Synaptic transmission is a highly dynamic process. Vesicle release rates change several orders of magnitude in response to Ca 2+ influx [1, 2] , and during repeated synaptic activity, the number of vesicles released by an action potential (AP) rapidly change [3] . Synaptic vesicle release is tightly controlled by specialized proteins, including SNAREs, SM proteins, and Ca 2+ -sensors, among others [4] . Many of these are involved in the last step of the release process in which the fusion of the lipid membranes of the vesicle and presynaptic terminal occurs. This process can be described in terms of an energy landscape. Here a fusion energy barrier represents the activation energy that is required for the intermediate steps during membrane fusion, such as overcoming electrostatic repulsion of the membranes [5] and lipid stalk formation [6] . In our previous work we showed that additive changes in the fusion energy barrier produced supralinear changes in the vesicle fusion rate, as predicted by transition state theory [7] . We hypothesized that an energy barrier model could explain the supralinear relationship between Ca 2+ -concentration and release rates [1] if Ca 2+ binding to the release sensor would decrease the fusion energy barrier [7] . The latter assumption has not been tested experimentally. Synaptotagmin-1 (Syt1) is the Ca 2+ -sensor that is responsible for fast release in hippocampal synapses [8] [9] [10] . It was recently suggested that Syt1 lowers the fusion energy barrier by reducing electrostatic repulsion between membranes upon binding of Ca 2+ [5] . However, Syt1 is also involved in translocating vesicles to the plasma membrane [11] [12] [13] [14] , and inhibiting spontaneous and asynchronous release [15] [16] [17] [18] [19] [20] . Both these functions could potentially be involved in energy barrier modulation. Furthermore, in the absence of Syt1, slower Ca 2+ -sensors that drive asynchronous release become prominent [8, 9, 21] . Synaptotagmin-7 has been shown to trigger asynchronous release [22] [23] [24] , but is also identified as a Ca 2+ sensor for short-term facilitation [25, 26] . The latter has been proposed to be due to its concerted action with Syt1 on the fusion energy barrier [7, 25, 27] .
In this study, we tested the assumptions that (1) Syt1 can reduce the fusion energy barrier when activated, and (2) PTP can be produced by activation of a second pathway that reduces the fusion barrier independently of Syt1, thereby amplifying the action of Syt1. Changes in the energy barrier were probed in several mutant variants of Syt1 and during PTP, using hypertonic sucrose (HS) stimulation. We found that mimicking activation of Syt1's Ca 2+ -binding C2A domain reduced the energy barrier. Syt1's release inhibitory function acts independently from the energy barrier, indicating that additional release promoting factors contribute to spontaneous release. We found that after PTP or phorbol ester application the energy barrier was reduced, independently of the vesicle pool size and positional priming. Furthermore, this reduction did not require Syt1, and most likely is induced by activation of a second sensor. Altogether, these findings support a dual-sensor energy barrier model for supralinear Ca 2+ -sensitivity of release and changes in synaptic strength after PTP.
Syt1 is well established to be the fast Ca 2+ -sensor for synaptic vesicle release in many synapses [8, 10] . However, Syt1 is also know to act as an inhibitor of spontaneous and asynchronous release [15] [16] [17] [18] [19] [20] 28, 29] . This inhibition may act directly on the fusion machinery [5, 30, 31] , suggesting an increase in the fusion energy barrier [5] . Alternatively, Syt1 may inhibit a second high-affinity Ca 2+sensor [15, 28] , reducing sensitivity to local Ca 2+ -fluctuations [32] [33] [34] , but likely not affecting the energy barrier. To discriminate between these two possibilities, we investigated whether the energy barrier in a resting synapse was altered in the absence of Syt1, comparing wild type (WT) and Syt1 KO glutamatergic hippocampal neurons. Syt1 deficiency did not affect the number of synapses (Fig. 1A ,B) or dendrite length (Fig. 1A,C) . However, electron microscopy (EM) revealed a significant reduction in membrane-proximal synaptic vesicles in Syt1 KO synapses (Fig. 1 Supp.1), as observed before [13] . Voltage clamp recordings revealed that spontaneous miniature excitatory post-synaptic current (mEPSC) frequency was more than doubled (Fig. 1E ), while first evoked EPSC charge was strongly reduced in Syt1 KO synapses, compared with WT ( Fig. 1F ,G).
As described previously, several synaptic parameters that provide information about priming and fusion [7] can be obtained by fitting a minimal vesicle state model to HS responses. These include the pool of primed vesicles or readily releasable vesicle pool (RRP) as defined by the total number of vesicles released by an osmotic shock from 500mM HS, maximal HS release rate (k2,max), and change in fusion energy barrier (ΔEa (RT)) (For detailed methodology see: Schotten et al., 2015) .
In order to examine changes in the energy barrier and the RRP, we applied a range of HS concentrations to WT and Syt1 KO synapses (Fig. 1H) . As shown previously [7] , kinetics of the responses became faster, while the delay of the onset of response decreased for increasing concentrations (Fig. 1 supp. 2). The readily releasable pool (RRP), quantified from model fits of the current response to 500mM HS, was not changed in Syt1 KO synapses (Fig. 1I) , despite the reduced number of membrane-proximal vesicles found with EM. The fraction of the RRP depleted by 250mM sucrose (Fig. 1J) , a proxy for the energy barrier height [5, 35] , was not changed. Beyond 250mM, HS-induced release rates even tended to be lower in Syt1 KO synapses than in WT (Fig.   1K ), corresponding to an increased fusion energy barrier under these conditions (Fig. 1L) .
Therefore, we conclude that Syt1 in the non-activated state (i.e. without Ca 2+ bound) does not increase the energy barrier for synaptic vesicle fusion, despite its inhibitory effect on spontaneous release.
Syt1 KO abolishes synchronous release triggering [8] [9] [10] and impairs vesicle priming [11] [12] [13] [14] . To control for potential effects from these properties on HS induced release, we used the Syt1 9Pro mutation to study the link between the inhibition of spontaneous release and the energy barrier in isolation. In this mutant, the flexible linker between Syt1's two Ca 2+ -sensing C2 domains is fixed, selectively impairing inhibition of spontaneous release, without affecting evoked release [29, 36] .
To further minimize activation of Ca 2+ -sensors due to resting levels of intracellular Ca 2+ , all recordings, with the exception of first evoked release, were done in 0mM extracellular Ca 2+ with 20µM BAPTA-AM. We expressed either Syt1 WT or Syt1 9Pro in Syt1 KO neurons, with Syt1 abundance in synapses exceeding endogenous levels to the same extent (Fig. 2 Supp. 1). We found a strong increase in mEPSC frequency in Syt1 9Pro synapses compared to Syt1 WT ( Fig.   2A ,B). The first evoked EPSC was unaffected (Fig. 2C,D) . Applying 250mM and 500mM HS (Fig.   2E , Fig. 2 supp. 2), we found no difference in RRP (Fig. 2F) , or depleted RRP fraction at 250mM (Fig. 2G ). Release rates in Syt1 9Pro synapses in the presence of BAPTA-AM remained higher at 0mM sucrose (spontaneous release) compared with Syt1 WT (Fig. 2H) . However, at 250mM and 500mM HS we found no effect on the release rates and corresponding fusion energy barriers (Fig.   2H ,I). These data confirm that suppression of spontaneous release by Syt1 is not achieved by increasing the fusion energy barrier.
Next, we tested whether binding of Ca 2+ to Syt1's C2 domains lowers the energy barrier, as predicted by our energy barrier model for AP evoked release [7] . To be able to test this with our HS assay, which is too slow to detect energy barrier changes during AP induced Ca 2+ binding, we analyzed two different Syt1 mutants that mimic the effect of persistent activation by Ca 2+ . We used the D232N mutation to neutralize a negatively charged residue in the C2A domain, which has been shown to increase Ca 2+ -triggered release [28, 37] . Alternatively, we mimicked the Ca 2+ -mediated association with phospholipids by increasing the hydrophobicity of the C2 domains, through insertion of tryptophan mutations in the C2 domains [38] (M173W, F234W, V304W, I367W; Syt1 4W). Given the high peak currents observed in previous preparations, we recorded the Syt1 D232N gain-of-function mutant, and matching Syt1 WT, in 2mM extracellular Ca 2+ to avoid voltage-clamp artifacts. Synaptic expression of Syt1 WT or Syt1 D232N in Syt1 KO neurons exceeded endogenous Syt1 levels to the same extent (Fig. 2 Supp. 1). We confirmed previous findings in mass cultures [28, 37] of increased mEPSC frequency (Fig. 3A,B) and increased first evoked release in Syt1 D232N expressing synapses (Fig. 3C,D) . HS evoked release revealed no significant difference in RRP size (Fig. 3E,F, Fig. 3 supp. 1A), but depleted RRP fraction at 250mM was increased in Syt1 D232N expressing synapses (Fig. 3G) . Release rates at 175mM and 250mM HS were increased 1.7 to 1.9 fold, and the fusion energy barrier was reduced by 0.5 to 0.6 RT (Fig. 3H ,I), while a similar trend was observed for higher concentrations. Hence, constitutively activating Syt1 by removing negative charge from its Ca 2+ -sensing domain increases vesicle fusion by decreasing the fusion energy barrier.
In Syt1 4W expressing synapses, we found a strong increase in mEPSC frequency ( 2H) and the release rate ( Fig. 3 Supp. 2I) were increased, both indicating a reduction of the fusion energy barrier by 0.5 RT (Fig. 3 Supp. 2J). However, we found no significant differences at other HS concentrations, and at 500mM and 750mM release rates trended towards a decrease (Fig. 3 Supp. 2H). Such a reversal of phenotype cannot readily be explained through energy barrier modulation alone, suggesting an interaction between HS and the 4W mutations (see discussion).
Our data at 250mM are in line with our findings with the Syt1 D232N mutant, corroborating the conclusion that activation of Syt1 C2A domain decreases the fusion energy barrier. Hence, supralinear Ca 2+ -sensitivity through multiplicative effects on the release rate [1, 7] is likely supported by reductions of the energy barrier by Syt1.
Having established that activation of Syt1's C2A domain reduces the fusion energy barrier, we next investigated whether induction of short-term plasticity (STP) through repetitive stimulation also leads to a reduction. We assessed changes in the fusion barrier after induction of PTP in the presence and absence of Syt1. PTP is a form of STP which lasts tens of seconds to minutes [39] , allowing sufficient time to measure its effects using HS stimulation [40, 41] . It has previously been suggested that PTP acts by decreasing the fusion energy barrier [40, 41] . However, other studies have shown that an increase in the RRP after PTP can explain a large part of the potentiation of the EPSC [42, 43] . To resolve this, we induced synaptic release either through APs or HS before (Naive; Fig. 4A ), and 5 seconds after a train of 100 APs at 40Hz (PTP; Fig. 4A ), to measure PTP, changes in the fusion energy barrier, and potentiation of RRP in the same cell. We have shown previously that our HS assay is sensitive enough to detect accelerated recovery of the RRP after 40Hz stimulation [44] . To maximize observable effects on the probability of vesicle release, we lowered extracellular Ca 2+ to 1mM for this experiment. PTP increased EPSC charge by 39% (Fig.   4B ,C), even though the RRP, as assessed from 500mM HS, was not fully recovered at this point ( Fig. 4E,F, Fig. 4 Supp. 1A). This resulted in a 41% increase in vesicle release probability, calculated as the ratio of the AP and HS induced EPSC charges (Fig. 4D ). PTP increased the depleted RRP fraction at 250mM (Fig. 4G) , and increased HS release rates 17 to 37% (Fig. 4H ), indicating about a 0.2-0.3 RT reduction of the fusion barrier (Fig. 4G ,I). These results confirm previous findings that PTP does not increase the RRP [40, 45] , and shows that it is associated with a decrease in the fusion energy barrier.
PTP induction is known to involve activation of Munc18-1 and PKC [43, 46] , but the role of synaptotagmin in this pathway is less clear. We showed previously that phosphorylation by PKC plays a role in Syt1-, but not in Syt2 expressing synapses [47] . However, whether Syt1 is required for the energy barrier reduction after PTP is not known. To investigate this, we performed a similar set of PTP experiments in Syt1 KO autapses, using 4mM extracellular Ca 2+ . In Syt1 KO autapses, PTP also increased vesicle release probability ( Fig. 5A -C), while the RRP remained incompletely recovered (Fig. 5D,E, Fig. 5 Supp. 1A). Additionally, similar to WT autapses, we observed after PTP an increase in depleted RRP fraction at 250mM (Fig. 5F ), and increased HS release rates ( Fig. 5G ), corresponding to a decrease in the fusion energy barrier of 0.3-0.6RT (Fig. 5H) . Hence, reductions of the energy barrier due to PTP, do not require Syt1. Furthermore, as the RRP was not yet fully recovered after PTP, the contribution from the decreased energy barrier to potentiation of the EPSC is independent of priming. These findings suggest a model in which independent pathways for release cooperate to potentiate synaptic strength.
PTP acts via the same pathway as phorbol ester mediated potentiation [35, [46] [47] [48] [49] [50] . We showed previously that activation of the diacylglycerol (DAG) pathway with 1µM phorbol 12,13-dibutyrate (PDBu) reduced the fusion energy barrier [7] . In another study we showed that preventing Syt1 to be phosphorylated by PKC blocked potentiation of AP induced release by phorbol esters but not the potentiation of HS responses [47] . To gather further proof for a Syt1-independent pathway for energy barrier reduction after PTP we investigated whether the PDBu-induced reduction also 
Previously, we proposed that transition state theory can be used to describe the process of vesicle fusion. In this framework, the fusion reaction is defined as the transition from the primed state to the fused state, with the activation energy that is required for the transition to occur, also referred to as the fusion energy barrier (Fig. 7A ) [7] . According to the Arrhenius equation, there is an exponential relation between the activation energy and the rate of a reaction. This, implies that additive changes in the height of the fusion energy barrier lead to multiplicative effects on the fusion rate [7] . We showed that supralinear Ca 2+ -dependence of release follows from this principle, when assuming an energy barrier reduction ∆ for each Ca ion that binds (Fig. 7C , upper row) [1, 7] . We now propose that the same framework can be used to describe asynchronous release and STP. This can be realized by adding additional release sensors to the model and adding their effects in the energy barrier domain (Fig. 7B ) (Schotten et al., 2015; eq. 4) . When multiple sensors are activated (Fig. 7A ,B), the new fusion energy barrier height is given by:
with the number of sensors, ∆ the energy barrier reduction induced by sensor , and , the basal energy barrier height. Applying the Arrhenius equation [7] gives the corresponding new fusion rate 2, :
with + = − ̅ the basal fusion rate, = ∆ ̅ the factor by which + needs to be multiplied to account for activation of sensor , and each additional sensor (i.e. ,ℎ,…) after that (Fig. 7B ). is an empirical prefactor, ̅ the gas constant, and the temperature. During synaptic activity these sensors may be directly activated by Ca 2+ , or indirectly, through other pathways such as the diacylglycerol (DAG) pathway [51] . Through differences in activation and kinetic properties of different sensors, their combined effect could give rise to a diverse repertoire of vesicle release patterns in response to different patterns of presynaptic activity.
Based on our experimental findings, we propose a qualitative model for PTP, by combining the fast Ca 2+ sensor with five activation states from the allosteric model [1, 7] , with a slow DAG sensor with one activation state. This gives a two-dimensional reaction scheme with in total 12 different vesicle states, each with its own associated fusion barrier (Fig. 7C ). As in the original allosteric model [1] , substantial activation of the fast sensor only occurs by peak Ca 2+ levels reached during the AP due to its low Ca 2+ -affinity, which synchronizes vesicle fusion to the moment of AP firing promoters with small individual effects, may achieve meaningful changes in EPSC size [7, 25, 27] .
We explored how the Syt1 D232N mutation could affect Ca 2+ sensitivity in this model. Based on proposed electrostatic effects on the fusion barrier [5] , the effect of adding one charge to the C2A domain can be modelled by increasing the basal fusion rate + to +, = + 0.5 ∆ ̅ = + 0.5 . This is under the assumption that one charge is half as effective as two charges during Ca 2+ binding [5] , with ∆ the energy barrier reduction from one bound Ca 2+ (Fig. 7. Supp. 1A,B) . A two-fold increase in SNARE binding was also reported for this mutation, though only after Ca 2+ -binding [37] . Therefore, this does not affect the basal release rate + , but can be modelled by replacing 
When all sensors are in the non-activated state, the basal release rate constant + in our model is associated with one effective energy barrier representing the fusion pathway. This includes intermediate steps such as stalk formation, hemifusion and pore formation (Fig. 7A ) [1] . In other studies its height has been estimated to be 30 kBT based on experiments with pure lipid bilayers and from course-grained simulations of the underlying intermediate fusion states [52] [53] [54] .
Previously, we concluded that changes in spontaneous release rates after genetic or biochemical manipulations did not correspond with the energy barrier shifts measured with HS [7] . Here we showed both in Syt1 KO (Fig. 1) and Syt1 9Pro expressing synapses (Fig. 2 ) that mEPSC frequencies were increased, in line with previous studies in autapses [5, 20, 55] and networks [28, 29, 36, 56] . It remains enigmatic why others found a similar increase in spontaneous release in networks but not in autapses after Syt1 deletion [57, 58] , but differences in culture protocol [59] , or genetic background could play a role. Despite the increase in spontaneous release in our Syt1
KO and Syt1 9Pro expressing synapses, the fusion energy barrier assessed with HS was not changed ( Fig. 1L; Fig. 2I ). These findings indicate that for hippocampal autapses the rate constant for spontaneous release is not equal to the basal release rate constant + as assessed with HS in the model, and that additional mechanisms may also contribute to AP independent release of vesicles. As spontaneous release is to a large extend Ca 2+ dependent [28, 60] , a possible mechanism may be rapid spontaneous Ca 2+ fluctuations [32] [33] [34] . When such fluctuations occur locally at individual fusion sites, Ca 2+ activation of a release sensor will reduce the energy barrier only locally and very briefly and not constitutively across all synapses simultaneously. We estimated previously that in such a scenario the frequency of Ca 2+ fluctuations increases the release rate constant in an additive manner by 2-4 10 -4 s -1 in WT autapses [7] . This will dominate the release rate at 0mM sucrose but is negligible compared to release rates induced by higher concentrations, corresponding to undetectable changes in the energy barrier. Interestingly, recording spontaneous release in 0mM extracellular Ca 2+ and in the presence of the 20µM BAPTA seemed to reduce its frequency less drastically as reported in other studies (compare Fig. 1E and 2B) [28, 56] . Moreover, differences in mEPSC frequency in Syt1 9Pro expressing synapses remained under these conditions. This might suggest that in our experiments the BAPTA loading was insufficient to block all spontaneous events. BAPTA-AM was applied after recording evoked release, with its incubation time restricted to 10 min to ensure the recording remained stable enough for HS measurements. Alternatively, part of the spontaneous release could be Ca 2+ independent and through a different pathway than evoked release, either from a subset of synapses [61, 62] or from a different vesicle pool [63, 64] . In this case, changes in the fusion barrier of this pathway could have been missed if spontaneous released vesicles are a small subset of the total pool, or when these vesicles are somehow less sensitive to HS stimulation.
Several mechanisms have been proposed to explain the inhibitory effect of Syt1 on spontaneous release [17, 18, 28, 29] . These include Syt1 clamping a second sensor for slow release [15, 21] , clamping fusion directly by arresting SNARE complexes [30, 31] , or increasing electrostatic repulsion between lipid membranes [5] . The latter two mechanisms imply an increase in the energy barrier in the presence of Syt1, which we did not observe with our HS assay (Fig. 1) .
Furthermore, Syt1 9Pro expressing synapses showed increased spontaneous release, but no changes in the energy barrier and normal AP induced release. This indicates that Syt1's inhibitory role on spontaneous release is independent of its release-promoting role. We conclude that Syt1
does not increase the fusion energy barrier in its non-activated state. This conclusion does not support a model in which Syt1 suppresses spontaneous release by inhibiting the fusion step itself.
Our data is most consistent with either a model where Syt1 clamps a slow sensor with high affinity for Ca 2+ , making the system less sensitive to spontaneous Ca 2+ fluctuations, or with an additional fusion pathway for spontaneous release for a subset of vesicles, under the control of the clamping function of Syt1 (see discussion above).
A central assumption of our model is that activation of Syt1 by Ca 2+ binding lowers the fusion barrier [5, 27, 65, 66] . Several competing models have been proposed for this [66] . Both the Syt1 D232N mutant, where Ca 2+ -binding is mimicked, and the Syt1 4W mutant where hydrophobicity is increased, showed increased spontaneous and HS-induced release rates up to 250mM HS, in line with a reduced fusion energy barrier. Interestingly, for 500mM and 750mM we also found a slightly reduced fusion barrier in WT cells compared to Syt1 KO cells (Fig. 1L) , possibly due to activation of Syt1 at basal Ca 2+ levels. An electrostatic energy barrier model has been proposed, which assumes Ca 2+ -binding to Syt1 reduces the fusion barrier by diminishing electrostatic forces between opposing membranes [5] . Adding a single positive charge to the C2A domain in the D232N mutant yielded a reduction between 0.5 and 0.6 RT. Assuming linear scaling of the fusion barrier with charge [5] , this implies a 5 to 6 RT (or 2.9 to 3.5 kCal mol -1 ) reduction when Syt1 is fully activated after binding 5 Ca 2+ ions, adding 10 charges in total [1] . This is in the same order of magnitude as the estimated 10 RT (5.9 kCal mol -1 ) reduction during AP induced release in hippocampal neurons [38] , but about 3 times smaller than the 17 RT reduction predicted for full occupation of Synaptotagmin 2 (Syt2) in the calyx of Held [1] . These results suggests that either differences exist in the efficiency of the fusion machinery in the two systems, or that our method has a limited ability to capture the full effect of Syt1 activation on the fusion barrier (see also discussion below). Alternatively, the energy barrier reduction and increased spontaneous release rate in the D232N mutant do not come from electrostatic effects, but from increased Ca 2+dependent SNARE binding [37] at basal Ca 2+ levels. Modeling these scenario's (reduced electrostatic repulsion or increased Ca 2+ -dependent SNARE binding) with the energy barrier model, predicted in both cases an increase in Ca 2+ sensitivity with little effect on cooperativity (Fig.   7 supp. 1). These results are in line with previous studies in GABAergic neurons [28, 37] with similar values for the apparent cooperativity . However, caution has to be taken to directly compare model predictions to these experimental studies, which show the IPSC amplitude (not peak release rate) as a function of the extracellular (not intracellular) Ca 2+ concentration. Interestingly, adding a positive charge to the C2A domain at a different position (D238N) was shown to reduce Ca 2+ sensitivity in the same study [37] . This makes increased Ca 2+ -dependent SNARE binding a more plausible explanation for fusion barrier effects in the D232N mutant, but more research is needed.
In contrast to our HS measurements after PDBu [7] or PTP stimulation, we could not detect changes in the fusion barrier with concentrations beyond 250mM for these Syt1 mutants. This may point to a possible interaction of the mechanisms by which sucrose and Syt1 induce vesicle fusion, which may be a limitation of the method for some specific conditions. Properties that contribute to the lateral pressure of the membrane, such as membrane fluidity, bilayer thickness, hydration state of lipid headgroups, and interfacial polarity and charge, can change in response to osmotic pressure [67] . This could render the membrane bending properties of Syt1 less effective or different at higher sucrose concentrations. In case of the Syt1 4W mutation, opposite effects of increased hydrophobicity of the C2 domains on membrane fusion could dominate at different osmotic conditions. Enhanced affinity for phospholipids may promote membrane-membrane interactions, increasing the chance to cross the fusion barrier during no or mild osmotic stress. At conditions where the energy barrier is substantially reduced, deeper insertions of the C2AB domains in the plasma membrane may lead to less curvature, rendering the vesicles less fusogenic [68] . Based on these considerations, we conclude that activation of Syt1 by Ca 2+ promotes vesicle release by reducing the fusion energy barrier.
PTP and activation of the DAG-pathway are well established to increase synaptic strength [39, 51] .
Previous studies have suggested that energy barrier modulation contributes to STP [7, 25, 27, 35, 40, 41] , while other studies suggested increased vesicle priming [42, 43] or decreased un-priming [69] . Using our HS assay, we found a decreased fusion barrier, but incomplete recovery of the RRP, after PTP (Fig. 4, 5) . Furthermore, we found no change in RRP size after application of PDBU (Fig. 6E ), in line with previous studies [7, 35, 46, 70] , except one [71] . This indicates that, in cultured hippocampal neurons, lowering of the fusion barrier, and not increased vesicle priming or decreased un-priming, is a major factor in PTP. This is in line with the notion that activation of the DAG-pathway only increases the "effective" pool size of AP releasable vesicles [70, 72, 73] . This process, also referred to as 'superpriming', involves conversion of slowly releasing vesicles into rapidly releasing vesicles [74] [75] [76] [77] [78] , and could be interpreted as a transition 
We postulated that PTP occurs through activation of a pathway that lowers the energy barrier independently of Syt1. Indeed, we found a similar reduction of the energy barrier after PDBu application or PTP induction in the presence or absence of Syt1. This reduction most likely requires activation of a second sensor [15, 21] . According to our model, a second sensor both amplifies the Syt1 induced fusion rates and triggers release by itself (Fig. 7) . However, the latter may occur at a slower rate than Syt1 induced release, and represent the increase of asynchronous release after tetanic stimulation [19, 20] and the increase in spontaneous release after PDBu (Fig.   6 ). For PTP different sensors and/or pathways may be involved [39, 51] , including the DAG pathway. DAG-analogs enhance spontaneous release, AP induced release, and vesicle priming and reduce the fusion energy barrier [1, 7, 35, 42, 43, [46] [47] [48] 70, 79] . Munc13 is directly activated by DAG [80] , contributes to short-term synaptic plasticity [35, 50, [81] [82] [83] [84] and modulates the fusion barrier [35] . PKCs have been identified as relevant DAG targets in hippocampal neurons [46] and the Calyx of Held [43] . Phosphorylation of synaptotagmin by PKC has been shown to play a role in STP in Syt1-, but not Syt2-, expressing synapses [47] . Interestingly, preventing phosphorylation of Syt1 did not affect the fusion barrier and an effect on priming was proposed.
In conclusion, lowering of the fusion energy barrier during PTP occurs independently of Syt1, likely by Ca 2+ and/or DAG activation of an additional, slow sensor. However, an alternative mechanism is a reduction of electrostatic repulsion between opposing negative membranes through accumulation of residual Ca 2+ [5, 85] .
Several mechanisms have been proposed for synaptic plasticity, including ways to increase the presynaptic Ca 2+ signal (for review see [27] ), (activity dependent) channel-attachment of vesicles [86, 87] , Ca 2+ dependent vesicle priming [42, 43] or inhibition of un-priming [69] , and tightening of the SNARE-complex [78] . in corticothalamic and hippocampal synapses [22] [23] [24] [25] [26] [27] 88] . Its role as a facilitation sensor, with a multiplicative effect on the fusion rate, is supported by the finding that multiplication of membrane bound Syt1 and Syt7, as a proxy for the activation of both sensors, can account for the observed facilitation [27] . However, a dual sensor model could not explain all features of vesicle release in the Drosophila neuromuscular junction [69] . In its current form our model for PTP is a qualitative and reduced model which does not include (Ca 2+ -dependent) priming of vesicles, spatial distribution of vesicles or detailed Ca 2+ dynamics, nor the effect of Syt1 or other sensors on these processes. Furthermore, it does not explicitly describe all successive steps in the fusion pathway [6] and the different roles of Syt1 during these steps [14, 89, 90] , but models fusion as a single step using one effective energy barrier. Despite these limitations, the model is able to explain the increase in fusion rate upon Ca 2+ binding and increase in release probability during PTP, the latter with the relatively small changes in fusion barrier we found. This suggest that, while other mechanisms also may contribute, modulation of the fusion barrier is an important mechanism by which the synapse controls its efficacy on the short-term scale. 
Hippocampi Autaptic hippocampal cultures were prepared as described previously [91] . Briefly, micro-islands were prepared with a solution containing 0.1 mg/ml poly-D-lysine (sigma), 0.7 mg/ml rat tail collagen (BD Biosciences) and 10 mM acetic acid (Sigma) applied with a custom-made rubber stamp (dot diameter 250 μm). Next, rat astrocytes were plated at 6-8K per well in pre-warmed DMEM (Invitrogen), supplemented with 10% FCS, 1% Penicillin-Streptomycin and 1% nonessential amino acids (All Gibco). Hypertonic sucrose stimulation was performed as described previously [7] . Briefly, gravity infused external solution was alternated with 7 s of perfusion with hypertonic solution by rapidly switching between barrels within a custom- 
Offline analysis was performed using custom-written software routines in Matlab R2018b Ca 2+ -dependent release rates were simulated using the previously described allosteric model [1] . Simulations with the allosteric model [1] , reveal that both increased positive charge ( +, ) and increased SNARE binding ( 232 ) lead to higher release rates, though only for +, was Ca 2+ -independent release also increased. Linear fits of the steepest part of the curves indicate no clear change in Ca 2+ -cooperativity compared to WT.