A Three-Pool Model Dissecting Readily Releasable Pool Replenishment at the Calyx of Held

Although vesicle replenishment is critical in maintaining exo-endocytosis recycling, the underlying mechanisms are not well understood. Previous studies have shown that both rapid and slow endocytosis recycle into a very large recycling pool instead of within the readily releasable pool (RRP), and the time course of RRP replenishment is slowed down by more intense stimulation. This finding contradicts the calcium/calmodulin-dependence of RRP replenishment. Here we address this issue and report a three-pool model for RRP replenishment at a central synapse. Both rapid and slow endocytosis provide vesicles to a large reserve pool (RP) ~42.3 times the RRP size. When moving from the RP to the RRP, vesicles entered an intermediate pool (IP) ~2.7 times the RRP size with slow RP-IP kinetics and fast IP-RRP kinetics, which was responsible for the well-established slow and rapid components of RRP replenishment. Depletion of the IP caused the slower RRP replenishment observed after intense stimulation. These results establish, for the first time, a realistic cycling model with all parameters measured, revealing the contribution of each cycling step in synaptic transmission. The results call for modification of the current view of the vesicle recycling steps and their roles.

Although vesicle replenishment is critical in maintaining exo-endocytosis recycling, the underlying mechanisms are not well understood. Previous studies have shown that both rapid and slow endocytosis recycle into a very large recycling pool instead of within the readily releasable pool (RRP), and the time course of RRP replenishment is slowed down by more intense stimulation. This finding contradicts the calcium/calmodulin-dependence of RRP replenishment. Here we address this issue and report a three-pool model for RRP replenishment at a central synapse. Both rapid and slow endocytosis provide vesicles to a large reserve pool (RP) ,42.3 times the RRP size. When moving from the RP to the RRP, vesicles entered an intermediate pool (IP) ,2.7 times the RRP size with slow RP-IP kinetics and fast IP-RRP kinetics, which was responsible for the well-established slow and rapid components of RRP replenishment. Depletion of the IP caused the slower RRP replenishment observed after intense stimulation. These results establish, for the first time, a realistic cycling model with all parameters measured, revealing the contribution of each cycling step in synaptic transmission. The results call for modification of the current view of the vesicle recycling steps and their roles. styryl dye (e.g., FM1-43) during low and intermediate frequency stimulation that releases all recycling vesicles 18 . If this concept holds, two predictions can be made: 1) the majority of vesicles residing in the RP are irrelevant to synaptic transmission under many physiological conditions, and 2) interference of this small recycling pool will have a crucial and rapid influence on the RRP replenishment. However, our previous studies challenged the presence of a small recycling pool. First, by simultaneously recording presynaptic capacitance and postsynaptic EPSC in the absence or presence of glutamate at rat calyces, we suggest a large recycling pool ,46 times the size of RRP, which is close to the total vesicle amount measured by electron microscopy 19,20 . Such a large recycling pool confirms that almost all vesicles are mobilised to maintain synaptic transmission upon high frequency stimulation 20 . Second, we have shown that blocking of both rapid and slow endocytosis does not affect the rate of RRP replenishment 21 , which rules out the possibility that endocytosed vesicles recycle within the RRP or a small recycling pool because it predicts slower RRP replenishment when endocytosis is blocked. Therefore, our previous results suggest that endocytosed vesicles are retrieved into a large recycling pool instead of a small one.
The RRP replenishment time course is often bi-exponential with a calcium/calmodulin-dependent rapid component of ,1 s or less [22][23][24][25] . However, the source of vesicles responsible for rapid and slow RRP replenishment is unclear. Original candidates that were considered include vesicles formed by rapid endocytosis and the small recycling pool 18 . However, both candidates have been ruled out based on our previous studies 20,21 . Furthermore, we found that the RRP replenishment time course was slowed down by more intense stimulation 21 . Since the RRP replenishment is calcium/calmodulin-dependent, stronger stimulation should increase the intracellular calcium concentration, and facilitate calmodulin function to speed up the RRP replenishment 23,25 . Thus, a mechanism other than calcium/calmodulin regulation must be involved.
Here, we provide a realistic three-pool model with all parameters experimentally measured, which shows the contribution of each step in exo-and endocytosis, and explains why the RRP replenishment is composed of rapid and slow components, and why the RRP replenishment could be slowed down by intense stimulation. We further applied this model to evaluate the contribution of endocytosis under prolonged action potential-like stimulation train. The current view of vesicle cycling may need to be modified to include the large recycling pool 20 and the new intermediate pool in order to accommodate these new findings.

Methods
Slice preparation and electrophysiology. Slice preparation was similar as described previously 7,26,27 . Briefly, Postnatal day 7-10 (p7-p10) old Wistar rats of either sex were decapitated and the brain stem slices of ,200 mm thick containing the medial nucleus of the trapezoid body (MNTB) were prepared using a vibratome (VT 1200s, Leica, Germany). Recordings were made at room temperature (22-24uC). Whole-cell capacitance measurements were made with the EPC-10 amplifier together with the software lock-in amplifier (PatchMaster, HEKA, Lambrecht, Germany). Exocytosis and endocytosis are represented by capacitance changes after conditioning stimulation 20,27 . Measurements of the RRP size and RRP replenishment time course were similar to previous reports 21,26 . The presynaptic pipette (3.5-5 MV) solution contained (in mM): 125 Cs-gluconate, 20 CsCl, 4 MgATP, 10 Na 2 -phosphocreatine, 0.3 GTP, 10 HEPES, 0.05 BAPTA (pH 7.2, adjusted with CsOH). Measurements of the AMPA receptor-mediated EPSC were made by whole-cell patch at the postsynaptic principle neurons. The postsynaptic pipette (2.5-4 MV) solution contained (in mM): 125 K-gluconate, 20 KCl, 4 Mg-ATP, 10 Na 2 -phosphocreatine, 0.3 GTP, 10 HEPES, and 0.5 EGTA (pH 7.2, adjusted with KOH). The series resistance (,10 MV) was compensated by 90% (lag 10 ms). For recordings of the EPSC, kynurenic acid (1 mM) was added in the bath solution to relieve saturation and desensitisation of postsynaptic AMPA receptors. The holding potential was -80 mV for both presynaptic and postsynaptic recordings if not mentioned. Statistical analysis used a t test unless otherwise noted, and means are presented as 6 SE. All the methods were carried out in accordance with the approved guidelines and all animal experimental protocols were approved by the Animal Care and Use Committee of Fudan University.
Three-pool vesicle cycling model. With a large recycling pool ,46 times the size of RRP, we could not find any existing two-pool model that can fit the bi-exponential RRP replenishment with the rapid component being reduced by more intense stimulus 20,21 . We proposed a new model composed of three vesicle pools, a reserve pool (RP), an intermediate pool (IP) between the RP and the RRP, and a RRP with reversible first order kinetics between RP and IP (k 2 , k -2 ) and between the IP and RRP (k 1 , k -1 ). The kinetic scheme for these three pools is: Endocytosed vesicles enter only the RP, not the IP or RRP 21 , and the percentage of rapid and slow endocytosis was from our previous study 27 . As blocking endocytosis does not affect RRP replenishment 21 , to simplify the mathematical reasoning, we did not include the endocytosed vesicles when calculating all of the parameters and included them back using MATLAB Simbiology toolbox (v2014a, the Mathworks, USA) to generate the vesicle cycling in each time step. The simplified scheme is shown below: This model could explain the bi-exponential time course of replenishment by assuming a rapid rate constant for k 1 and k -1 , a slow rate constant for k 2 and k -2 , and a small IP size. The small IP could be depleted more by a more intense stimulus, explaining why the replenishment rapid amplitude was decreased, instead of increased, after more intense stimulation. In the following, we performed quantitative calculations to determine the parameters (initial size of IP, RP, and k 1 , k -1 , k 2 , and k -2 ) that fit our data.
From scheme 2, where RP, IP, and RRP are the corresponding amount at time t after stimulation.
From the law of conservation of mass, where ' denotes the steady state, or the resting condition. (We assumed them the same here to simplify calculation.) Based on equations 3-5, we obtained the second order differential equation of RRP: The solution of this differential equation is: where t 1~{ and A 2 is a constant (the integral constant). Based on equation 7, at the steady state (t 5 '), RRP ' 5 A 1 1 A 2 . For simplicity, we normalised the RRP ' to 1. Thus, Equation 7 indicates that the RRP replenishment time course is bi-exponential. Equations 8-9 indicate that the time constants for both rapid and slow RRP are independent of the stimulation intensity but depend on only four kinetic constants, k 1 , k 21 , k 2 , and k 22 . These features are consistent with our experimental result that the RRP replenishment time course is bi-exponential, and that the time constants for rapid and slow RRP replenishment did not change significantly after 1-10 pulses of 20 ms depolarisation (Fig. 1). Such a consistency further strengthened our model.   In the steady state (t 5 '), or resting conditions, Because the recycling pool, which included RRP ' , IP ' , and RP ' , was 46 times the size of RRP '
To solve these five parameters, we varied the IP ' value from 0.5 to 10 with an incremental step of 0.1. For each of these IP ' values, we obtained a set of rate constants (k 1 , k -1 , k 2 , and k -2 ) from equations 8, 9, 14, and 15. With each of these IP ' values and their corresponding rate constants (k 1 , k -1 , k 2 , and k -2 ), we numerically calculated the IP, RP, and RRP changes as a function of time after depletion of the RRP by a single 20 ms depolarisation. The numerical calculation was based on equations 3-4 with a Dt of 0.1 ms or less using MATLAB Simbiology toolbox (v2014a, the Mathworks, USA). The calculated RRP replenishment time course was compared to the experimentally measured time course after a 20 ms depolarisation using the Kolmogorov-Smirnov test and the least-squares test. The best fitting group for the parameters is as follows: IP ' 5 2.7, RP 5 42.3, k 1 5 0.8892, k -1 5 2.4008, k 2 5 0.0093, and k -2 5 0.1546 (unit: sec -1 ).
After 10 pulses of 20 ms depolarisation at 10 Hz, which induced a capacitance jump of 1260 6 72 fF (n 5 11), the RRP replenishment could also fit a bi-exponential function with A 1 5 0.33, t 1 5 0.38 s, A 2 5 0.67, t 2 5 7.8 s (Fig. 1D). Compared to the fitted replenishment curve after a 20 ms depolarisation (dotted curve in Fig. 1D, same as Fig. 1B), the rapid component of replenishment (replenishment rapid ) decreased, whereas the slow component of replenishment (replenishment slow ) increased. Similarly, after 10 pulses of 20 ms depolarisation at 1 Hz, the RRP replenishment also slowed down (Fig. 1F, A 1 5 0.29, t 1 5 0.25 s, A 2 5 0.71, t 2 5 7.9 s). Our results contradict previous studies that suggested a calcium/calmodulin-dependent mechanism 23,25 . The total calcium charge dramatically increased from a single 20 ms depolarisation pulse to 10 depolarisation pulses of 1 or 10 Hz, but the RRP replenishment slowed down instead of speeding up, which could not be explained by the up-regulation of calmodulin function (Fig. 1G). Furthermore, it is also very interesting that the time constant of the RRP replenishment was very similar among different stimulation protocols (Figs. 1B, D and F).
Rapid and slow vesicle traffic among three pools underlie rapid and slow RRP replenishment. Our observation that the replenishment rapid amplitude was significantly reduced when calcium charge (QICa) was increased by ,8 times in Fig. 1G could be resolved if 10 depolarising pulses depleted most of the recycling pool that provided vesicles to the RRP. However, we have shown that the recycling pool was ,46 times the size of RRP 20 , and it was only slightly reduced by 10 depolarising pulses at 1 or 10 Hz, which only released vesicles equivalent to ,3-6 times the size of RRP. This slight reduction of the recycling pool could not account for the significant decrease in the replenishment rapid amplitude. Therefore, we proposed a new threepool model to account for this phenomenon (see Methods for details).
From scheme (1), the RRP size can be derived as a function of time after depletion of the RRP. The analytical solution of the RRP (equation 7) is a bi-exponential function, which is consistent with our experimental observation (Figs. 1D, F). Based on the previously measured recycling pool size, which was the sum of the three pools (RRP ' 1 IP ' 1 RP ' 5 46, where ' denotes the resting condition and all parameters are normalised to RRP ' ), we found that the numerically calculated RRP replenishment time course after a 20 ms depolarisation best fit the observed data (Fig. 1B) when IP ' 5 2.7, RP ' 5 42.3 (RRP ' was normalised to 1), k 1 5 0.8892, k 21 5 2.4008, k 2 5 0.0093, and k 22 5 0.1546 sec 21 (calculated from equations 8-9 and 14-15).
The above parameters were obtained by comparing the model with the observed RRP replenishment after a single 20 ms depolarisation ( Fig. 2A, black curve). To further determine whether these parameters were appropriate, we used the model with these parameters to generate several predictions that were not related to the single 20 ms depolarisation data. The prediction was made by numerical calculation of the RRP replenishment using equations 3-4. First, the model-predicted time course of the RRP replenishment after 10 pulses of 20 ms depolarisation at 10 Hz matched well with the observed time course (Fig. 2B, black curve, p 5 0.93, K-S test). The predicted time course was fitted by a bi-exponential equation with parameters (A 1 5 0.37, t 1 5 0.3 s, A 2 5 0.63, t 2 5 8.3 s, Fig. 2B, black curve) similar to those obtained from fitting the observed data (Fig. 1D). Second, the model-predicted RRP replenishment matched well with the measured one after 10 depolarising pulses at 1 Hz (Fig. 2C, black curve, p 5 0.90, K-S test). The model-predicted parameters were also very close to those in observed ones (A 1 5 0.22, t 1 5 0.2 s, A 2 5 0.78, t 2 5 6.5 s). Third, the model-generated exocytosis during each time step matched well with the experimental results. As the model was derived from the RRP replenishment data, it would be supportive if the model could also predict exocytosis. For 10 depolarising pulses at 10 Hz, it is difficult to accurately measured the capacitance jump after each stimulus 27 , so we only compared the total capacitance jump. The model predicted a total DCm of 2.46 times the RRP evoked by 10 depolarising pulses at 10 Hz. By multiplying this value with the capacitance jump induced by a 20 ms depolarisation, which was the RRP size, it predicted a DCm of 1131 6 61 fF (1127 6 61 fF if endocytosed vesicles are not included, n 5 11), which closely matched the measured DCm after 10 depolarising pulses at 10 Hz (1260 6 72 fF, n 5 11, p 5 0.2, Fig. 2D). For 10 depolarising pulses at 1 Hz, we could accurately compare the capacitance jump after each stimulus. The model predicted a gradual decrease of the capacitance jump induced by each stimulus during 10 depolarising pulses at 1 Hz, which matched the measurement well (p 5 0.7 with endocytosis, K-S test, Fig. 2E). The predicted total exocytosis amount (with endo: 2.3 6 0.1 pF, without endo: 2.2 6 0.1, n 5 6) also closely matched the measured net exocytosis (2.3 6 0.1 pF, n 5 6, p 5 0.8 with endocytosis, Fig. 2F). All these matches between predictions and experimental results (Figs. 2B-F) further strengthened our model with parameters described above.
The fast IP-RRP kinetics (k 1 5 0.8892, k 21 5 2.4008) and the slow RP-IP kinetics (k 2 5 0.0093, k 22  replenishment was bi-exponential with rapid (t 1 ) and slow (t 2 ) time constants being controlled mostly by k 1 and k 21 , and k 2 and k 22 , respectively. Our numerical solution to t 1 and t 2 also further illustrated why the time constants in different stimulation protocols are roughly the same (equations 8-9). Our numerical calculation (equations 3-4) also showed that the IP size was 2.7 immediately after a 20 ms depolarisation, but decreased to ,0.9-1.4 immediately after 10 pulses of depolarisation at 1-10 Hz. The IP size after stimulation controlled the replenishment rapid amplitude, which explains why the replenishment rapid component was reduced after 10 pulses of depolarisation at 1-10 Hz.
High temperatures have been shown to lead to accelerated endocytosis 30 and faster recovery from synaptic depression at calyces 31 . Recently, ultra-fast endocytosis was observed at hippocampal neurons at 34uC 32 . To test whether our model could also be applied at physiological temperatures, we performed similar experiments at a more physiological temperature (,34uC). At higher temperatures, RRP replenishment was dramatically accelerated after a 20 ms depolarisation or 10 pulses of 20 ms depolarisation at 1-10 Hz (Figs. S1, see Supplementary Information I for details) and still fit our model well if we multiplied all of the rate constants by a ratio of 2-4.
Neither slow nor rapid endocytosis recycles vesicles within a small recycling pool. We previously showed that both rapid and slow endocytosis do not recycle vesicles within the RRP 21 . The RRP replenishment showed no difference after blocking endocytosis with GTPcS, which ruled out the possibility of a small recycling pool. We further used the current model to verify this conclusion.
In scheme (1), we compared the influence of endocytosis in three circumstances: 1) endocytosed vesicles directly recycle within the RRP, 2) endocytosed vesicles enter the IP, and 3) the endocytosed vesicles enter the RP. Endocytosed vesicles did not directly enter the RRP because blocking endocytosis did not affect RRP replenishment (Fig. 3). Endocytosed vesicles did not enter the IP because the recycling pool size was 46 times the size of RRP 20 , whereas the IP ' size was only 2.7. Furthermore, a significant amount of endocytosis occurred during 10 pulses of 20 ms depolarisation at 1 Hz 27 . If these endocytosed vesicles directly enter the IP, RRP replenishment should be accelerated (Fig. 2C). In contrast, RRP replenishment was slower compared to a single 20 ms depolarisation (Figs. 1D, F). Our model also confirmed that, if the endocytosed vesicles entered the RRP or IP, RRP replenishment would be accelerated, which was not consistent with the experimental observations ( Figs. 2A-C). Therefore, we conclude that endocytosed vesicles enter the RP before being mobilised to the IP.
The impact of endocytosis on synaptic transmission. Endocytosis not affecting RRP replenishment raises doubts about the role of endocytosis. To determine the impact of endocytosis during repetitive firing, we mimicked the physiological firing frequency of 50 Hz by depleting the RRP by ,6-12% for each action potential in our model. We used 50 Hz because the calyx may fire spontaneously at a mean rate of ,50-60 Hz in vivo 33 . We used 6-12% because an action potential may deplete ,6% of the RRP 34,35 and the release probability may be facilitated by ,30-100% during stimulation 36,37 . Based on our previous study 27 , we assumed that ,70% of fused vesicles were retrieved rapidly with a time constant of ,1.5 s, and the remaining 30% were retrieved slowly with a time constant of ,15 s. With scheme (1), the model predicted that the release evoked by a single action potential reached a steady state of 6-11% of the first response (Fig. 4B), which was similar to the steady-state reduction of the EPSCs evoked by axonal fibre stimulation at 50 Hz in the presence of 1 mM kynurenic acid, which prevents postsynaptic AMPA receptor saturation (Figs. 4A-B, n 5 4 synapses).
In the absence of endocytosis, the model (scheme 2) predicted a gradual decline in release gradually to 0 (Fig. 4C). Compared to the prediction in the presence of endocytosis (scheme 1), the decline was obvious only after stimulation for . 10 s at 50 Hz (Fig. 4C, right). This effect was not trivial to the calyx of Held synapse. The calyx fires spontaneously at a mean rate of ,50 Hz in vivo and, without any previous firing, an action potential releases several hundred vesicles that ensure firing of a postsynaptic action potential 33 . With firing at 50 Hz, the release induced by an action potential decreases to ,6-11% (Fig. 4B), which is still sufficient to induce a postsynaptic action potential 38 . Without endocytosis, release will eventually decrease to 0 (Fig. 4C), which abolishes postsynaptic firing. Thus, endocytosis is essential for maintaining transmitter release and synaptic transmission during high frequency firing. We could not confirm this suggestion experimentally by blocking endocytosis with GTPcS, because a GTP-independent endocytosis develops during strong stimulation 39 . However, the gradual decrease in release when endocytosis is blocked in shibire mutants is consistent with our suggestion 4,5,40 .

Discussion
Based on our previous finding that both rapid and slow endocytosis recycled vesicles to a large recycling pool instead of within the RRP or a small recycling pool, we proposed a model composed of three pools, a large RP ,42.3 times the size of RRP, a RRP and a small IP ,2.7 times the size of RRP in between 20 . We found that rapid IP-RRP kinetics, slow RP-IP kinetics, and limited IP size are responsible for the rapid and slow components of RRP replenishment, and the slower RRP replenishment with more intense stimulation, as observed at many synapses 13,22,35,41,42 . This realistic model reveals the contribution of each vesicle cycling step in the maintenance of synaptic transmission, and thus, in the generation and recovery of STD during repetitive stimulation.
There are other explanations for the two components of RRP replenishment. Garcia-Perez et al. reported similar RRP replenishment at hippocampal synapses and provided ''delayed depression'' as an explanation, which lacked experimental verification 43 . Otsu et al. proposed two general models that accounted for the fast and slow time constants of RRP replenishment 42 . However, neither model could explain why blocking endocytosis does not affect RRP replenishment. First, our previous results ruled out the possibility that fused vesicles can recycle within the RRP 21 . Second, the relatively small RP size (8-12 times the RRP), which could be dramatically decreased during STD (more than 50% decrease 42 ), and the fast docking/ undocking kinetics between RP and RRP suggest a significant role of endocytosis in RRP replenishment, but this is also ruled out by our results. Pyle et al. proposed a similar two-pool model, suggesting that the RRP could be refilled by either rapid retrieval within the RRP or new recruitment from the reserve pool at the hippocampus 13 , which still contradicts our findings 21 . A recent study showed that exocytosed vesicles are not generally reused within 40 s, which further strengthens our conclusion that rapid reuse may not contribute to rapid RRP replenishment 44 . With all parameters experimentally The rapid component of the RRP replenishment time course has been hypothesised to be caused by a calcium/calmodulin-dependent mechanism [22][23][24][25] . A recent study also showed that Munc13-1, the downstream target of the calcium/calmodulin signaling pathway, controls synaptic vesicle replenishment 45 . However, these studies still could not explain our observation of a decrease in the amplitude, but not the time constant, of replenishment rapid with higher calcium influx during more intense stimulation (Figs. 1D, F). Accordingly, our three-pool model solves this problem by adding a small IP, which is responsible for the rapid and slow components of the RRP replenishment time course. The IP controls the amplitude of the replenishment rapid . More intense stimulation caused greater depletion of the IP, which decreased the replenishment rapid amplitude. By ruling out the possibility that rapid RRP replenishment is provided by vesicles made from rapid endocytosis or from a small recycling pool, we conclude that the RRP is replenished from the IP. Although currently more detailed characteristics of this pool remain unclear, a recent study showed that in synapsin triple knock-out mice, the RRP replenishment was significantly slowed down and the number of synaptic vesicles distally from the active zones was strongly decreased, whereas those localised at the active zones remained unchanged 46 . Furthermore, most of the synapsin-defined vesicle pool in that study presented as a part of the traditional RP, comprising ,95% of the total synaptic vesicles 18,47,48 . Another report using synapsin I/II double knock-out mice proposed a local reserve pool three times the size of RRP at hippocampus 49 , which is also very similar to our conclusion. Morphological evidence from EM also showed that synaptic vesicles could be interconnected by synapsin at a distance from AZ 50 . Our result is consistent with all these findings, and we further include endocytosis to give a more complete vesicle recycling model. It would be of great interest to examine whether synapsin is the key molecular entity that can differentiate the IP from the RP and RRP at calyces in the future 18 .
A previous study showing that blocking calmodulin function slowed down endocytosis and RRP replenishment suggested that slowing down of RRP replenishment under stronger stimulation might be caused by occlusion of the active zone by proteins participating in exocytosis 6,51 . However, a recent report showed that blocking PKA slowed down endocytosis, but did not affect the recruitment of synaptic vesicles to the RRP 52 . Furthermore, under mild stimulation, blocking calmodulin did not block endocytosis but still slowed down RRP replenishment, both of which suggest independent mechanisms for RRP replenishment and endocytosis 52 . Although our three-pool model was developed for stimulation stronger than a 20 ms depolarisation, it may not necessarily be in conflict with the finding of a calcium/calmodulin-dependent acceleration in the RRP replenishment 25,53 , as the later mechanism could be saturated by the calcium influx during a single 20 ms depolarisation. Previous studies showed that a 10-20 ms depolarisation pulse can induce enough calcium influx to deplete the RRP at the calyx of Held synapse 7,26 . In such a case, the slowing of RRP replenishment is dominated by the decrease in IP size. For stimulation milder than a 20 ms depolarisation, our model may be modified to include the calcium effect so that the IP-RRP rate constant (k 1 and k 21 ) or the IP size is calcium/calmodulindependent.
Bi-exponential recovery from STD has been observed in many synapses 13,22,35,41,42 where our model may also be helpful. For example, at frog auditory hair cell synapses, recovery draws mainly from the preformed vesicles rather than the rapid, freshly endocytosed vesicles, which is consistent with our model 41 . At hippocampal synapses, several new findings, such as the synapsin-mediated vesicle interconnection 50 and local reserve pool model 49 , also imply the potential usefulness of our model.
Although our three-pool model was proposed from RRP replenishment, it could also be used to accurately dissect the exocytosis at each time step during stimulation (Figs. 2D-F). Furthermore, we evaluated the impact of endocytosis using our three-pool model and concluded that endocytosis is important in maintaining synaptic transmission during high frequency stimulation, which often happens in the central nervous system. Thus, we concluded that the three-pool model is a useful tool for revealing the contribution of each vesicle cycling step in the maintenance of synaptic transmission, and the generation and recovery of STD during repetitive stimulation. shows the large initial EPSC and the small stabilised EPSC for comparison. (B) The model-predicted (curves) and the measured (n 5 4, circle) amplitudes of the EPSCs during a 50 Hz action potential train. Predicted traces for different depleting percentages after a single action potential are shown in different colours (yellow: 6%, red: 9%, green: 12%). Data were normalised to the first response. Each circle represents the mean amplitude from four synapses (for clarity, s.e.m. is not included). Experimental data were collected from horizontal brain slices, where a bipolar electrode was positioned in the midline of the trapezoid body to induce presynaptic action potentials and thus EPSCs 54 . The model included endocytosis (scheme 1). (C) The model-predicted EPSC amplitude during action potential stimulation at 50 Hz with (scheme 1, colours meanings are the same as B) and without (scheme 2, black) endocytosis. Left and right panels show the same data at different scales. www.nature.com/scientificreports