The release of inhibition model reproduces kinetics and plasticity of neurotransmitter release in central synapses

Calcium-evoked release of neurotransmitters from synaptic vesicles (SVs) is catalysed by SNARE proteins. The predominant view is that, at rest, complete assembly of SNARE complexes is inhibited (‘clamped’) by synaptotagmin and complexin molecules. Calcium binding by synaptotagmins releases this fusion clamp and triggers fast SV exocytosis. However, this model has not been quantitatively tested over physiological timescales. Here we describe an experimentally constrained computational modelling framework to quantitatively assess how the molecular architecture of the fusion clamp affects SV exocytosis. Our results argue that the “release-of-inhibition” model can indeed account for fast calcium-activated SV fusion, and that dual binding of synaptotagmin-1 and synaptotagmin-7 to the same SNARE complex enables synergistic regulation of the kinetics and plasticity of neurotransmitter release. The developed framework provides a powerful and adaptable tool to link the molecular biochemistry of presynaptic proteins to physiological data and efficiently test the plausibility of calcium-activated neurotransmitter release models.


Introduction
Synaptic release of neurotransmitters forms the basis of information transfer in the brain. It is well established that synaptic vesicle (SV) fusion with the plasma membrane is mediated by SNARE (soluble N-ethylmaleimide-sensitive factor attachment protein receptor) proteins, namely VAMP2 on the SV (v-SNARE) and syntaxin1 and SNAP25 on the plasma membrane (t-SNAREs) in most of central synapses [1][2][3] . v-and t-SNAREs can constitutively assemble (or 'zipper') into a complex that brings opposing membranes together and provides the energy required for fusion. In addition to synapses, similar SNARE proteins mediate the fusion of virtually all membranous organelles in living cells 4

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A distinct property of SV exocytosis is that it is tightly coupled to neuronal activity and controlled by action potential (AP)-evoked increases in presynaptic 2 [] Ca + . To achieve this, presynaptic terminals maintain a readily releasable pool (RRP) of vesicles that are docked at the presynaptic active zone (AZ). When an AP reaches the presynaptic terminal, it depolarises the presynaptic membrane and transiently activates voltage-gated Ca 2+ channels (VGCCs) located in the AZ, resulting in the formation of local Ca 2+ nano/microdomains near RRP vesicles (

[] local
Ca + ~10 -100 µM). Ca 2+ ions activate the fast, low-affinity vesicular Ca 2+ release sensor synaptotagmin 1 (Syt1, or its closely related isoforms Syt2 and Syt9 in different types of synapses), which triggers SV exocytosis and synchronous neurotransmitter release on a millisecond timescale 3,5 . VGCCs close within several milliseconds after an AP, resulting in the collapse of Ca 2+ nano/microdomains. However, the presynaptic Ca 2+ level remains elevated in the low micromolar range for tens to hundreds of milliseconds. This long-lasting increase in residual , which is especially prominent during bursts of neuronal activity, triggers delayed asynchronous neurotransmitter release and also contributes to facilitation of synchronous release upon arrival of another AP. This short-term plasticity of vesicular release allows presynaptic terminals to process the neuronal spiking code and provides a basis for synaptic computation and selective information transfer in the brain 6,7 . Asynchronous release and synaptic facilitation are, in large part, mediated by the presynaptic membrane-associated high-affinity Ca 2+ -release sensor synaptotagmin 7 (Syt7), which can be activated by 2 [] residual Ca + [8][9][10][11] . Thus, it is emerging that synaptic release of neurotransmitters is synergistically regulated by low-and high-affinity synaptotagmins acting on the same pool of vesicles or even on the same SNARE complex. How this occurs in molecular terms remains poorly understood.
The current prevailing view is that each RRP vesicle contains several partially assembled SNARE complexes ('SNAREpins') that are arrested ('clamped') in this state by synaptotagmins and the soluble presynaptic protein complexin. The SNAREpins are thought to be released by Ca 2+ activation of synaptotagmin molecules and act cooperatively to drive rapid SV exocytosis leading to neurotransmitter release [12][13][14] . However, it has not been quantitatively tested whether this 'release of inhibition' model can adequately describe the millisecond kinetics of synchronous neurotransmitter release, or if additional mechanisms, such as membrane bending and/or membrane bridging by Syt1 [15][16][17][18][19][20][21] , are also critical. 21 . Interestingly, the primary site is accessible to only fast, low-affinity Ca 2+ sensors (Syt1, Syt2 and Syt9), whilst the tripartite site appears to be universally accessible to all synaptotagmin isoforms, including Syt7. Dual synaptotagmin binding at primary and tripartite interfaces has the potential to explain, in molecular terms, how different synaptotagmin isoforms cooperatively regulate neurotransmitter release and short-term plasticity [10][11][12][13] . However, this hypothesis remains to be tested.
One difficulty in addressing these questions is that measuring the spatiotemporal dynamics of Ca 2+ at the AZ is challenging due to its spatial scale (200 -600 nm) and the inherently low signal-to-noise ratio of fluorescent Ca 2+ indicators when imaging with millisecond resolution. Another obstacle is that, at present, it is not possible to directly track the molecular states of different synaptotagmin isoforms on RRP vesicles. Data-constrained realistic computational models of presynaptic terminals are therefore essential tools that can bypass the limitations of experimental approaches. Indeed, we have previously created a set of computational tools to model presynaptic Ca 2+ dynamics at different types of synapses during physiological patterns of activity 26-30 .
Here we describe an experimentally constrained computational modelling framework that allows us to model activation of Syt1 and Syt7 by physiologically relevant Ca 2+ transients that occur at the presynaptic AZ and to test how their activation triggers SV exocytosis for different molecular models of the fusion clamp. We find that release of inhibition is sufficient to explain the millisecond kinetics of AP-evoked SV exocytosis. Our results indicate that, irrespective of the triggering Ca 2+ signal's shape, or the nature of the fusion clamp, the majority of synchronous vesicular fusion occurs when 3 SNAREpins are simultaneously free from inhibition. Furthermore, our simulations reveal that the Syt1/SNARE interaction at the primary site alone can account for the millisecond kinetics of AP-evoked synchronous release and that binding of Syt1 or Syt7 to SNARE complexes at the tripartite interface provides an additional level of regulation of vesicular fusion. In particular, dual Syt1/Syt7 binding to the same SNAREpin can explain the role of Syt7 in the regulation of short-term synaptic plasticity and kinetics of vesicular release.

Computational implementation of the release of inhibition model.
We assumed that each RRP vesicle was associated with several partially assembled SNAREpins that were clamped in this state by Syt1 and Syt7 isoforms along with complexin ( Figure 1A). We considered three synaptotagmin clamp architectures based on the available structural and functional data. In all cases the primary interface was occupied by Syt1. Indeed, the primary interface is selective for Syt1 (and its similar isoforms Syt2 and Syt9) but not for Syt7. It has also been shown that Syt1 can simultaneously interact with the lipid bilayer via PIP2 interaction and SNAREs via the primary interface 24 . It is thus likely, that Syt1 binding at the primary interface occurs at an early stage of vesicle docking, preceding the SNARE assembly process. In contrast, the tripartite interface is generated only when SNAREs are partially-zippered and can bind complexin. Furthermore, the tripartite interface binding motif is present in both Syt1 and Syt7 21 . Therefore, the three synaptotagmin fusion clamp architectures we considered were where the tripartite interface was either unoccupied (single clamp, Syt1 P ) or occupied (dual clamp) either by Syt1 (Syt1 P /Syt1 T ) or by Syt7 (Syt1 P /Syt7 T ) ( Figure 1A). To model these three limiting cases, we assumed that all SNAREpins on a given RRP vesicle share the same clamp architecture. Biochemical and physiological analyses have shown that a small number of SNAREs are sufficient to achieve fast, Ca 2+ synchronised neurotransmitter release [31][32][33] . Furthermore, recent cryo-electron tomography analysis in cultured hippocampal synapses demonstrated a circular symmetric arrangement of six protein densities at the interface between docked SVs and the presynaptic membrane, each possibly corresponding to a single SNARE-associated exocytic module 34 . Therefore, we assumed that each RRP vesicle was associated with six SNAREpins.
It is well established that Ca 2+ binding leads to rapid insertion of the aliphatic loops of synaptotagmin C2 domains into the membrane and that this step is critical for triggering neurotransmitter release 35,36 . Indeed, structural and biochemical analyses have indicated that a Ca 2+ -triggered reorientation of Syt1 C2 domains displaces Syt1 from the primary SNARE interface 24, 37 . Therefore, we assumed that Ca 2+ binding and subsequent membrane loop insertion of synaptotagmin C2 domains induces removal of the fusion clamp, i.e. 'release of inhibition' ( Figure 1B). Based on the previously established critical roles of the Syt1 C2B domain 38,39 and the Syt7 C2A domain 8,9 , for simplicity, we only considered activation of these domains in our model. The C2 domains of Syt1 and Syt7 associated with RRP vesicles are likely to be in close proximity to the membrane 24, 40, 41 . Hence, we modelled Ca 2+ triggered loop insertion as a first order reaction described by membrane insertion ( in k ) and dissociation ( out k ) rates. Combined with the two-site protein-ligand binding model described by Ca 2+ binding ( on k ) and unbinding ( off k ) rates, the model of Syt1 and Syt7 C2 domain dynamics is described by the kinetic scheme in Figure 1B. This model assumes that Ca 2+ is not able to dissociate from the C2 domain while it is membrane-inserted, and that reversal of membrane insertion leads to immediate restoration of the SNARE fusion clamp.
Finally, we assumed that the repulsive forces between a SV and the plasma membrane constitute a potential energy barrier, which is lowered by the independent energetic contributions of individual assembled SNARE complexes. SV fusion was triggered when the barrier was overcome by thermal fluctuations at a rate given by the Arrhenius equation ( Figure  1C) 42,43 . The parameters of the complete Markov model were constrained using the available biochemical and structural data 13 Figure 1).
In line with the Ca 2+ uncaging experiments we simulated vesicular release in response to 2 [] Ca + steps in the range of 1 -32 µM for the three limiting cases of the clamp architecture ( Figure 1A). In all three cases, the peak release rates exhibited a power law dependency on the 2 [] Ca + step, with exponents between 2.7 and 4.3 (Figure 2A, B). In agreement with the experimental data recorded at the calyx of Held described by the benchmark allosteric model, sub-millisecond fusion rates predicted by the release of inhibition models were apparent for 2 [] Ca + steps above 4 µM or 8 µM, depending on the clamp architecture. The release rate was greatest in the case of a single Syt1 clamp at the primary interface. The introduction of an additional Syt1 or Syt7 clamp at the tripartite interface reduced the release rate but enhanced Ca 2+ cooperativity. The predictions of the allosteric model lie between these limiting clamping cases, demonstrating that the release of inhibition model can indeed explain the experimentally observed kinetics of vesicular release. The model output further suggests that the occupancy of the tripartite interface by different synaptotagmin isoforms could provide an efficient mechanism for the dynamic regulation of Ca 2+ -triggered vesicular release.
To estimate how many SNARE complexes are needed to drive fast synchronous vesicular fusion we monitored the number of unclamped SNAREpins associated with each vesicle prior to fusion. We found that for all clamp architectures, fast fusion (peak release rate above 10 -2 ms -1 ) required at least 3 uninhibited SNAREpins. This value is consistent with previous experimental and modelling estimates for the number of SNAREs required to mediate synchronous release of neurotransmitters 31,32,43 . Indeed, the apparent rate of synchronous vesicle fusion in our modelling framework is limited by the time taken for 3 SNAREpins to be released from the fusion clamp, which depends on the 2 [] Ca + increment and the clamp architecture ( Figure 2C). In the case of 3 unclamped SNAREpins the vesicular fusion rate predicted in our model by the Arrhenius equation is 8.1 ms -1 ( Figure 1C). This value is orders of magnitude greater than the upper limit for how quickly the synaptotagmin clamp can be restored, which is limited by the rate of C2 domain membrane dissociation ( out k = 0.67 ms -1 for Syt1 and out k = 0.02 ms -1 for Syt7, see Methods). This implies that once 3 SNAREpins are simultaneously unclamped, vesicle fusion is inevitable. In line with this prediction, the peak release rate was directly proportional to the fraction of vesicles with 3 uninhibited SNAREpins, irrespective of the synaptotagmin clamp architecture ( Figure 2D).

The release of inhibition model recapitulates synchronous release in response to AP-evoked [Ca 2+ ] transients at the AZ.
We next examined whether the release of inhibition model could replicate the vesicular release dynamics observed at presynaptic terminals in response to AP stimulation. AP-evoked Ca 2+ dynamics at vesicular release sites have not been directly measured, largely because of the small size of the AZ and the high speed of Ca 2+ kinetics. Therefore, we and others have developed three-dimensional, experimentally constrained models of Ca Figure 3B, C).
In line with the analysis of step 2 [] Ca + increments ( Figure 2A, B), the model-predicted vesicular release kinetics in response to AP-evoked Ca 2+ influx depended on the architecture of the synaptotagmin clamp ( Figure 3). For all coupling distances tested, the vesicular release probability was highest when the tripartite interface was unoccupied (single Syt1 P clamp).
Adding either a second Syt1 or Syt7 clamp at the tripartite interface reduced the vesicular release by similar amounts. The amplitude of AP-evoked 2 [] Ca + transients decreased with increasing coupling distance, which resulted in a corresponding reduction of both the peak release rate and the overall release probability ( Figure 3C). The decrease was steeper when the tripartite site was occupied by either Syt1 or Syt7 due to increased Ca 2+ cooperativity.
Notably, the predictions of the benchmark allosteric model were within the range of the predictions of the three limiting cases of clamping architectures. These results further demonstrate that the release of inhibition model can reproduce the The release of inhibition model reproduces Syt7-dependent short-term facilitation.
Short-term plasticity of synaptic neurotransmitter release is commonly assessed by measuring vesicular release in response to pairs of APs. We therefore tested how the molecular architecture of the synaptotagmin clamp shapes vesicular release in response to paired-pulse stimulation ( Figure 4). Using the VCell model described in Figure 3 we computed 2 [] Ca + responses to different inter-stimulus intervals (10 to 500 ms) and coupling distances (30 to 80 nm). We next simulated vesicular release for different synaptotagmin clamp architectures in response to the obtained Ca 2+ dynamics and calculated the paired-pulse ratio  Figure 4A). In the case of the single Syt1 clamp at the primary interface (Syt1 P ), we observed depression of vesicular release in response to the 2 nd AP, which was most prominent at short coupling distances where transients had the greatest amplitude. The depression can be explained by depletion of the RRP vesicles due to the absence of vesicle replenishment in these simulations and the relatively high release probability at the 1 st AP ( Figure 3C and Figure 4A). In contrast, in the case of the dual Syt1 clamp (Syt1 P /Syt1 T ) the release probability at both the 1 st and the 2 nd APs was low, and the PPR was close to 1 for the whole range of coupling distances and inter-spike intervals tested. Strikingly, inclusion of Syt7 at the tripartite interface (Syt1 P /Syt7 T ) led to a facilitation of vesicular release at the 2 nd AP ( Figure 4A-C). The increase of PPR was most noticeable (2-to 3-fold) at shorter inter-stimulus intervals (10 -50 milliseconds) and longer coupling distances (> 40 nm).
The observed facilitation can be explained by the slower membrane dissociation kinetics of Syt7 relative to Syt1 45 . The 1 st AP induces the insertion of Syt1 and Syt7 C2 domains into the membrane, which leads to release of the fusion clamp at a fraction of SNAREpins. If fusion of a given vesicle was not successfully induced during the 1 st AP, then the clamp on its SNAREpins would be restored more slowly by Syt7 than by Syt1, because Syt7 stays longer in the membrane ( out k = 0.02 ms -1 for Syt7 and 0.67 ms -1 for Syt1). This means that at the time of arrival of the 2 nd AP these unfused vesicles are expected to have up to 40% of Syt7 clamps already released ( Figure 4D), conferring an increase in the probability of SV fusion, The observed short-term facilitation (STF) mediated by Syt7 diminished as the inter-pulse interval increased, due to progressive restoration of the Syt7 clamp, and disappeared within 500 ms, consistent with experimental data 11,57 . Indeed, the dependency of PPR on the interstimulus interval for a given coupling distance aligned well with that of the average number of free Syt7 clamps immediately before onset of the 2 nd AP ( Figure 4C, D). In contrast, the dependency of Syt7-mediated STF on coupling distance was non-monotonic, with PPR reaching maximal values at coupling distances between 50 -60 nm ( Figure 4B). This was due to the competing effects of increased vesicle depletion after the 1 st AP at short coupling distances versus decreased removal of Syt7 clamps on unfused vesicles at longer coupling distances.

Mixed single and dual fusion clamp model can recapitulate vesicular release properties at plastic synapses.
We next assessed whether the release of inhibition model can explain the complex patterns of vesicular release observed in response to bursts of neuronal activity. To test this, we chose the mossy fibre bouton (MFB) -CA3 pyramidal neuron synapse in the hippocampus as a model environment. This synapse, which is also called a 'detonator synapse', has a very low initial release probability ( v p for individual RRP vesicles is in the range of 0.01 -0.03) and shows strong STF of synchronous release (up to 10-fold) and prominent asynchronous release after high frequency bursts of activity 58,59 . STF in MFBs is mediated by at least two different mechanisms: (i) progressive increase of peak .
We previously constrained Ca 2+ dynamics at MFB release sites during high-frequency bursts of APs using a three-dimensional VCell model 27, 28 . Here we used the previously estimated Considering that neither the single nor the dual clamp architecture could fully recapitulate all the different facets of vesicular release at MFBs, we tested if a mixture of single and dual synaptotagmin clamps could better describe the physiological data. We considered two models. In both cases, on average, half of the SNAREpins were clamped by Syt1 at the primary interface only, whilst the remaining SNAREpins had a dual clamp arrangement with either Syt1 or Syt7 at the tripartite interface (Mixed Syt1 model and Mixed Syt7 model respectively, Figure 6A). In comparison to the full dual clamp models considered above, partial removal of the clamp from the tripartite interface increased the initial release efficacy for individual RRP vesicles to the physiological level, (1)  Figure 4D). This result is consistent with the decreased STF observed in MFB synapses of Syt7 knockout versus wild type mice 8 .
We also tracked the asynchronous release component triggered by elevated 2 [] residual Ca + after the AP burst ( Figure 5C and Figure 6D). As expected, we found that the rate of asynchronous release depended on the fusion clamp architecture. The asynchronous release was prominent in the single Syt1 P , dual Syt1 P /Syt7 T and Mixed Syt1 and Syt7 models, whereas no asynchronous release was observed in the case of the dual Syt1 P /Syt1 T clamp model.
These results further illustrate that the balance between single and dual synaptotagmin clamp arrangements could provide a mechanism for the regulation of both short-term synaptic plasticity and the kinetics of vesicular release.

Discussion
Our computational analysis shows that the release of inhibition model, i.e. Ca 2+ -triggered removal of the SNARE fusion clamp, can indeed explain the kinetics of evoked neurotransmitter release. Our simulations further show that fast SV fusion requires simultaneous release of inhibition of at least 3 SNAREpins. Thus, the kinetics of vesicular fusion depend on how rapidly this state is reached, which is in turn determined by the shape and the amplitude of the Based on the available structural data 21 we considered three possible limiting cases of the fusion clamp architecture: with a single Syt1 clamp at the primary interface (Syt1 P ) and dual Syt1 and/or Syt7 clamps at primary and tripartite interfaces (Syt1 P /Syt1 T and Syt1 P /Syt7 T ). Our analysis shows that the release of a single or dual synaptotagmin clamp can account for submillisecond kinetics of Ca 2+ triggered neurotransmitter exocytosis. Furthermore, the dual binding Syt1 P /Syt7 T arrangement also reproduced STF of SV exocytosis in response to pairs or burst of APs. This result shows that the release of inhibition model also provides a mechanism by which Syt7 can regulate short-term plasticity.
The functional importance of the primary interface has been well established, both in live synapses and under reconstitution conditions 22, 23, 33, 60 . In contrast, the relevance of the tripartite interface remains unclear because the interaction of SNAREs/synaptotagmins/complexin at this site cannot be measured biochemically and is thus expected to be very weak 21, 33, 37, 61, 62 . However, considering the high local concentration of the vesicular release machinery components at RRP vesicles, it is reasonable to expect that the tripartite interface can be at least partially occupied under physiological conditions. In fact, our simulation argues that the weak interaction at this site may play an important functional role. We find that under all conditions tested the release rates predicted by the single Syt1 P clamp model were higher than those predicted by the benchmark empirical allosteric model. In contrast, the vesicular fusion rates predicted by both Syt1 P /Syt1 T and Syt1 P /Syt7 T dual clamp models were below physiological levels. Thus, the dynamic occupancy of the tripartite interface by either Syt1 or Syt7 could provide direct control of kinetics and plasticity of neurotransmitter release by changing the strength and Ca 2+ -activation properties of the SV fusion clamp. Indeed, we find that a mixed model combining both single and dual clamp architectures can closely describe the release kinetics and short-term plasticity in response to trains of APs in hippocampal MFB terminals. While our parsimonious model describes the key molecular elements of Ca 2+ activation of synaptotagmin and removal of the fusion clamp, it has several simplifications. We assumed that release of the fusion clamp occurs simultaneously with Ca 2+ -triggered membrane insertion of the C2 domain. This is likely the case for the primary interface 24 , but the kinetics of synaptotagmin/complexin/SNARE interactions at the tripartite interface are not currently known. Similarly, we assumed that restoration of the clamp occurs instantaneously after reversal of synaptotagmin membrane insertion. Thus, the current model provides an upper estimate for the magnitude of synchronous release and lower estimates for asynchronous release and short-term facilitation. Furthermore, in addition to synaptotagmins and canonical SNAREs considered in our model, different modes of Ca 2+ -evoked release might utilize vesicles with distinct compositions of SNAREs and Ca 2+ sensors (e.g. VAMP4 63 , VAMP7 64 and Doc2 65 ).
For simplicity, we only modelled the activation of Syt1 C2B and Syt7 C2A domains. Considering that the C2A and C2B domains act synergistically 66 , inclusion of the second C2 domain in the model will increase the overall Ca 2+ / membrane affinity of synaptotagmin molecules and the Ca 2+ cooperativity. At present, the binding modalities of Syt7 to the SNARE complex remain unknown; thus, we modelled Syt7 binding to SNAREs via the tripartite interface based on structural homology 21 . However, it is worth noting that the output for the Syt1/Syt7 dual clamp model will be the same even if Syt7 binds at a different site. Finally, the current model does not account for possible roles of Syt1 oligomerisation 67, 68 , mechanical coupling among different SNAREpins 43 , and membrane remodelling activities of Syt1 that occur after the release of inhibition [15][16][17][18][19][20][21] . Nevertheless, the model can be easily modified to implement any of the above mechanisms as well as other fusion clamp architectures. Therefore, the developed modelling framework provides a powerful and adaptable tool to complement experimental work and gain insights into how the presynaptic vesicular release machinery decodes Ca 2+ signals and translates them into complex patterns of neurotransmitter release.

Release of inhibition model parameters.
We considered that within the physiological range of The rate of SNARE-mediated SV fusion was determined by assuming that the repulsive forces between a docked SV and the plasma membrane amount to an energy barrier of 0 E ≈ 26 kBT 42 . Overcoming this barrier requires bringing the SV to within around 1-2 nm of the plasma membrane such that membrane fusion is spontaneously induced 14 . The full assembly of a single SNARE complex from a half-zippered state has been estimated to provide E ∆ ≈ 4.5 kBT of work towards overcoming the resting energy barrier 43 . We assumed that E ∆ is made immediately available to the vesicle in the form of potential energy when a SNAREpin is freed from its synaptotagmin clamp, effectively lowering the energy barrier to membrane fusion.
Thus, with n uninhibited SNAREpins, the barrier to fusion has a height of 0 E nE −∆ and is spontaneously overcome through thermal fluctuations at a rate given by the Arrhenius simulations. Specifically, we used the direct Gillespie algorithm 49 which proceeds by iteratively generating a randomised time at which the system next changes its state and then randomly selecting the identity of the new state. The Ca 2+ binding and SV fusion dynamics of the allosteric model were described by a six-state kinetic scheme with a single occupied state which is updated at each step of the algorithm. The release of inhibition models consisted of either six (in the case of Syt1 P ) or twelve (in the cases of Syt1 P /Syt1 T and Syt1 P /Syt7 T ) fourstate kinetic schemes ( Figure 1B), one for each Syt C2 domain. Rather than updating a unique state in the resultant macroscopic Markov chain which had either 4 6 or 4 12 states, we monitored each synaptotagmin C2 domain concurrently and updated one of their states according to the algorithm. We assumed that at the start of each simulation both the Ca 2+ sensor in the benchmark allosteric model and all SNARE-associated synaptotagmin C2 domains in the release of inhibition models were in the Ca 2+ unbound state.
In simulations shown in Figures 2, 3 and 4 we did not include the mechanism for vesicle replenishment and individual stochastic simulations terminated when vesicle fusion occurred. In simulations describing vesicular release in response to a 10 x 100 Hz AP train we included a mechanism for SV replenishment. Upon vesicle fusion the release site remained unoccupied for a fixed refractory time of 2.5 ms -1 after which a SV was replenished in the initial state with the rate of rep k = 0.02 ms -1 , as was estimated in our previous work 28 .
For each scenario the collection of stochastic simulations yielded a set of times at which SV fusion occurred. We used the cumulative count of these vesicle fusion times, normalised to the total number of stochastic simulations, as an estimate for the expected cumulative number with a moving average smoothing applied to limit the sensitivity of peaks to stochastic variation.
In order to assess the accuracy of these release estimates generated using the Monte Carlo approach we compared the  Figure 3). For each scenario considered with both the allosteric and release of inhibition models, by default, stochastic simulations were set to continue until 10 5 release events had been recorded. This corresponded to an average error of less than 0.1%. However, due to resource constraints and differences in computational demand between scenarios, this was not always achieved, and the total number of simulated release events varied. Across all scenarios the minimum number of release events recorded was 2,250 (Syt1 P /Syt1 T at a 2 µM step), corresponding to an average error of less than 1%, making this the expected upper limit of prediction errors due to stochastic variation.

Simulation of [Ca 2+ ] transients within a presynaptic terminal.
Three-dimensional modelling of AP-evoked presynaptic Ca 2+ influx, buffering, diffusion and extrusion was performed in the Virtual Cell (VCell) simulation environment (vcell.org) using the fully implicit adaptive time-step finite-volume method on a 10-nm meshed geometry as described in detail in our previous studies. Specifically,  Figure 1. Computational implementation of the release of inhibition model (A). At rest, the full zippering of SNAREs on RRP vesicles is inhibited ('clamped') by binding of synaptotagmin and complexin molecules. Based on structural data, three synaptotagmin/SNARE clamp architectures were considered in the model (right). In all cases Syt1 occupies the primary interface. The tripartite interface is either unoccupied (single clamp, Syt1 P ) or occupied (dual clamp) by Syt1 (Syt1 P /Syt1 T ) or Syt7 (Syt1 P /Syt7 T ). Crystal structure (PDB ID: 5W5C) 21 .

Figures
(B) The binding of two Ca 2+ ions to a synaptotagmin C2 domain leads to its subsequent membrane insertion (described by the reaction scheme on the right) and release of its SNARE fusion clamp allowing full zippering of SNAREs which provides energy for membrane fusion.
(C) The fusion rate is determined by the number of free SNARE complexes that reduce the effective membrane fusion energy barrier, illustrated here as a Gaussian landscape (right). Each SNAREpin was assumed to independently contribute to the lowering of the membrane fusion barrier which is spontaneously overcome at a rate given by the Arrhenius equation (see Methods). Note that only two out of six SNARE complexes are shown in the cartoons on the left that represent a vertical cross-section of the SV.      (A) We considered two partial dual clamp models where on average 3 out of 6 SNAREpins had a single Syt1 P clamp, and the other 3 had dual Syt1 P /Syt1 T or Syt1 P /Syt7 T clamps. (B) Simulated proportion of membrane-inserted Syt1 and Syt7 when Ca 2+ is instantaneously removed from the system (i.e. after fast dilution in EGTA containing buffer). The membrane dissociation curves closely follow single exponential decay functions with the rate constants from stopped-flow experiments, indicating a negligible contribution from the secondary minor exponential component.