tanaka et al., 2021). Therefore, all experiments were carried out in 3 mM external calcium. Under these conditions, our δ estimate is 0.7 (Figure 6), higher than our previous estimates (0.45–0.47: Malagon et al., 2020; Miki et al., 2016). The difference is likely due to species difference (mice in the present work, vs. rats in previous studies), since the estimate by Miki et al., 2016 rested on a similar approach to that of the present work. Thus, selecting mice rather than rats for the present experiments, together with using a high external calcium concentration, contributed to enhancing docking site occupancy. In addition, we were able to further increase δ (from 0.7 to 0.9 according to the analysis of Figure 6) by applying a PTP protocol. This result is consistent with previous work at the calyx of Held (Lee et al., 2010) and at hippocampal mossy fiber synapses (Vandael et al., 2020), as well as with our recent finding that at PF–MLI synapses, PTP increases SV docking of a specific subclass of SVs originating from a local, calcium-sensitive recycling pathway (Tran et al., 2023).

Finally, to maximize p_r, we combined the effects of the potassium channel blocker 4-AP with those of the high external calcium concentration. In agreement with earlier results in rats (Malagon et al., 2020), this combination allowed us to reach p_r values close to 1 (estimated at 0.9 in 4-AP both before and after PTP induction: Figure 6). Combining large values of δ and p_r in the present work led to a P₁ value close to 1 during PTP (P₁ = 0.88, compared to a maximum P₁ value of 0.51 in our previous work: Malagon et al., 2020). Obtaining a p_r value close to 1 was important here as it ensured that initially occupied docking sites would be cleared after a single AP, thus freeing the way for the docking of SVs initially in the replacement site during the following inter-stimulus interval.

Our conclusions depend on the accuracy of our N estimates. N estimates in the present work are particularly reliable because (1) SV counting eliminates potential errors linked to receptor saturation or desensitization in classical EPSC studies and (2) high P conditions make N estimates via variance–mean analysis or binomial analysis accurate (Malagon et al., 2020).

Even though high P conditions result in accurate N determination, one possible pitfall could be that under these conditions, certain SV release events could be too close in time to be distinguished, leading to s_i undercount. Undercounting should worsen as release probability or docking site number grow, and to be worst for i = 1. s_i undercount could lead to left shifts of variance–mean and binomial probability plots and hence to N underevaluation. Against this possibility, our estimates of the numbers of overlapping events at short intervals indicate a small extent of undercounting even under conditions of high release probability (see Methods). Secondly, our N estimates obtained either with variance–mean analysis (Figure 3B) or with binomial analysis (Figure 3C, D) were independent of release probability. Finally, undercounting at high P values predicts that apparent values of s₁ should grow sublinearly as a function of the estimated N value, while apparent P₁ values should increase as a function of N. Contrary to this prediction, we found that s₁ values increased linearly as a function of N, and that our P₁ estimates were independent of N (Figure 3—figure supplement 1). Altogether, it appears that undercounting did not significantly affect our N estimates.

Our results indicate that a single docking site can be associated with up to 2 SVs at simple PF–MLI synapses, thus giving strong experimental support in favor of the RS/DS model. Nevertheless, it is important to stress that under physiological conditions, the actual RRP size is likely significantly less than 2 SVs per docking site. In our control conditions, with 3 mM Ca_o, we obtained an estimate of 0.85 SV per docking site with the SMN method. This value is an underestimate since the residual synaptic responses were significant near the end of the AP train for these data (Figure 5A, top), indicating incomplete RRP depletion (Neher, 2015). A more realistic estimate based on the sum of ρ and δ values obtained in our simulations for this condition is 1.65 SVs per docking site (with estimated values of 1 and 0.65 for ρ and δ, respectively: Figure 6). After PTP induction, corresponding estimates are 2.09 SVs per docking site (SMN method: Figure 5D, top panel) and 1.9 SVs per docking site (sum of ρ and δ in relevant simulations, see Figure 6). Earlier studies in the rat suggested a value of 0.9 for ρ, independently of Ca_o, and a value δ = 0.2 in 1.5 Ca_o and δ = 0.5 in 3 Ca_o, suggesting RRP sizes of 1.1 SVs and 1.4 SVs per docking site, respectively (Malagon et al., 2020; Miki et al., 2016). These results suggest that the RRP size varies across species and across experimental conditions. They further indicate that synapses do not operate at full RRP capacity under ordinary physiological conditions. Finally, our results together with previous work suggest that synapses modulate their RRP size during certain forms of synaptic plasticity, as discussed above for the case of PTP.

Central mammalian synapses are very diverse functionally, and this is reflected in differences in the structure and molecular composition of their AZs (Sakamoto et al., 2022). PF–MLI synapses, as well as other synapses of the cerebellar molecular layer involving PF signaling (including mossy fiber-granule cell synapses and PF–Purkinje cell synapses), are characterized by a high level of synaptic facilitation as well as by fast SV replenishment (Atluri and Regehr, 1998; Bao et al., 2010; Hallermann et al., 2010; Ritzau-Jost et al., 2014; Saviane and Silver, 2006). In contrast, other synapses such as the calyx of Held display less facilitation and slower SV replenishment (Taschenberger et al., 2005; Taschenberger et al., 2016; Lin et al., 2022). At synapses between hippocampal mossy fibers and CA3 interneurons, where synaptic depression is prominent, the RRP size per docking site was recently estimated with the SMN method at 1.6 SVs in 3 mM Ca_o (Tanaka et al., 2021), compared to 0.85 SV in the present study. Based on these results and on the simulations in the present work, it can be speculated that synapses with high p values exhibiting synaptic depression may more readily reach conditions where the ratio of RRP size to N is larger than 1, compared with synapses with low p values exhibiting synaptic facilitation. Future work will be needed to test this prediction.

The finding of 2 SVs per docking site implies the existence of two separate SV-binding sites able to accommodate two SVs simultaneously. In EM studies performed at amphibian (Szule et al., 2012) and mammalian (Nagwaney et al., 2009) neuromuscular junctions, as well as in hippocampal cultured neurons (Cole et al., 2016), two sets of SVs likely belonging to the RRP have been identified. These EM data are consistent with the suggestion that the RRP comprises two classes of SVs that bind at distinct distances from release sites, with distance differences on the order of one SV diameter. In such a situation an RRP size of 2 per release site is plausible. Other EM studies identified a separate set of SVs located at a distance of about 5–10 nm from the plasma membrane. For these SVs, docking appears to involve a short distance movement from their pre-docked resting state to a fully docked state where they are in direct contact with the plasma membrane (Chang et al., 2018). This second set of EM results is consistent with the suggestion of two mutually exclusive pre-docked and docked states (Neher and Brose, 2018). In such a situation each docking site can accommodate maximally one SV, such that the maximal RRP size is 1 per docking site (LS/TS model, Neher and Brose, 2018; Figure 6—figure supplement 2). Altogether, some EM results appear to favor the RS/DS model (RRP size up to 2 SVs per docking site) while other EM results appear to favor the RS/DS model (RRP size up to 1 SV per docking site). It is possible that these differences reflect differences in synapse structure depending on synaptic class.

Various potential functional advantages can be envisaged for having up to 2 bound SVs per docking site.

Firstly, the RRP capacity is increased, since the RRP size can reach up to 2 SVs per docking site, compared to up to 1 SV per docking site in the LS/TS model. The increased RRP capacity translates into a larger responsiveness of the synapse at the onset of AP train stimulation. This is potentially important for simple synapses, having but a few docking sites, as a larger total number of released SVs improves the reliability of synaptic output during the first APs in a train.

Secondly, a mechanism of facilitation based on a calcium-dependent increase in docking occupancy (Miki et al., 2016; Neher and Brose, 2018; Silva et al., 2021) is more feasible if each docking site can accommodate up to 2 SVs compared to 1 SV. This is because the complement of SVs available to refill the docking sites is larger in the former case than in the latter (Miki et al., 2016).

Third, doubly occupied docking sites contribute to spreading the release of the RRP over a wider range of AP numbers. For docking sites that are doubly occupied at train onset, the movement of SVs from replacement site to docking site must await clearing of the docking site by exocytosis, thus delaying the release of the SV initially occupying the replacement site to later AP numbers in the train. This effect, together with facilitation, counterbalances the synaptic depression following release of docked SVs, and helps retaining a relatively stable synaptic output as a function of AP number during trains.

A fourth potential functional advantage of doubly occupied docking sites is that the replacement site can act as an entry gate into the RRP. A high occupancy of the replacement site may result in a reduction of the flow of SVs into the RRP, independently of the state of occupancy of the docking site. By controlling the filling state of a separate replacement site, in ways that remain to be investigated, the synapse may be able to control RRP replenishment rate.

C57BL/6 mice (10–16 days old; either sex) were used for preparation of acute brain slices. Animals were purchased from Janvier Laboratories (RRID:MGI:2670020). They were housed and cared for in accordance with guidelines of Université Paris Cité (approval no. D 75-06-07; animal rearing service of the BioMedTech Facilities, INSERM US36, CNRS UMS2009).

200-μm thick sagittal slices were prepared from the cerebellar vermis as follows. Mice were decapitated and the cerebellar vermis was carefully removed. Dissections were performed in ice-cold solution containing the following (in mM): 130 NaCl, 2.5 KCl, 26 NaHCO₃, 1.3 NaH₂PO₄, 10 glucose, 1.5 CaCl₂, and 1 MgCl₂ (artificial cerebrospinal fluid or ACSF). After cutting with a vibratome (VT1200S; Leica), slices were incubated in ACSF at 34°C for at least 45 min before being used for experiments.

Whole-cell patch-clamp recordings were obtained from MLIs (comprising both basket and stellate cells). The extracellular solution contained (in mM): 130 NaCl, 2.5 KCl, 26 NaHCO₃, 1.3 NaH₂PO₄, 10 glucose, 3 CaCl₂, and 1 MgCl₂ (pH adjusted to 7.4 with 95% O₂ and 5% CO₂). The internal recording solution contained (in mM): 144 K-gluconate, 6 KCl, 4.6 MgCl₂, 1 EGTA (Ethylene glycol-bis tetraacetic acid), 0.1 CaCl₂, 10 HEPES (4-(2-hydroxyethyl)-1-piperazineethanesulfonic acid), 4 ATP-Na, 0.4 GTP-Na (pH 7.3, 300 mosm/l). All recordings were done at 32–34°C, after adding gabazine (3 μM) to block GABA_A receptors. To establish a single GC–MLI connection, puffs using a glass pipette filled with the high K⁺ internal solution were applied to identify a potential presynaptic GC. The same pipette was then used for extracellular electrical stimulation of the GC, with minimal stimulation voltage (10–40 V; 150 μs duration). If the resultant EPSCs, particularly those that occurred after a short stimulation train, were homogeneous, then it was likely that only one presynaptic cell was stimulated.

Recordings were only accepted as a simple synapse recording after analysis if the following three criteria were satisfied (Malagon et al., 2016): (1) the EPSC amplitude of the second release event in a pair was smaller than that of the first, reflecting activation of a common set of receptors belonging to one postsynaptic density; (2) all the EPSC amplitudes follow a Gaussian distribution with a coefficient of variation <0.5; and (3) the number of release events during the baseline recording was stable.

A broad-spectrum blocker of voltage-dependent K⁺ channels, 4-aminopyridine (4-AP), was used at a final concentration of 15 μM to enhance the release probability (see below). 4-AP was dissolved in water and stock aliquots were kept at −20°C.

It was recently shown that increasing the external calcium concentration leads both to an increase in the occupancy of docking sites at rest, δ, and to an increase of the release probability of docked SVs, p_r (Blanchard et al., 2020; Eshra et al., 2021; Kobbersmed et al., 2020; Malagon et al., 2020; Tanaka et al., 2021). Both effects should help minimizing the difference between the number of SVs released after two APs and the number of SV-binding sites. Therefore, in the present work, we used an elevated external calcium concentration (3 mM). We also used the potassium channel blocker 4-AP, which is very effective in increasing release probability at various synapses including PF–MLI synapses (Heuser et al., 1979; Ishikawa et al., 2003; Malagon et al., 2020; Tan and Llano, 1999). In addition, PTP has been reported to increase the proportion of SVs in the fast releasing pool at the calyx of Held (Lee et al., 2010). At hippocampal mossy fiber synapses, PTP involves increases in the RRP size and in the number of docked SVs (Vandael et al., 2020). We likewise found an increase in SV docking during PTP at PF–MLI synapses (Tran et al., 2023). Based on these results, we used in the present work a PTP protocol to increase docking site occupancy (δ), starting in a solution containing 3 mM external calcium and 4-AP. PTP was performed by applying 60 consecutive trains of 8 APs at 100 Hz, with an inter-stimulus interval of 2 s (Tran et al., 2023).

Finally, we used high stimulation frequencies (100–200 Hz) to maximize synaptic depression and to separate as much as possible RRP consumption from RRP replenishment (rate s in Figure 1A; Schneggenburger et al., 1999).

Offline analysis of electrophysiological data was performed using Igor Pro (WaveMetrics). Statistical analysis was conducted using Igor Pro. Data are expressed as mean ± standard error of the mean (SEM). Error bars in all graphs indicate SEM. Details of statistical tests are described in the text or figure legends. Statistical significance was accepted when p < 0.05. The number of cells tested is indicated by a lowercase n, each derived from a different animal. Within each cell, data were averaged in each experimental condition across a number of trials that was 20 or larger.

The time of occurrence and the amplitude of individual release events were determined based on deconvolution analysis, as described previously (Malagon et al., 2016). In brief, for each synapse, an mEPSC (miniature excitatory postsynaptic current) template was obtained and fitted with a triple-exponential function with five free parameters (rise time, peak amplitude, fast decay time constant, slow decay time constant, and amplitude fraction of slow decay). These five parameters were then used for deconvolution of the template and of individual data traces, producing a narrow spike (called spike template) and sequences of spikes, respectively. Next, each deconvolved trace was fitted with a sum of scaled versions of the spike template, yielding the timing and amplitude of each release event. The amplitude was further corrected for receptor saturation and desensitization, using the exponential relationship between individual amplitudes and the time interval since the preceding release events. Events that were at least 1.7 times larger than the average mEPSC were split into two (Malagon et al., 2016) (see below). s₁ was determined as the number of SVs released within 5 ms after the first AP of a train. s₂ was the number of SVs released within 5 ms after the second AP.

The mean percentage of splitted events was 4.3% in control experiments, 2.9% in 4-AP, and 3.7% after PTP. In response to the first AP, the percentage of splitting was 10.0% in control experiments, 10.3% in 4-AP, and 12.3% after PTP. These results indicate little SV undercounting linked to insufficient time separation between events.

The amplitudes and kinetics of the mEPSC template were unchanged after addition of 4-AP or after PTP. Therefore, the initial template obtained in 3 mM Ca_o was used throughout each experiment. These results confirm that the changes associated with our experimental manipulations are purely presynaptic.

As in our previous work, we found that latency distributions were biphasic, and that they could be fitted with a biexponential decay curve. The fast decaying component, with time constant τ_f, reflected the release of docked SVs, while the slow decaying component, with time constant τ_s, reflected two-step release (originating from the RS: Miki et al., 2018). Values of τ_f and τ_s in 3 mM Ca_o were 0.47 and 4.0 ms, close to previous values in the same condition (Miki et al., 2018). The percentage of slow decay grew as a function of i from 0% for i = 1 to 50% for i = 8, again in agreement with our previous study. In 4-AP, τ_f increased to 0.70 ms, probably reflecting a prolongation of the duration of presynaptic calcium entry, while τ_s did not change significantly.

When comparing latency distributions before and after addition of 4-AP, we also found a shift of the rising phase of the latency histograms to the right, corresponding to an additional latency component of 0.2 ms. This additional latency likely corresponds to a delay of calcium entry following a lengthening of the AP waveform in the presence of 4-AP.

Variance–mean analysis (Figure 3A, left, B) was performed using Igor Pro as described previously (Miki et al., 2016) to estimate the number of docking sites (N). Briefly, plots of var(s_i) as a function of <s_i> were fitted using a parabola with an initial slope of 1. The intersection of this parabola with the x-axis of the plot gave the maximum N value, which when approached to the closest integral, corresponds to the number of docking sites. To obtain P_i, s_i is divided by N. In conditions of high p_r, as in the example in Figure 3A, right, the data points approach the intersection of the parabola, as they reach the maximal output of the synapse. The group analysis presented in Figure 3B was performed after normalizing mean and variance of individual synapses to N = 4.

According to the binomial distribution, the probability that s_i, the number of SVs released after AP number i, equals k is p(k) = P_i^k (1 − P_i)^N−k N!/(k!(N − k)!), where P_i is the release probability per docking site and N is the number of docking sites (Malagon et al., 2016). The values of N and P were obtained by minimizing the summed squared deviations between the binomial prediction and data (Figure 3C, D). This fitting was carried out for s₁ and s₂ of each synapse and its values compared with the result of the variance–mean curves. This analysis is more robust under high P conditions, so the 4-AP data were used to determine N. Group average analysis across experimental conditions was performed on synapses with the same number of docking sites (N = 4; Figure 3D).

Covariance analysis reveals whether the fluctuations of one paramater around its mean value are linked together with the fluctuations of another parameter, either positively (positive covariance) or negatively (negative covariance). In the present work, we analyze the covariance between the sum S_i = (s₁ + s₂ + … + s_i) and s_i+1. A negative covariance is expected if SVs compete for binding to docking sites, with an amplitude depending on the mode of occupancy of docking sites (Miki et al., 2016; Scheuss and Neher, 2001). The covariance was determined experimentally as cov(S_i, s_i+1) = <S_i − <S_i>> <s_i+1 − <s_i+1>> and was used to assess the validity of docking site models using Monte Carlo simulations.

Here, we assess the contribution of replenishment from upstream pools (s transition) to the sum (P₁ + P₂) using the model of Figure 6. Because this model assumes an initial ρ value of 1, replenishment SVs (originating in the IP) cannot advance beyond the RS during the first inter-AP interval. Consequently, there is no contribution of upstream pools to P₁, and the only contribution of upstream pools to P₂ comes from RS, following partial replenishment of these sites during the first inter-AP interval. Using the model of Figure 6 and Monte Carlo simulations, we found that in PTP, the value of ρ at the end of the first inter-AP interval was ρ₂^total = 0.460, of which the contribution coming from replenishment was ρ₂^{replenishment} = 0.097. Because these SVs are in replacement sites, they can contribute to P₂ release only in the form of two-step release (Miki et al., 2018). From an analysis of the time course of averaged release rate across experiments (as in Miki et al., 2018), we estimated the time course of two-step release as an exponential with a time constant of 4 ms, and the amplitude of two-step release at 0% and 20% of total synchronous release after AP number 1 and AP number 2, respectively. For AP number 2, the share of total synchronous release due to two-step release in our 5 ms long measurement window is 2-stepratio = 0.2 × (1 − exp(−5/4)) = 0.14. Combining this ratio with ρ₂^{replenishment}/ρ₂^total, we obtain the percentage of the P₂ response coming from replenishment:

The corresponding ratio for P₁ is P₁^{replenishment}/P₁^total = 0 since 2-stepratio = 0 after the first AP.

Given the experimental values P₁^total = 0.88 and P₂^total = 0.67 (Figure 4), it can be calculated that 1.3% of the sum (P₁ + P₂) comes from replenishment SVs in PTP. Lower percentage values would apply in control or in 4-AP, which have lower 2-stepratio values than PTP. Overall, these calculations suggest that the contribution of replenishment SVs to the sum (P₁ + P₂) may be neglected.

Monte Carlo simulation of two-step SV docking and release (Figure 6) was performed using Igor Pro as described previously (Miki et al., 2016; Tran et al., 2022). For Figure 6—figure supplement 1, the IP was added to the RS/DS model and transitions and replenishment conditions were adapted accordingly.

In the LS/TS model transitions are equivalent to the RS/DS model (Figure 6—figure supplement 2), however only one SV can occupy the DS at a time, being either in TS or LS. The replenishment step was adapted to fit this condition. As in the RS/DS model, the distal–proximal (TS–LS) transition is sequential and release can only happen from distally bound (TS) vesicles.

For the models, parameter values are shown in figures or figure legends and were obtained by fitting using least mean squares of free parameters. For the RS/DS model with IP, parameters were kept as in the RS/DS original fitting and a new fitting was performed for the two new parameters (IP size and IP replenishment probability). Calculations were done 5000 times for each condition and the averaged values are displayed.

The funders had no role in study design, data collection, and interpretation, or the decision to submit the work for publication.

We thank Profs. Erwin Neher and Takafumi Miki for helpful comments on the manuscript. This work was supported by CNRS (UMR 8003), by Fondation pour la Recherche Médicale (grant SPF201809007190 to VT) and by the European Community (ERC Advanced Grant ‘Single Site’ nb. 294509 to AM).

C57BL/6 mice (10–16 days old; either sex) were used for preparation of acute brain slices. Animals were housed and cared for in accordance with guidelines of Université Paris Cité (approval no. D 75-06-07).

1. Sent for peer review: August 7, 2023
2. Preprint posted: August 21, 2023 (view preprint)
3. Preprint posted: September 19, 2023 (view preprint)
4. Preprint posted: December 12, 2023 (view preprint)
5. Version of Record published: January 5, 2024 (version 1)

You can cite all versions using the DOI https://doi.org/10.7554/eLife.91087. This DOI represents all versions, and will always resolve to the latest one.

© 2023, Silva et al.

This article is distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use and redistribution provided that the original author and source are credited.