Introduction
Regulated neurotransmitter (NT) release from presynaptic terminals is crucial for information transfer across chemical synapses. NT release is triggered by action potentials (APs), which are transient de- and repolarizations of the presynaptic membrane potential that induce Ca2+ influx through voltage-gated channels. The resulting brief and local elevations of the intracellular Ca2+ concentration ([Ca2+]i) trigger the fusion of NT-containing synaptic vesicles (SVs) from the so-called readily releasable pool (RRP), whose SVs are localized (docked) at the plasma membrane and molecularly matured (primed) for fusion (Kaeser and Regehr, 2017; Südhof, 2013; Verhage and Sørensen, 2008). A high Ca2+ sensitivity of NT release is needed to achieve fast responses to the very short AP-induced Ca2+ transient and correspondingly, the SV fusion rate depends to the 4th-5th power on the [Ca2+]i (Bollmann et al., 2000; Burgalossi et al., 2010; Heidelberger et al., 1994; Schneggenburger and Neher, 2000). Accordingly, previous models of NT release have assumed the successive binding of five Ca2+ ions to a sensor that regulates release (Bollmann et al., 2000; Lou et al., 2005; Schneggenburger and Neher, 2000). However, how these macroscopic properties arise from the molecular components involved in SV fusion is still unknown.
The energy for SV fusion is provided by the assembly of the neuronal SNARE complex, which consists of vesicular synaptobrevin/VAMP and plasma membrane bound SNAP25 and syntaxin proteins (Jahn and Fasshauer, 2012; Südhof, 2013). Ca2+ sensitivity of SV fusion is conferred by the vesicular protein synaptotagmin (syt), which interacts with the SNAREs (Brewer et al., 2015; Littleton et al., 1993; Mohrmann et al., 2013; Schupp et al., 2017; Zhou et al., 2015; Zhou et al., 2017). Several syt isoforms are expressed in synapses. Depending on the synapse type (e.g. mouse hippocampal pyramidal neurons or the Calyx of Held), syt1 or syt2 is required for synchronous, Ca2+-induced fusion (Geppert et al., 1994; Kochubey et al., 2016; Kochubey and Schneggenburger, 2011; Südhof, 2013). These two syt isoforms are highly homologous and contain two cytosolic, Ca2+-binding domains, C2A and C2B (Südhof, 2002), of which the C2B domain has been shown to be essential, and in some cases even sufficient, for synchronous NT release (Bacaj et al., 2013; Gruget et al., 2020; Kochubey and Schneggenburger, 2011; Lee et al., 2013; Mackler et al., 2002). The C2B domain contains two Ca2+ binding sites on its top loops (Fernandez et al., 2001). In addition, a second binding site allows the C2B domain to bind to the signaling lipid phosphatidylinositol 4,5-bisphosphate (PI(4,5)P2) located in the plasma membrane (Bai et al., 2004; Fernández-Chacón et al., 2001; Honigmann et al., 2013; Li et al., 2006; Xue et al., 2008), but might also participate in (possibly transient) SNARE interactions (Brewer et al., 2015; Zhou et al., 2015; Zhou et al., 2017). A third site, located in the far end of the C2B domain (R398 and R399 in mouse syt1), is also involved in both SNARE- and membrane contacts (Nyenhuis et al., 2021; Xue et al., 2008; Zhou et al., 2015). Via these interactions, the syt C2B domain can induce close membrane-membrane contact in vitro (Araç et al., 2006; Chang et al., 2018; Honigmann et al., 2013; Nyenhuis et al., 2021; Seven et al., 2013; Xue et al., 2008), stable vesicle-membrane docking (Chang et al., 2018; Chen et al., 2021; de Wit et al., 2009), as well as dynamic vesicle-membrane association upon Ca2+ influx into the cell (Chang et al., 2018).
Despite its central role as the Ca2+ sensor for NT release, the intrinsic Ca2+ affinity of the isolated syt C2B domain is remarkably low (KD ≈ 200 µM, Radhakrishnan et al., 2009; van den Bogaart et al., 2012), much lower than the Ca2+ sensitivity of NT release (Bollmann et al., 2000; Schneggenburger and Neher, 2000). However, binding of the C2B domain to PI(4,5)P2, which is enriched at synapses (van den Bogaart et al., 2011a), drastically increases its Ca2+ affinity (van den Bogaart et al., 2012). Similarly, the affinity for PI(4,5)P2 increases upon Ca2+ binding (Pérez-Lara et al., 2016; van den Bogaart et al., 2012). This indicates a positive allosteric coupling between the binding sites for Ca2+ and PI(4,5)P2, which promotes dual binding of Ca2+/PI(4,5)P2 (Li et al., 2006; Radhakrishnan et al., 2009; van den Bogaart et al., 2012). As binding of both molecules to syt is involved in fusion (Kedar et al., 2015; Li et al., 2006; Mackler et al., 2002; Mackler and Reist, 2001; Wang et al., 2016; Wu et al., 2021a; Wu et al., 2021b), this positive allosteric coupling might be central to syt’s function in triggering Ca2+-induced exocytosis (van den Bogaart et al., 2012).
In this paper, we developed a mathematical model in which the dual binding of the C2B domain to Ca2+ and PI(4,5)P2 promotes fusion. The model, which is based on the measured affinities and allostericity of Ca2+ and PI(4,5)P2 binding, describes stochastic binding/unbinding reactions at the level of individual syts and stochastic SV fusion events. The model predicts that each C2B domain engaging in dual Ca2+/PI(4,5)P2 binding lowers the energy barrier for fusion by ~5 kBT. Our results indicate that during fast NT release most fusion events occur once three syts per SV simultaneously engage their C2B domains in dual Ca2+/PI(4,5)P2 binding. This simultaneous engagement of multiple syts crucially relies on the positive allosteric coupling between Ca2+ and PI(4,5)P2 binding. We explored consequences of putative mutations affecting Ca2+/PI(4,5)P2 binding and/or the allosteric coupling between the binding sites of both species and suggest that changes of the allostericity contribute to dominant negative effects. Moreover, dynamic changes of PI(4,5)P2 accessibility for the syts (e.g. induced by SV movement to the plasma membrane) are predicted to dramatically impact synaptic responses. We conclude that allosterically stabilized Ca2+/PI(4,5)P2 dual binding to the C2B domain forms the molecular basis for synaptotagmins to exert their cooperative control of neurotransmitter release.
Results
An experiment-based model of the triggering mechanism for SV fusion based on molecular interactions between syt, Ca2+, and PI(4,5)P2
To develop an experiment-based model of NT release based on molecular properties of syt, we first described the reaction scheme of a single C2B domain. The C2B domain binds PI(4,5)P2 and two Ca2+ ions (Fernández-Chacón et al., 2002; Honigmann et al., 2013; Mackler et al., 2002; van den Bogaart et al., 2012; Xue et al., 2008). We assumed the simplest case of simultaneous association of both Ca2+ ions to the syt1 C2B domain. Therefore, in our model the C2B domain can be in four different states (Figure 1A): (1) an ‘unbound’ state, (2) a PI(4,5)P2-bound state, (3) a state with two Ca2+ ions bound, and (4) a ‘dual-bound’ state in which the C2B simultaneously engages Ca2+/PI(4,5)P2 binding. The affinities for Ca2+ and PI(4,5)P2 were set to those measured in vitro (KD,2Ca2+ and KD,PIP2)(van den Bogaart et al., 2012). Binding of PI(4,5)P2 to the C2B domain was shown to increase the domain’s affinity for Ca2+ and vice versa, indicating a positive allosteric coupling between the two binding sites (van den Bogaart et al., 2012). We therefore implemented a positive allosteric stabilization of the dual-bound state in the model (illustrated by the red shaded areas of the C2B domain in Figure 1A) by introducing the allosteric factor (A=0.00022, see Materials and methods van den Bogaart et al., 2012) which slows down the Ca2+ and PI(4,5)P2 dissociation from the dual-bound state.
Figure 1.
A molecular model of NT release triggered by Ca2+ and PI(4,5)P2 binding to the syt1 C2B domain.
(A) The reaction scheme of a single syt C2B domain. Each syt can be in one of four binding states: Nothing bound (top left), PI(4,5)P2 bound (top right), two Ca2+ ions bound (bottom left), and PI(4,5)P2 and two Ca2+ ions bound (bottom right). Simultaneous binding of Ca2+ and PI(4,5)P2 to the syt C2B domain is referred to as dual binding. The factor A<1 on the dissociation rates (β and δ) from the dual-bound state represents the positive allosteric effect of simultaneous PI(4,5)P2 and Ca2+ binding and leads to stabilization of the dual-bound state. The ratio between dissociation rate and association rate constants (β/α and δ/γ) is equal to the respective dissociation constants of syt1 determined in vitro (KD,2Ca2+ = 2212 µM2 and KD,PIP2 = 20 µM, van den Bogaart et al., 2012). An alternative reaction scheme where Ca2+ binding leads to association of the C2B domain with the plasma membrane is shown in Figure 1—figure supplement 1. Our model is not influenced by the assumptions on whether Ca2+ binding to syt leads to plasma membrane or vesicle association. (B) The stoichiometry at the SV fusion site. We assume 15 syts per SV (Takamori et al., 2006), and that the association of the syt C2B domain to PI(4,5)P2 is limited to a finite number of slots (here illustrated for
Figure 1—figure supplement 1.
Alternative reaction scheme of a single syt in which Ca2+ binding leads to association to the plasma membrane.
Reaction scheme of a single syt C2B domain alternative to the one shown in Figure 1A. Instead of an association to the vesicular membrane, Ca2+ binding to the C2B domain in this illustration leads to an association with the plasma membrane. In this illustration, the dual-bound state affects the curvature of plasma membrane. Our model does not make a distinction between either of the two illustrations.
Figure 1—figure supplement 2.
Reaction scheme for all reactions of an entire SV.
The diagram shows the possible (un)binding reactions and indicates the relative fusion rate of an SV with
We next extended the model to the level of the complete SV. On average, SVs contain 15 copies of syt1 (Figure 1B; Takamori et al., 2006), which may work together to regulate SV fusion. Spontaneous release occurs at low rates (with a rate constant ‘L+’), reflected by a high initial energy barrier for SV fusion (Figure 1C). Because syt’s stimulation of SV fusion likely relies on the simultaneous binding of both Ca2+ and PI(4,5)P2 (Kedar et al., 2015; Li et al., 2006; Mackler et al., 2002; Mackler and Reist, 2001; Wang et al., 2016; Wu et al., 2021a; Wu et al., 2021b), we assumed that each dual-bound C2B domain promotes exocytosis by lowering this barrier. How this might be achieved exactly is unknown, but could involve bridging plasma and SV membranes (Figure 1A), changing the curvature of the plasma membrane (Figure 1—figure supplement 1), changing the local electrostatic environment, or directly or indirectly promoting SNARE complex assembly (Bhalla et al., 2006; Martens et al., 2007; Ruiter et al., 2019; Schupp et al., 2017; Tang et al., 2006; van den Bogaart et al., 2011b; Zhou et al., 2015; Zhou et al., 2017). We assumed that multiple syts may progressively lower the energy barrier by the successive engagement of their C2B domains in dual Ca2+/PI(4,5)P2 binding, and investigated the simplest scenario, in which each dual-bound C2B domain contributed the same amount of energy (
At least three PI(4,5)P2 binding slots are required to reproduce release kinetics from the calyx of Held synapse
A hallmark of the NT release reaction is its large dynamic range in response to Ca2+ stimuli as impressively demonstrated by experimental data from the calyx of Held synapse where release latencies (defined as the time of the fifth SV fusion after the stimulus) and exocytosis rates have been measured for a broad range of Ca2+ concentrations using Ca2+ uncaging (Bollmann et al., 2000; Kochubey and Schneggenburger, 2011; Lou et al., 2005; Schneggenburger and Neher, 2000; Sun et al., 2007). At this well-established model synapse, fast NT release is controlled by syt2, which is functionally redundant with syt1 in neurons (Kochubey et al., 2016; Xu et al., 2007).
We evaluated whether our model could reproduce this Ca2+ dependence by simulating release latencies and peak release rates in response to step-like Ca2+ stimuli. The ability to reproduce the experimental data depended on the number of ‘slots’ for syt PI(4,5)P2 binding (Figure 2A). We first fitted the free parameters in our model by optimizing the agreement (i.e. by reducing a pre-defined cost function, see Materials and methods) between model predictions and release rates and latencies determined experimentally by Kochubey and Schneggenburger (Figure 2A; Kochubey and Schneggenburger, 2011). During this fitting process, we took the entire distribution of the experimentally obtained release latencies into account by using the likelihood function (see Materials and methods). This was not feasible for the experimental peak release rates (since accurate computation of the maximum rate of stochastic events is not feasible), which were therefore compared to the closed form solution of the model (see Materials and methods). Because the affinities for Ca2+ and PI(4,5)P2, and the allosteric coupling between both species (KD,2Ca2+, KD,PIP2 and
Figure 2.
The model reproduces the Ca2+ dependency of SV fusion when at least three syts can simultaneously bind PI(4,5)P2.
(A) Best fit results for different choices of
Figure 2—figure supplement 1.
RRP distribution.
We assumed the RRP size to follow a gamma distribution with mean 4000 and SD 2000.
Figure 2—figure supplement 2.
Exploration of the number of dual bindings formed before fusion of an SV with Mslots = 3.
(A) The Ca2+ signal used in simulations with step (left) and ramp (right) Ca2+ stimuli. In simulations with step Ca2+, the concentration rises instantly at t=0 from the basal Ca2+ concentration of 50 nM to various constant concentrations. In simulations with ramp Ca2+, the Ca2+ concentration increases linearly from the basal concentration of 50 nM to 100 µM Ca2+ with various rise times. (B) The number of dual bindings formed before fusion for various Ca2+ concentrations (step Ca2+, left) or Ca2+ rise times (ramp Ca2+, right) as depicted in A. The bars show proportion of 10,000 stochastically simulated SVs. The number of dual bindings formed before fusion increased with increasing step Ca2+ concentrations and decreasing Ca2+ rise times. At high concentrations or fast rise times, most fusions took place after forming three dual bindings. (C) Average number of dual bindings formed before fusion in simulations of 10,000 SVs with Ca2+ signals as depicted in A. The average number of dual bindings formed before fusion increases with increasing step Ca2+ concentration and decreases with increasing Ca2+ rise time. A plateau is reached at an average of three dual bindings at high step Ca2+ concentrations and low rise times. Error bars show ± standard deviation.
Figure 2—figure supplement 3.
Exploration of the number of dual bindings formed before fusion of an SV with Mslots = 6.
(A) The Ca2+ signal used in simulations with step (left) and ramp (right) Ca2+ stimuli. In simulations with step Ca2+, the concentrations rises instantly at t=0 from the basal Ca2+ concentration of 50 nM to various constant concentrations. In simulations with ramp Ca2+, the Ca2+ concentration increases linearly from the basal concentration of 50 nM to 100 µM Ca2+ with various rise times. (B) The number of dual bindings formed before fusion for various Ca2+ concentrations (step Ca2+, left) or Ca2+ rise times (ramp Ca2+, right) as depicted in A. The bars show percentages of 10,000 stochastically simulated SVs. The number of dual bindings formed before fusion increased with increasing step Ca2+ concentrations and decreasing Ca2+ rise times. At high concentrations or fast rise times, most fusions took place after forming three to four dual bindings. (C) Average number of dual bindings formed before fusion in simulations of 10,000 SVs with Ca2+ signals as depicted in A. The average number of dual bindings formed before fusion increases with increasing step Ca2+ concentration and decreases with increasing Ca2+ rise time. A plateau is reached at an average of 3.4 dual bindings at high step Ca2+ concentrations and low rise times. Error bars show ± standard deviation.
Figure 2—figure supplement 4.
Forcing fusion from a state in which 5–6 syts are dual binding Ca2+ and PI(4,5)P2 causes a too steep Ca2+ dependency of the peak release rates.
(A) Best fit results for a model with 6 slots forced to show most fusion events when 5/6 dual-bounds were formed. We achieved this by setting
Figure 2—figure supplement 5.
Exploration of how the estimated number of dual binding syts for fusion depends on the number of Ca2+ ions bound to one C2B domain.
(A) The best fit results for a model with six slots and only 1 Ca2+ ion binding per syt. Solid lines indicate median release latencies (A1) and mean peak release rates (A2). Shaded area shows 95% prediction interval. Best fit parameters: number of Ca2+ ions = 1,
Figure 2—figure supplement 6.
A model with two sequential Ca2+ binding steps compared to the simplified model with the simultaneous binding of two Ca2+ ions.
(A) Extended reaction scheme of a single syt C2B domain in which Ca2+ binding occurs in two separate steps. Unbinding of the second Ca2+ binding step is reduced by the factor 1/coop. The allosteric interaction between Ca2+ and PI(4,5)P2 is only induced once both Ca2+ ions are bound. Similarly, the energy barrier is only reduced once the two Ca2+ ions and PI(4,5)P2 are bound. The equations on the right show how the new model parameters (indicated by the subscript 1) are computed from the parameters in the simplified reaction scheme. (B) Simulation results from the simplified reaction scheme (black) and extended reaction scheme (red). For these simulations the best fit parameters from fitting with three slots were used. For these simulations, the coop was set to 5e4. It was not possible to simulate a model including sequential Ca2+ binding with 15 syts. Therefore, the model was simplified to contain 6 syts and the PI(4,5)P2 concentration was increased to 3.33 µM to compensate this (Figure 5—figure supplement 2). Solid lines indicate median and mean release latencies and peak release rates, respectively. Dotted lines indicate 95% prediction intervals.
Figure 2—figure supplement 7.
Effect of the free parameters on release latencies and peak release rates.
(A–E) Effect on release latencies (left) and peak release rates (right) when varying
Table 1.
Fixed parameters in the model.
Parameter | Description | Value | Reference |
---|---|---|---|
| Number of syts per SV | 15 | Takamori et al., 2006 |
| Number of binding slots for syts to PI(4,5)P2 (see Figure 2) | Varied from 1 to 6 | This paper |
| Number of RRP vesicles | Mean: 4000, sd: 2000, gamma distribution | Wölfel and Schneggenburger, 2003 |
[Ca2+]0 | Resting [Ca2+]i | 0.05 µM | Helmchen et al., 1997 |
KD,2Ca2+ | Dissociation constant of C2B for two Ca2+ ions | 2212 µM2 | van den Bogaart et al., 2012 |
KD,PIP2 | Dissociation constant of C2B for PI(4,5)P2 | 20 µM | van den Bogaart et al., 2012 |
| Allosteric factor see Materials and methods for calculation | 0.00022 | van den Bogaart et al., 2012 |
| Ca2+ unbinding rate constant | KD,2Ca2+ ∙ α | Computed using best fit α (see Table 2) |
| PI(4,5)P2 unbinding rate constant of C2B | KD,PIP2 ∙ γ | Computed using best fit α (see Table 2) |
| Basal fusion rate | 4.23 ∙10–4 s–1 | Computed using data from Kochubey and Schneggenburger, 2011 |
We systematically varied the number of slots (
Our model made it possible to inspect the fate of each individual fusing SV, including the number of synaptotagmins dually binding Ca2+ and PI(4,5)P2 just before fusion. Remarkably, even in models with more than three slots (
Table 2.
Best fit model parameters and corresponding costs with different number of slots.
Parameter | Description | Mslots = 1 | Mslots = 2 | Mslots = 3 | Mslots = 4 | Mslots = 5 | Mslots = 6 |
---|---|---|---|---|---|---|---|
Ca2+ association rate constant | 0.03712 | 34.99 | 24.70 | 25.08 | 24.51 | 24.11 | |
PI(4,5)P2 association rate constant | 1.425·105 | 572.6 | 124.7 | 121.3 | 124.31 | 126.6 | |
[PI(4,5)P2] (µM) | Effective PI(4,5)P2 concentration for syt | 0.009658 | 0.2523 | 1.109 | 0.4528 | 0.3048 | 0.2320 |
Factor on the release rate for each Ca2+/PI(4,5)P2 dual bound C2B domain (resulting from a fusion barrier reduction of Esyt) | 4.259·106 (15.3) | 1298 | 128.2 | 152.1 | 159.6 (5.07) | 163.5 | |
Added delay | 0.3211 | 0.3761 | 0.3803 | 0.3866 | 0.3876 | 0.3881 | |
Costs | Quantification of goodness of fit | 581.9 | –92.50 | –139.4 | –130.3 | –127.7 | –126.5 |
We next investigated to which extent the estimated number of syts working together for fusion depended on some of the assumptions of our model. For instance, if each syt dual-binding Ca2+/PI(4,5)P2 had a lower effect on the vesicle fusion rate, might this be compensated by more syts working together during fusion? We investigated this by manually forcing a lower individual contribution to the energy barrier for fusion in a model with six slots and refitting the remaining parameters. Under such conditions, the dependence of the peak release rate on [Ca2+]i became too steep, indicating that too many syts working together make the Ca2+ sensitivity unnaturally high (Figure 2—figure supplement 4). We then investigated how the assumption of simultaneous binding of two Ca2+ ions to the C2B domain affected the conclusions. If each C2B domain only bound a single Ca2+ ion, the dependence of the peak release rate on [Ca2+]i was too shallow, even in a model with six slots. Allowing the number of Ca2+ ions binding to one C2B domain to vary in a macroscopic version of the model with six slots predicted the binding of 1.53 Ca2+ ions per C2B domain and most NT release commencing with four or fewer cooperating syts (Figure 2—figure supplement 5). This confirms that most C2B domains need to bind two Ca2+ ions to exert their effect. Simulating a model with consecutive Ca2+ binding to the two binding sites of the C2B domain on all syts of RRP SVs would be computationally too costly (and would involve additional, unknown parameters). However, we show that our simplification of simultaneous binding aligns with such a more complex model if the binding of the second Ca2+ ion is favored (Figure 2—figure supplement 6), which is reasonable based on the proximity to negatively charged lipid headgroups following the insertion of the C2B domain into the plasma membrane. Thus, while our model is a simplification of the reality, the main conclusion on the number of slots needed (Mslots ≥3) and the number of syts sufficient to mediate fast NT release (≤4), are robust estimates. Because our molecular model assuming three slots (
The best fit parameters for three slots revealed rapid association rate constants for Ca2+ and PI(4,5)P2 to the C2B domain and PI(4,5)P2 levels corresponding to a concentration of ~1 µM in an in vitro setting (Table 2). Predicted responses obtained using the best fit parameters were sensitive to changes of either of these parameters (Figure 2—figure supplement 7). For instance, higher levels of PI(4,5)P2 decreased the release latencies and increased the rate of fusion, and changing the Ca2+ association rate constant (
The number of syt proteins pre-associated to PI(4,5)P2 at rest influences the SV’s Ca2+ responsiveness
The steady state concentration of PI(4,5)P2 determines the probability of syts associating to PI(4,5)P2 at rest. With the best fit parameters, our model predicts that at rest ([Ca2+]i=50 nM) most SVs associate to PI(4,5)P2 by engaging one (~42%), two (~33%) or three (~8%) syts (Figure 3A, see Figure 3—figure supplement 1 for behavior in the model with
Figure 3.
Syts binding to PI(4,5)P2 prior to Ca2+ stimulus underlies very fast SV fusion.
(A) PI(4,5)P2 binding status of SVs at steady state. At resting [Ca2+]i of 50 nM, more than 40% of SVs have bound a single PI(4,5)P2 molecule (not including those that have formed a dual binding), more than 30% have bound two PI(4,5)P2, while less than 10% have bound three PI(4,5)P2. Close to no SVs form dual bindings at steady state. (B) Cumulative fusion of SVs after 50 µM step Ca2+ at t=0, grouped according to their initial PI(4,5)P2 binding state. During the first ~0.5ms, release is dominated by SVs having two or three syts bound to PI(4,5)P2 prior to the stimulus. The insert shows that the SVs having prebound three PI(4,5)P2 constitute the majority of the first five SVs that fuse in response to the Ca2+ step and therefore largely impact the release latency. (C) Cumulative release probability of SVs over time after 50 µM step Ca2+ at t=0, grouped according to initial PI(4,5)P2 binding state. The dominance of SVs having pre-bound to PI(4,5)P2 with two or three syts in panel B is explained by their high release probability compared to SVs with no or only one PI(4,5)P2 bound. Figure 3—figure supplement 1 shows the same analysis for a model with Mslots = 6. Simulation scripts can be found in Source code 1. Depicted simulation results can be found in Figure 3—source data 1.
Figure 3—figure supplement 1.
Syts binding to PI(4,5)P2 prior to the Ca2+ stimulus underlies very fast SV fusion (model with Mslots = 6).
(A) PI(4,5)P2 binding status of SVs at steady state. At resting [Ca2+]i of 50 nM, more than 40% of SVs have bound a single PI(4,5)P2 molecule (not including those that have formed a dual binding), more than 15% has bound two PI(4,5)P2, while less than 5% has bound three PI(4,5)P2. Very few SVs have bound more than 3 PI(4,5)P2 and almost no SVs form dual bindings at steady state. (B) Cumulative fusion of SVs after 50 µM step Ca2+ at t=0, grouped according to their initial PI(4,5)P2 binding state. During the first ~0.5ms, release is dominated by SVs having two or three syts bound to PI(4,5)P2 prior to the stimulus. The zoom-in shows that the SVs having three or four syts prebound to PI(4,5)P2 constitute the majority of release of the first five SVs and therefore determines the release latency. (C) Cumulative release probability over time of SVs after 50 µM step Ca2+ at t=0, grouped according to initial PI(4,5)P2 binding state. The dominance of SVs having pre-bound to PI(4,5)P2 with two to four syts in panel B is explained by their high release probability compared to SVs with no or only one PI(4,5)P2 bound.
Allosteric stabilization of Ca2+/PI(4,5)P2 dual binding is necessary to synchronize multiple C2B domains for fast SV fusion
An important feature of our model is the inclusion of a positive allosteric interaction between Ca2+ and PI(4,5)P2 binding to the C2B domain which we based on increased affinities measured in vitro (van den Bogaart et al., 2012). To explore the physiological relevance of this allostericity, we investigated how individual SVs engaged their syt C2B domains in Ca2+/PI(4,5)P2 dual binding in response to a stepwise increase of [Ca2+]i to 50 µM (Figure 4A) with or without this allosteric coupling. We did this by following the fate of the RRP SVs in stochastic simulations, four of which are illustrated in Figure 4B. Under normal conditions (with allostericity), syt C2B domains quickly associated both Ca2+ and PI(4,5)P2 and their respective allosteric stabilization slowed the dissociation of either species resulting in a lifetime of their dual binding of ~1.3 ms on average. This enabled the successive engagement of three dual-bound C2B domains for most RRP SVs (including all four illustrated SVs). The average waiting time for fusion for the RRP SVs was ~1.1 ms (Figure 4B, fusion indicated by circles). By inspecting the average behavior of the entire RRP of SVs it became clear that the overall release rate closely followed the population of SVs engaging three C2B domains in dual Ca2+/PI(4,5)P2 binding, illustrating the importance of engaging three syts for fast SV fusion in this model (Figure 4C). We also simulated the postsynaptic response produced by this NT release by convolving the SV release rate with a typical postsynaptic response to the fusion of a single SV (see Materials and methods), which revealed synchronous and large Excitatory Post Synaptic Currents (EPSCs)(Figure 4D).
Figure 4.
The positive allostericity between Ca2+ and PI(4,5)P2 allows multiple syt C2B domains to engage in Ca2+/PI(4,5)P2 dual binding.
(A) Ca2+ signal used in simulations ([Ca2+]i=50 µM). This constant Ca2+ concentration was used for all simulations depicted in this figure. (B) The path towards fusion for four example SVs using stochastic simulations of the best fit model (with allostericity). The differently colored graphs show the number C2B domains engaging in Ca2+/PI(4,5)P2 dual binding for the four example SVs. The large dots indicate SV fusion. (C) Average number of SVs having one (blue), two (olive) and three (green) C2B domains engaging in Ca2+/PI(4,5)P2 dual binding and the fusion rate (red) over time in simulations including the entire RRP. In the best fit model, the number of SVs with three syts dual-binding Ca2+/PI(4,5)P2 peaks approximately at the same time as the fusion rate. The decrease in number of SVs with one or two C2B domains dual binding Ca2+/PI(4,5)P2 reflects formation of additional dual bindings. The decrease in total number of SVs is caused by fusion of RRP vesicles. (D) Excitatory Postsynaptic Currents (EPSCs) from three stochastic simulations with a fixed RRP size of 4000 SVs. The model predicts synchronous EPSCs with a small variation caused by the stochasticity of the molecular reactions. (E) The path towards fusion for four example SVs (similar to panel A) in the model without allostericity in stochastic simulation. All parameters other than the allosteric factor,
Figure 4—figure supplement 1.
Fitting of the model without allosteric interaction between Ca2+ and PI(4,5)P2 fails to reproduce the Ca2+ dependency of NT release.
(A–B) The best fit results for a model with 3 slots and no allosteric interaction between Ca2+ and PI(4,5)P2 (A=1). In A the median release latency and the 95% prediction interval of the best fit model are shown. Note that the y-axis range is different from Figure 2A, but the proportions of the ticks is maintained to help comparison. (B) The mean peak release rate as a function of [Ca2+]i and the corresponding 95% prediction interval. Best fit parameters used to generate these curves are:
We then explored what would happen without the allosteric stabilization of Ca2+/PI(4,5)P2 dual binding (by setting A=1; Figure 4E). In this case, the C2B domains still quickly associated Ca2+ and PI(4,5)P2, but without the allosteric slowing of Ca2+/PI(4,5)P2 dissociation the lifetime of dual-bound C2B domains was dramatically reduced to an average of ~0.0003 ms. This made it very improbable to engage multiple C2B domains in dual Ca2+/PI(4,5)P2 binding (Figure 4E). In turn, without the simultaneous engagement of multiple syts dual-binding Ca2+/PI(4,5)P2, NT release became very unlikely. In fact, none of the randomly chosen four RRP SVs fused within 4 ms (Figure 4E). Inspection of the average behavior of the entire RRP revealed that only few SVs engaged more than one syt C2B domain in dual Ca2+/PI(4,5)P2 binding, resulting in a very low fusion rate (Figure 4F). Correspondingly, postsynaptic EPSCs were severely disrupted, and most release events were ill-synchronized single SV fusion events (Figure 4G). It was furthermore not possible to fit a model without the allosteric stabilization to the experimental dataset (Figure 4—figure supplement 1). Thus, the positive allosteric coupling between Ca2+ and PI(4,5)P2 is fundamental for the syts to simultaneously and persistently engage multiple C2B domains per SV in Ca2+/PI(4,5)P2 dual binding.
Many syts per SV speed up exocytosis by increasing the probability of Ca2+/PI(4,5)P2 dual binding
Our model suggests that only a few syts simultaneously binding Ca2+ and PI(4,5)P2 are required to promote fast SV fusion (Figure 2). Yet, a total of 15 copies are expressed per SV on average (Takamori et al., 2006), which raises the question why SVs carry such excess and whether and how the additional syt copies contribute to the characteristics of Ca2+-induced synaptic transmission. To investigate this, we simulated Ca2+ uncaging experiments with reduced numbers of syts per SV while keeping all other parameters in the model constant. With fewer syts, release latencies increased and peak release rates reduced. Defects were particularly prominent for reductions to less than three copies per SV (Figure 5A). Further exploration indicated that the responses slowed down upon reductions in syt copy number because it took SVs longer to simultaneously engage three C2B domains in dual Ca2+/PI(4,5)P2 binding and that fewer SVs reached this state (Figure 5B).
Figure 5.
Simulations with reduced syt expression predict a reduction in SV fusion.
(A) Model predictions of median release latencies (A1) and mean peak release rates (A2) as a function of [Ca2+]i for different numbers of syts per SV. All simulations were performed with 1000 repetitions using the best fit parameters obtained by fitting with
Figure 5—figure supplement 1.
Comparing the two different model implementations.
QQ-plots comparing the first five fusion times obtained using stochastic simulations with an implementation based on the closed-form solution of the model and using the Gillespie algorithm for three different [Ca2+]i (see Materials and methods). The black line represent 1:1 correspondence, which would only happen in deterministic simulations. Red squares indicate fusion time simulated with both methods for 1000 repetitions.
Figure 5—figure supplement 2.
Upregulation of PI(4,5)P2 can compensate for loss of syts.
(A) Release latencies (A1) and peak release rates (A2) for a model with 15 syts (green) and with 3 syts before (red) and after (blue) refitting of [PI(4,5)P2]. Experimental data points in panels A are replotted from Kochubey and Schneggenburger, 2011. (B) The average number of SVs with three dual bindings formed (top) and the corresponding release rates (bottom) as a function of time upon stimulation with a Ca2+ flash of 50 µM for a model with 15 syts (green), and with 3 syts before (red) and after (blue) refitting of [PI(4,5)P2]. (C) The cost values associated with the Ca2+ uncaging data for different levels of syt with the original best fit parameters (black line) and after refitting [PI(4,5)P2] for each choice of nsyts (blue line). (D) The fold-increase in [PI(4,5)P2] obtained by refitting the model as a function of the number of syts. (E) Representative AP-evoked response of a model with 3 syts per SV obtained after increasing [PI(4,5)P2] plotted together with representative responses for a model with 3 and 15 syts with the original [PI(4,5)P2]. (F) Average amplitudes of simulated AP-evoked responses at original [PI(4,5)P2] and using the increased values.
While Ca2+ uncaging stimuli are exquisitely suited to map the full range of synaptic responses, synaptic transmission is physiologically triggered by APs that induce short-lived Ca2+ transients. To stochastically predict responses to such time-varying Ca2+ stimuli, we implemented our model using the Gillespie algorithm. After verifying that this model implementation agreed with the initial implementation (Figure 5—figure supplement 1), we simulated responses to a typical AP-induced Ca2+ wave that RRP SVs experience (Figure 5C, top panel)(Wang et al., 2008). With 15 syts per SV, AP-induced EPSCs were large and synchronous, but reducing their number decreased response amplitudes (Figure 5C). Removal of one syt already reduced the average EPSC amplitude by ~10% and removal of half (7/15) of its copies reduced it by ~72% (Figure 5—figure supplement 2, for representative example traces see Figure 5C). Note, however, that our model only describes the functioning of syt1 /syt2 and therefore does not include other Ca2+ sensors, like syt7 and Doc2B, which may mediate release in case of syt1 /syt2 loss (Bacaj et al., 2013; Kochubey et al., 2016; Kochubey and Schneggenburger, 2011; Luo and Südhof, 2017; Sun et al., 2007; Wen et al., 2010; Yao et al., 2011).
As the number of syts per SV has a large impact on fusion kinetics, we wondered to what extent fluctuations in the number of syts per SV affected the variance in AP-evoked responses in case of their imperfect sorting. Strikingly, however, varying the number of syts per SV over a large range (Poisson distribution with mean = 15, Figure 5D1, E) did not increase the variability of AP-evoked in synaptic responses while fluctuations of the RRP size strongly impacted them (Figure 5D2, E). This shows that although release kinetics strongly depend on the average number of syts per SV, the system is rather insensitive to fluctuations around this number between individual SVs. Taken together, our data show that although only a subset of syts are required to simultaneously bind Ca2+ and PI(4,5)P2 to induce fusion, all SV syts contribute to the high rates of NT release by increasing the probability that several syts simultaneously engage in dual Ca2+/PI(4,5)P2 binding.
Besides the number of syts, the PI(4,5)P2 levels also determine how likely it is for syts to engage in dual Ca2+/PI(4,5)P2 binding at an SV (see Figure 3 and Figure 2—figure supplement 7). We therefore reasoned that upregulation of PI(4,5)P2 levels, which are dynamically regulated (Jensen et al., 2022), could potentially compensate for reduced syt expression. To investigate this, we refitted the models with reduced syt levels to the experimental Ca2+ uncaging data (Kochubey and Schneggenburger, 2011) and only allowed the PI(4,5)P2 concentration in the slots ([PI(4,5)P2]) to vary. Strikingly, increasing [PI(4,5)P2] fully rescued the characteristics of NT release upon reductions in syt levels down to 3 syts per SV (corresponding to an 80% reduction) by restoring the number and speed of C2B domains engaging in Ca2+/PI(4,5)P2 dual binding (Figure 5—figure supplement 2A–C). The required increase in [PI(4,5)P2] ranged froma factor ~1.1 (14 syts) toa factor ~10 (3 syts, Figure 5—figure supplement 2D). These elevations also fully restored simulated AP-evoked responses when at least three syts per SV were present (Figure 5—figure supplement 2E, F). Altogether, these data indicate that upregulating [PI(4,5)P2] is a potential, powerful compensatory mechanism to rescue reductions of NT release in case the number of (functional) syts per SV is reduced to no less than three. We note that this compensatory mechanism may strongly influence experimentally observed effects of stoichiometric changes.
Evaluation of mutants affecting Ca2+ binding to the C2B domain reveals diverse effects on AP-evoked transmission
Ca2+ sensing of syts depends on negatively charged aspartate (D) sidechains of the C2B domain whose positions are optimal to bind Ca2+ ions (Fernandez et al., 2001). The local negative charges of the Ca2+ binding sites are reduced/neutralized upon Ca2+ binding. The Ca2+ binding pockets of the C2B domain have been extensively studied using various mutations (Bradberry et al., 2020; Guan et al., 2017; Kochubey and Schneggenburger, 2011; Lee et al., 2013; Mackler et al., 2002; Nishiki and Augustine, 2004; Shin et al., 2009). Mutations that remove or invert the negative charge of the Ca2+ binding sites (by mutation to asparagine (N) or lysine (K), ‘DN’ or ‘DK’) block Ca2+ binding and severely reduce exocytosis, even when co-expressed together with the wildtype protein (Bradberry et al., 2020; Kochubey and Schneggenburger, 2011; Lee et al., 2013; Mackler et al., 2002). Other mutations also interfere with Ca2+ binding and exocytosis but hold the same pocket charge (e.g. mutation to Glutamate, ‘DE’) (Bradberry et al., 2020). While both types of mutations may similarly interfere with Ca2+ binding, they may differentially affect the allosteric mechanism. The allosteric coupling between the Ca2+ and PI(4,5)P2 binding sites might be (in part) mediated by electrostatic interactions (van den Bogaart et al., 2012), which would imply that the negatively charged Ca2+ binding pocket repels PI(4,5)P2 until Ca2+ reverses the electrostatic charge, and vice versa. Following this assumption, charge-altering mutations within the Ca2+ binding pockets (‘DN’, ‘DK’) would partially activate the allosteric coupling mechanism and thereby affect the domain’s PI(4,5)P2 affinity (which would not be the case in mutants conserving the charges (‘DE’)). We explored this possibility in our model using two different hypothetical Ca2+ site mutants (Figure 6A). We investigated the effect of these mutants on AP-induced synaptic transmission under homozygous and heterozygous expression conditions (combined expression of mutant and WT with a total of 15 syts per SV; Figure 6B).
Figure 6.
Systematic evaluation of the effect of mutant syts on simulated AP-evoked fusion.
(A) Illustration of a WT syt and two mutant syts. The “
Figure 6—figure supplement 1.
The dominant negative effect of a mutant that is unable to bind Ca22+ depend on the mutants PI(4,5)P2 affinity.
(A) Schematic illustration of the ‘
The first mutant, the ‘
The second hypothetical mutation was designed to not only abolish Ca2+ binding, but to also mimic the Ca2+-bound state. Thereby, this mutant featured a high PI(4,5)P2 affinity as if the allosteric interaction between Ca2+ and PI(4,5)P2 was permanently ‘on’. This might represent an extreme example of a mutation electrostatically reducing/inverting the negative charges of the Ca2+ binding pocket (e.g. ‘DN’, ‘DK’). We termed this mutant the ‘
Rapid changes of accessible PI(4,5)P2 dramatically impact synaptic short-term plasticity
In our model, we describe the PI(4,5)P2 levels in concentration units, because our model is based on syt affinities for Ca2+ and PI(4,5)P2 determined in vitro (van den Bogaart et al., 2012). The estimated concentration of PI(4,5)P2 not only depends on the local density of PI(4,5)P2 in the membrane, but also on the accessibility syt has to PI(4,5)P2. While all species (Ca2+, PI(4,5)P2, and syt C2B) are homogenously accessible in the aqueous solution of the in vitro setting (van den Bogaart et al., 2012), at the synapse the syt C2 domains have constrained motility due to their vesicular association and PI(4,5)P2 is restricted to (clusters on) the plasma membrane (Milosevic et al., 2005; van den Bogaart et al., 2011a). This implies that the positioning of SVs with respect to the plasma membrane has an impact on the PI(4,5)P2 concentration accessible to syts. We so far assumed that all syts of RRP SVs are exposed to the same PI(4,5)P2 levels. This could be the case if all SVs are similarly docked to the plasma membrane. However, when considering more complex stimulation paradigms such as repetitive AP stimulation, this may no longer be valid as several studies reported activity-dependent changes in SV positioning on a millisecond timescale (Chang et al., 2018; Kusick et al., 2020; Miki et al., 2016). Rapid changes in accessible PI(4,5)P2 may thus contribute to short-term plasticity, the alteration of responses on a millisecond timescale (Abbott and Regehr, 2004; Kobbersmed et al., 2020; Neher and Brose, 2018; Silva et al., 2021). Recent studies reported that mutations of positively charged amino acids of the C2B domain (lysines, ’Ks’, implicated in binding of PI(4,5)P2 and/or the SNAREs and arginines, ‘Rs’, implicated in binding the plasma membrane and/or the SNAREs) resulted in a loss of SV docking and severely reduced neurotransmission (Chang et al., 2018; Chen et al., 2021; Li et al., 2006; Xue et al., 2008). Strikingly, SV docking in these mutants was rapidly restored within milliseconds after an AP which also led to enhanced synaptic transmission in response to a second AP given 10ms after the first (Chang et al., 2018). We explored such a situation in the context of our model by driving exocytosis with two successive AP-induced Ca2+ transients and assuming either constant PI(4,5)P2 levels for syts in wildtype synapses (i.e. all RRP SVs similarly docked) or initially reduced and activity-dependent increasing PI(4,5)P2 levels for syts in mutant synapses (where SVs docked after the first AP; Figure 7A). We studied the consequence of a mutation that would only affect SV docking at steady state (as may be the case upon mutation of the arginines 398 and 399 of mouse syt 1, ‘R398,399Q’) in (Figure 7). This resulted in a markedly decreased initial response (Figure 7B and C), but repeated activation induced a large facilitation of responses (indicated by a large paired pulse ratio: quotient of the second EPSC amplitudes divided by the first) (Figure 7D). We conclude that dynamic changes in the PI(4,5)P2 levels accessible to syts – which may be caused by activity-dependent SV relocation – strongly impact synaptic short-term plasticity. Mutations of the C2B domain that reduce its PI(4,5)P2 affinity (as is likely the case upon mutation of the lysine residues 325 and 327 in syt1 or 327, 328 and 332 in syt2) may be more detrimental because even when the effective PI(4,5)P2 concentration accessible to syts is restored upon activity-dependent SV redocking, syt association to PI(4,5)P2 will still be less probable.
Figure 7.
Paired-pulse stimulation in a membrane binding syt mutant.
(A) Time course of [Ca2+]i (blue) and [PI(4,5)P2](dashed black line: wildtype (WT), green line: mutant). Top panel illustrates the placement of vesicles with respect to the PM for SVs expressing WT syt (grey SVs) and SVs expressing a syt mutant deficient in membrane binding (green SVs, homozygous expression) before the first (left side of arrow) and second AP (right side of arrow). In WT conditions, most SVs reside close to the PM before the onset of the first stimulus. Before onset of the second pulse, WT SVs keep the same average distance to the PM. Mutant SVs, however, show a large distance to the PM at the onset of the first stimulus. Before the onset of the second AP, mutant SVs move closer to the PM due to a Ca2+-dependent mechanism (Chang et al., 2018). The bottom panel shows the Ca2+ (blue) and PI(4,5)P2 (green) transients over time in a paired pulse stimulus (10ms between stimuli). Due to the increased distance between the SV and the PM in the membrane binding mutant, mutant SVs are assumed to experience a lower [PI(4,5)P2] (solid green line) compared to WT SVs (dotted, black line) at the start of the first stimulus. Before the start of the second stimulus, mutant SVs move closer to the PM which increases the experienced [PI(4,5)P2] of these SVs. (B) Representative eEPSCs simulated using the Ca2+ and PI(4,5)P2 transients depicted in A. (C) Amplitude of the first eEPSC for WT and mutant. (D) Paired-pulse ratio (PPR) for WT and mutant. Data in C and D show mean ± SEM, using 50 repetitions and a variable RRP size (see Materials and methods for details, the same RRP values were used for both the mutant and the WT condition). Simulation scripts can be found in Source code 1. Depicted simulation results can be found in Figure 7—source data 1.
Discussion
Here, we propose a quantitative, experiment-based model describing the function of syt in SV fusion on a molecular level based on biochemical properties determined in vitro. In our model, syt acts by lowering the energy barrier for SV fusion by dual binding to Ca2+ and PI(4,5)P2. When allowing at least three dual-bound syts per SV at a time, this model can explain the steep Ca2+ dependence of NT release observed at the calyx of Held synapse (Kochubey and Schneggenburger, 2011). Exploring this model led to the following conclusions:
The positive allosteric interaction between Ca2+ and PI(4,5)P2 is crucial for fast SV fusion as it stabilizes the dual-bound state which allows multiple syts to successively lower the energy barrier for SV fusion;
At least three slots per SV for syt Ca2+/PI(4,5)P2 dual binding are needed to achieve the speed and Ca2+ sensitivity inherent to synaptic transmission;
Only few syts (≤4) work together for fast SV fusion on most SVs.
A high copy number of syts per SV ensures fast NT release by increasing the probability that several syts engage in Ca2+/PI(4,5)P2 dual binding;
Binding of syts to PI(4,5)P2 prior to the Ca2+ stimulus allows some SVs to fuse very fast (submillisecond).
The molecular resolution of this model can be used to study consequences of mutations.
A syt-dependent switch on the energy barrier for SV fusion
Exocytosis is a highly energy-demanding reaction, for which the formation of the neuronal SNARE complex provides the energy (Jahn and Fasshauer, 2012). In our model we assume that syts regulate this process by lowering the activation energy barrier for exocytosis when they engage in Ca2+/PI(4,5)P2 dual binding. However, how Ca2+/PI(4,5)P2 dual binding to syt exactly reduces this energy barrier is not known. One possibility is that the energy is provided by the SNAREs themselves and that Ca2+/PI(4,5)P2 dual binding to syt relieves a clamping function, which syt itself or the auxiliary protein complexin exerts on the SNAREs (Courtney et al., 2019; Schupp et al., 2017; Tang et al., 2006; Zhou et al., 2015; Zhou et al., 2017). Alternatively – or additionally – syt’s dual binding Ca2+/PI(4,5)P2 might promote SNARE-mediated fusion by changing the local electrostatic environment (Ruiter et al., 2019; Shao et al., 1997). Furthermore, dual-binding syts could bring SVs closer to the plasma membrane, potentially below an upper limit for full SNARE complex assembly (Araç et al., 2006; Chang et al., 2018; Honigmann et al., 2013; Hui et al., 2011; Lin et al., 2014; Nyenhuis et al., 2019; van den Bogaart et al., 2011b; Xue et al., 2008). In line with these hypothetical working mechanisms, our estimated effect each dual-bound C2B domain has on the energy barrier height (~5 kbT) is similar to the estimated energy barrier height for the final zippering step of the SNARE complex (Li et al., 2016). Syt’s Ca2+/PI(4,5)P2 dual binding might also promote fusion by inducing membrane curvature or favoring lipid rearrangement (Lai et al., 2011; Martens et al., 2007). In line with this reasoning, our estimated contribution of a syt engaging in Ca2+/PI(4,5)P2 dual binding is similar to estimates of syt1 membrane binding energies (Gruget et al., 2020; Gruget et al., 2018; Ma et al., 2017). In our model, we assume that multiple syts can simultaneously reduce the energy barrier for fusion. Here we assumed that all syts exert the same effect on this energy barrier and that the effects of more dual-bound syts are additive. Whether or not this is the case will depend on the precise mechanism by which they shape the energy landscape. We show here that the simplest model (constant and independent contribution) is sufficient to reproduce the biological response.
Both the C2A and C2B domain of syt cooperate in SV exocytosis (Bowers et al., 2020; Gruget et al., 2020; Lee et al., 2013; Wu et al., 2021b). However, the exact role of the C2A domain in triggering SV fusion remains debated (Fernández-Chacón et al., 2002; Lee et al., 2013; Paddock et al., 2011; Sørensen et al., 2003; Stevens and Sullivan, 2003; Striegel et al., 2012). As mutation of the Ca2+ binding pockets of the C2A domain did not affect the affinities of Ca2+ and PI(4,5)P2 in vitro (van den Bogaart et al., 2012), we focused on the C2B domain in our model. Moreover, we aimed at developing a minimal molecular model with the least number of parameters that can fully recapitulate physical responses of the synapse. This, however, does not exclude the possibility that our C2B domain-based model indirectly describes properties of the C2A domain. For instance, Ca2+ binding to the C2A domain may influence the Ca2+ affinity of the C2B domain (Sørensen et al., 2003). This property may affect the values of other parameters of the model (e.g. our estimate of the PI(4,5)P2 concentration), meaning that these effects might be captured indirectly when fitting experimental data.
Allostericity buys time to synchronize syts
Our modeling study proposes that the allostericity between Ca2+ and PI(4,5)P2 binding is essential for the syts to achieve fast, synchronous, and sensitive NT release (van den Bogaart et al., 2012, Figure 4—figure supplement 1). With their experiment, van den Bogaart et al., 2012 determined steady state affinities, which do not provide information on the association/dissociation rates. This means that the allosteric effect may either be due to speeding up the association or slowing down the dissociation of Ca2+/PI(4,5)P2 (Figure 1A). Here we implemented the latter, a reduction of the unbinding rates of both Ca2+ and PI(4,5)P2 when both species were bound to the C2B domain, which leads to a stabilization of the dual-bound state. A stabilization of the Ca2+-bound states was also essential to reproduce the Ca2+ dependence of release in the previously proposed five-site binding model (Heidelberger et al., 1994; Schneggenburger and Neher, 2000). Here we show in the context of our model that increasing the lifetime of Ca2+/PI(4,5)P2 dual binding is particularly important to achieve fast fusion rates as it allows several C2B domains to simultaneously engage to lower the fusion barrier (Figure 4). The drawback of the strong allosteric interaction between the Ca2+ and PI(4,5)P2 bindings sites might be its potential involvement in the strong dominant-negative effects of some C2B domain mutations (Figure 6).
The stoichiometry of the SV fusion machinery
Each SV contains multiple syt copies (Takamori et al., 2006), which can jointly participate in the fusion process. However, the number of syts that can simultaneously engage with PI(4,5)P2 located at the plasma membrane, and thus can cooperate during fusion, is likely limited. There are several possible explanations for this limit. First, the space between the vesicular and plasma membrane is limited and crowded by many synaptic proteins (Wilhelm et al., 2014). In addition, plasma membrane association of syt may require interaction with the SNAREs (de Wit et al., 2009; Mohrmann et al., 2013; Rickman and Davletov, 2003; Zhou et al., 2015), which limits the number of association points. Moreover, the inhomogeneous distribution of PI(4,5)P2 in the plasma membrane might put further constraints on association of syt to PI(4,5)P2 (Milosevic et al., 2005; van den Bogaart et al., 2011a). Other proteins able to promote SV fusion, like Doc2, might also rely on this limited number of membrane contact points/resource and compete with syt. Our model predicts that most SVs already bind one or two slots with syt at rest (Figure 3), and this might explain the ability of syt to clamp spontaneous transmission (Bouazza-Arostegui et al., 2022; Courtney et al., 2019; Kochubey and Schneggenburger, 2011; Schupp et al., 2017).
We found that at least three PI(4,5)P2 association sites (‘slots’) were required to explain the steep Ca2+ dependency of neurotransmitter release (Figure 2A–C). These findings are compatible with a cryo-EM analysis that identified six protein complexes between docked SVs and plasma membrane (Radhakrishnan et al., 2021). Interestingly, irrespective of the number of slots for models with three or more slots, our analysis suggests that most fusion events at [Ca2+]i > 1 μM occurred after engaging three syts in Ca2+/PI(4,5)P2 dual binding (Figure 2D–E). At lower [Ca2+]i (0.5–1 μM, Figure 2—figure supplement 2B and Figure 2—figure supplement 3B), the number of dual bindings leading to fusion was reduced to 1–2, indicating that higher [Ca2+]i recruits additional syts to increase fusion rates. Although our model indicates that only few syts are involved in fusion, more syts could be involved in upstream reactions.
The predicted number of three syts involved in fast exocytosis matches experimental estimates of the number of SNARE-complexes zippering for fast vesicle fusion (Arancillo et al., 2013; Mohrmann et al., 2010; Shi et al., 2012; Sinha et al., 2011; but higher estimates in the number of SNARE complexes actively involved in fusion have also been reported Wu et al., 2017). Moreover, our model is consistent with a previous model of neurotransmitter release at the frog neuromuscular junctions that estimated that fusion is triggered by the binding of two Ca2+ ions to each of three syts (Dittrich et al., 2013). That model, which describes Ca2+ dynamics in the AZ in detail, showed that many additional Ca2+ binding sites (20-40) were required to enhance fusion probability, because the probability of having a single Ca2+ molecule in the vicinity of SVs is extremely low. Similarly, our model predicts a relevance of a high vesicular syt copy number, because, even though fusion involves only a handful of syts, many copies per SV are necessary to speed up the collision with multiple slots (Figure 5). In fact, high protein abundance could play a general role in promoting collision-limited processes in SV fusion, and may provide an intuitive explanation for the many (~70) synaptobrevins on SVs which may assemble into SNARE complexes downstream of syt action (Takamori et al., 2006; van den Bogaart et al., 2011b).
Our model of dynamic assembly of multiple C2B domains in Ca2+/PI(4,5)P2 dual binding in response to Ca2+ is fundamentally different from studies suggesting that 12–20 syts need to preassemble in higher-order complexes (rings) to execute their function in fusion (Rothman et al., 2017). A testable property to distinguish these possibilities is the sensitivity to reducing the number of syts per SV. If SV fusion relied on preassembled syt-rings, it would immediately break down if the number of syts was reduced to a number preventing ring assembly, whereas our model predicts gradual effects of reduced syt copy numbers (even for titration below
Heterogeneity in PI(4,5)P2 concentration between different RRP SVs
The interaction between syt and PI(4,5)P2 has been shown to be essential in SV exocytosis (Bai et al., 2004; Li et al., 2006; Wu et al., 2021a), but also has been found to play a role in SV docking (Chang et al., 2018; Chen et al., 2021). Consistently, we observed that at resting synapses the majority of SVs (~83%) contain at least one syt bound to PI(4,5)P2 in our model (Figure 3). The number of syts bound to PI(4,5)P2 per SV at rest highly influenced the release probability, leading to heterogeneity within the RRP (Figure 3, Wölfel et al., 2007). As PI(4,5)P2 levels have a large impact on release kinetics (shown in this study, but also by Walter et al., 2017), heterogeneity between RRP SVs might further be enhanced by unequal PI(4,5)P2 levels. Additionally, the strong impact of PI(4,5)P2 levels on SV fusion indicates that the dynamic regulation of PI(4,5)P2 occurring at the seconds time scale might strongly influence synaptic plasticity (Jensen et al., 2022).
In our model, we described PI(4,5)P2 levels in concentration units to constrain our model by using in vitro PI(4,5)P2 affinity measurements (van den Bogaart et al., 2012). However, this concentration does not only encompass the density of PI(4,5)P2 in the plasma membrane, but also includes the accessibility of syt to PI(4,5)P2. Several studies have shown that PI(4,5)P2 is distributed heterogeneously over the plasma membrane in clusters that contain a high PI(4,5)P2 density (Honigmann et al., 2013; Milosevic et al., 2005; van den Bogaart et al., 2011a). Moreover, syts located closer to the plasma membrane will have increased access to PI(4,5)P2 compared to those located further away. Taken together, this indicates that the PI(4,5)P2 concentration is likely to vary between RRP SVs and also between individual syts on the SV. Furthermore, this implies that once a syt has engaged in PI(4,5)P2 binding the successive engagement of additional syts might be favored for some (those facing towards the PM) and disfavored for others (those facing from the PM). While knowledge of these details could be helpful to construct a more realistic version of our molecular model, we currently do not possess the methodology to measure these properties. Therefore, in our model, we simulated the simplest scenario where all syts have an equal probability of engaging in PI(4,5)P2 binding.
As the localization of syts with respect to the PM influences the accessibility of syt to PI(4,5)P2, mutations in synaptic proteins and stimulation protocols that alter SV docking will affect the PI(4,5)P2 concentration as it is implemented in our model (Chang et al., 2018; Chen et al., 2021; Kusick et al., 2020). Using a time-dependent PI(4,5)P2 concentration, we illustrated the impact this might have on the short term plasticity of synaptic responses (Figure 7). This is a simplification, as we did not take the individual SV/syt distances to the PM into account. This distance is affected by several synaptic proteins, including syt1, Munc13, and synaptotagmin7 (Chen et al., 2021; Imig et al., 2014; Liu et al., 2016; Quade et al., 2019; Tawfik et al., 2021; Voleti et al., 2017). A role of these proteins in short-term plasticity is firmly established, yet precise mechanistic details are still lacking (Jackman et al., 2016; Rosenmund et al., 2002; Shin et al., 2010). The extension of models based on molecular interactions such as presented here should allow reproduction of responses to more complex synaptic activity patterns relevant for neural processing. Particularly the molecular resolution of such models will be useful to conceptualize the importance of specific molecular interactions for physiological and pathological processes at the synapse.
Materials and methods
In this paper, we propose a model for SV fusion induced by Ca2+ and PI(4,5)P2 binding to
SV states and possible reactions in the analytical version of the model
In the analytical solution of the model, we describe for each SV the number of syts having bound two Ca2+ ions, PI(4,5)P2, or both species. Since syts were assumed to work independently, their order is not relevant, and we therefore do not need to describe the binding state of each individual syt. The possible binding states of an SV are described in Figure 1—figure supplement 2. Each state is represented by the triplet (
We numbered the states systematically following a lexicographic ordering, excluding the states that violate the inequalities described above. To illustrate, we write the ordering of all the states (
(0,0,0),(0,0,1),(0,0,2),(0,1,0),(0,1,1),(0,1,2),(0,2,0),(0,2,1),(0,3,0),(1,0,0),(1,0,1),(1,1,0),(1,1,1),(1,2,0),(2,0,0),(2,1,0).
Besides these binding states, an additional state,
Table 3.
Overview of possible reactions and their rates in the model.
Reaction | Condition | Triplet notation | Reaction rate |
---|---|---|---|
Binding of PI(4,5)P2 to unbound syt | n+m+k< | ( | ( |
Unbinding of PI(4,5)P2 |
| ( |
|
Binding of Ca2+2 to unbound syt | n+m+k< | ( | ( |
Unbinding of Ca2+2 |
| ( |
|
Binding of PI(4,5)P2 to form dual binding | n+k<Mslots and | ( |
|
Unbinding of PI(4,5)P2 from a dual binding | n> | ( |
|
Binding of Ca2+2 to form a dual binding |
| ( |
|
Unbinding of Ca2+2 from a dual binding | n>0 | ( |
|
Fusion | ( |
|
The reaction rates of (un)binding Ca2+ or PI(4,5)P2 are calculated as the number of syts available for (un)binding (computed using
The affinities for Ca2+ and PI(4,5)P2 binding to syt were set to previously determined dissociation constants (
The in vitro experiments revealed a change in syt1 Ca2+ affinity upon binding PI(4,5)P2, and vice versa (van den Bogaart et al., 2012), indicating a positive allosteric relationship between the two species. We assumed this allosteric effect was due to a stabilization of the dual-bound state by lowering of the unbinding rates of Ca2+ and PI(4,5)P2 with a factor (A=(3.3/221)2 = 0.00022) and occurs when both species have bound. Upon dual binding, both rate constants for unbinding Ca2+ and PI(4,5)P2 are multiplied by A, since any closed chemical system must obey microscopic reversibility (Colquhoun et al., 2004). Using the biochemically defined affinities, the number of free parameters in our model was constrained to:
The values of
The steady state of the system
The steady state of the system before stimulation was determined at a resting, global [Ca2+]i of 0.05 µM (except for simulations with Ca2+ levels below this basal value, for those we assumed [Ca2+]rest=[Ca2+]i). To compute the steady state, we assumed that no fusion took place, ignoring the very low fusion rate at resting [Ca2+]i. Under these conditions, the model is a closed system of recurrent states and obeys microscopic reversibility, that is for every closed loop state diagram, the product of the rate constants around the loop is the same in both directions (Colquhoun et al., 2004). Microscopic reversibility implies detailed balance, meaning that every reaction is in equilibrium at steady state. Thus, for any two states Si and Sj which are connected by a reaction, the steady state distribution obeys
where [Si] and [Sj] are steady state quantities and rij and rji are the reaction rates between Si and Sj. Using this property, we calculated the steady state iteratively by setting the population of the first state (state (0,0,0)) to 1, and thereafter iteratively computing the population of the following state (following the lexicographic ordering as described above) using the following formulae:
Afterwards, each state was divided by the sum of all state values and multiplied by the number of SVs in the RRP. In our model simulations, the size of the RRP was variable and followed a gamma distribution with a mean of 4000 SVs and a standard deviation of 2000 SVs (see Figure 2—figure supplement 1), based on experimental estimates from the calyx of Held (Wölfel and Schneggenburger, 2003). In the following calculations, we use to denote the steady state probability vector (i.e. normalised to sum to 1).
Computation of fusion probabilities and fusion rate
The analytical implementation of our model allowed us to compute the fusion rate and cumulative fusion probabilities with a constant [Ca2+]i after stimulus onset (t=0), thereby mimicking conditions in Ca2+ uncaging experiments. The constant [Ca2+]i makes the model a homogenous Markov Model. The transition rates of the model can be organized in the intensity matrix,
where
is the distribution of SV states at time t, i.e. a (1)
The fusion rate of a single SV can be calculated directly as the last element of the derivative of (Equation 1):
(2)
Multiplying (Equation 1) and (Equation 2) with the number of SVs yields the cumulative fusion function and fusion rate function, respectively. For simulation of release rates and release latencies (in Figures 2—5) and some figure supplements, we computed (Equation 1) and (Equation 2) using the best fit parameters from fitting with Mslots = 3 and nsyts = 15. This was done for 31 [Ca2+]i values ranging from 0.001 µM to 80 µM (0.001, 0.1, 0.2, …., 0.9, 1, 1.25, 1.5, 1.75, 2, 2.5, 3, 4, …, 9, 10, 20, 30, …, 80 µM) for
Computation of peak release rates
The peak of the fusion rate can be computed by multiplying the maximum value of the single SV fusion rate function, (Equation 2), with
For parameter exploration (Figure 2G) and for computing the release rates in the fitting routine, it was not feasible to calculate the fusion rate over 100ms with high temporal precision as described above. Instead, we implemented a custom search algorithm (scripts can be found in accompanying zip-file “Source_code1.zip”), which was constructed to shorten calculation time by taking advantage of the release rate function being unimodal. We first found a time point,
Stochastic simulation of release latencies
Release latencies, which are defined as the time point of the fifth SV fusion event after the onset of simulation, were simulated stochastically by drawing
Fitting the model to experimental data
We next fitted the model to already published data describing the Ca2+ dependence of NT release in the mouse calyx of Held (Kochubey and Schneggenburger, 2011). The data consist of measurements from Ca2+ uncaging experiments, where the release latency, defined as the time point of the fifth SV fusion event, and the peak release rate were estimated at different [Ca2+]i. Besides the four free model parameters, , an additional parameter,
Since the variance in the experimental data points also contains information on the underlying biological mechanism, we wanted to take the distribution of individual data points into account when obtaining estimates of the unknown parameters. We therefore derived the likelihood function, which describes how well the model captures the distribution of the release latencies. Obtaining this function for the peak release rates was not feasible. The experimental peak release rates were therefore compared to the average model prediction. Both measures of describing the correspondence between model simulations and experimental data were combined in a cost value which was optimized to estimate the best fit parameters (the lower this cost value the better the correspondence between model predictions and experimental data).
The best fit was obtained by minimizing the following cost function:
where
are the squared deviations of the peak release rates (1 /ms2) and is the logarithm of the likelihood of the release latencies (see derivation below). To combine the two measures of distance between model and experimental data, the squared deviation of the peak release rates was multiplied by a factor 2 before subtracting the logarithm of the likelihood of the release latencies. The cost value was minimized using the inbuilt Matlab function
The likelihood function of release latencies with fixed RRP size
To fit the model to the experimental release latency measurements, we derived the likelihood function, which is the probability density function of the model for given parameters evaluated at the experimental data points. Thus, optimizing the likelihood function yields parameters for which the data points are most likely if the model is true. We first derive the likelihood of release latency in the case of a fixed RRP size (
We define the stochastic variable
where
we obtain a sequence of stochastic variables,
with respect to
where
In the case of the release latency, we are interested in the fifth fusion event (
In the optimization we minimize minus the log-likelihood:
which is equivalent to maximizing the likelihood function.
The likelihood of release latencies with variable RRP size
In our model, the RRP size is assumed to follow a Gamma distribution. Let (3)
where
We now define the following variables:
(4)
By factoring out and substituting in the above equation we get
(5)
Furthermore, we have
(6)
Since
we can derive the following useful formula:
(7)
The third equality follows from the fact that the function in the second integral from above is the probability density function of a gamma distribution with shape parameter
with
We then minimize the sum of minus the log-likelihoods of the release latency observations.
Syt binding states in the Gillespie simulation of model
In the Gillespie algorithm, the binding state of each individual syt is tracked. The state of the system at time point
Determining the initial state of the system
The steady state (initial state,
Via the ordering of states explained above,
Gillespie algorithm-based simulations of the model
For stochastic evaluation of the model by the Gillespie algorithm (Gillespie, 2007), we next introduced the propensity function
the probability given (
For element
with
This makes
since it is exponentially distributed with rate
Similarly, the index
If the row index
Additionally, we define the transition matrix
A fourth random number, r4∈(0,1), drawn from the uniform distribution, determines which reaction,
The state of the corresponding SV and syt,
When simulating AP-evoked responses (Figures 5 and 6), we used a Ca2+ transient describing the microdomain [Ca2+]i sensed locally by primed SVs in the mouse calyx of Held upon AP stimulation (Wang et al., 2008). This Ca2+ transient also formed the basis for the Ca2+ signal used to simulate a paired pulse stimulus (Figure 7), where the transients were placed with a 10 ms interval. Additionally, for the paired pulse stimulus, we added a residual Ca2+ transient to the signal (exponential decay with amplitude: 0.4 µM, decay time constant: 0.154 s–1). Similar to the uncaging simulations, the [Ca2+]i before the onset of the stimulus was 0.05 µM. Since the Ca2+ concentration is a factor in the reaction rates, the propensity matrices
Simulating the model with mutant syts
For mutations in syt that affect the binding and unbinding rates of PI(4,5)P2 and Ca2+, the procedure described above was repeated with adjusted parameters when simulating a model containing only mutant syts. For a model in which mutant proteins were expressed together with WT syts (simulations of heterozygous condition in Figure 6), the procedure was changed slightly.
For a model with
Simulation of EPSCs
Simulated EPSCs were obtained using both model implementations. The analytical implementation of our model was used to simulate fusion times for a constant [Ca2+]i (Figure 4D and G). The Gillespie version of the model was used to simulate AP-evoked EPSCs with or without mutant syts (Figure 5C–E, Figure 5—figure supplement 2E-F, Figure 6C–D, Figure 6—figure supplement 1, and Figure 7B–D). In both approaches, the stochastically determined fusion times, determined as described above, were rounded up to the next 0.02ms, leading to a sampling rate of 50 kHz. The sampled fusion times were convolved with a mEPSC to generate simulated EPSCs. The standard mEPSC used for deconvolution followed the equation described by Neher and Sakaba, 2001:
with τ1=0.12 ms (time constant of fast decay), τ2=13 ms (time constant of slow decay), τ0=0.12 ms (time constant of rise phase),
Simulating AP-evoked EPSCs with variable number of syt
To investigate the effect of variability in the number of syts expressed per SV on variance between simulated AP-evoked traces (Figure 5), we first had to determine the steady state. For this we computed the probability vector of a single SV to be in the different SV-states at steady state (
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Abstract
Synaptic communication relies on the fusion of synaptic vesicles with the plasma membrane, which leads to neurotransmitter release. This exocytosis is triggered by brief and local elevations of intracellular Ca2+ with remarkably high sensitivity. How this is molecularly achieved is unknown. While synaptotagmins confer the Ca2+ sensitivity of neurotransmitter exocytosis, biochemical measurements reported Ca2+ affinities too low to account for synaptic function. However, synaptotagmin’s Ca2+ affinity increases upon binding the plasma membrane phospholipid PI(4,5)P2 and, vice versa, Ca2+ binding increases synaptotagmin’s PI(4,5)P2 affinity, indicating a stabilization of the Ca2+/PI(4,5)P2 dual-bound state. Here, we devise a molecular exocytosis model based on this positive allosteric stabilization and the assumptions that (1.) synaptotagmin Ca2+/PI(4,5)P2 dual binding lowers the energy barrier for vesicle fusion and that (2.) the effect of multiple synaptotagmins on the energy barrier is additive. The model, which relies on biochemically measured Ca2+/PI(4,5)P2 affinities and protein copy numbers, reproduced the steep Ca2+ dependency of neurotransmitter release. Our results indicate that each synaptotagmin engaging in Ca2+/PI(4,5)P2 dual-binding lowers the energy barrier for vesicle fusion by ~5 kBT and that allosteric stabilization of this state enables the synchronized engagement of several (typically three) synaptotagmins for fast exocytosis. Furthermore, we show that mutations altering synaptotagmin’s allosteric properties may show dominant-negative effects, even though synaptotagmins act independently on the energy barrier, and that dynamic changes of local PI(4,5)P2 (e.g. upon vesicle movement) dramatically impact synaptic responses. We conclude that allosterically stabilized Ca2+/PI(4,5)P2 dual binding enables synaptotagmins to exert their coordinated function in neurotransmission.
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