Allosteric stabilization of calcium and phosphoinositide dual binding engages three synaptotagmins in fast exocytosis

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 syt. We here 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 dual binding Ca2+/PI(4,5)P2 lowers the energy barrier for vesicle fusion by 4.85 kBT and that allosteric stabilization of this state enables the synchronized engagement of 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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Regulated neurotransmitter (NT) release from presynaptic terminals is crucial for information transfer 34 across chemical synapses. NT release is triggered by action potentials (APs), which are transient de-35 and repolarizations of the presynaptic membrane potential that induce Ca 2+ influx through voltage-36 gated channels. The resulting brief and local elevations of the intracellular Ca 2+ concentration ([Ca 2+ ]i) 37 trigger the fusion of NT-containing synaptic vesicles (SVs) from the so-called readily releasable pool 38 (RRP), whose SVs are localized (docked) at the plasma membrane and molecularly matured (primed) 39 for fusion (Kaeser and Regehr, 2017;Sudhof, 2013;Verhage and Sørensen, 2008). A high Ca 2+ sensitivity 40 of NT release is needed to achieve fast responses to the very short AP-induced Ca 2+ transient and 41 correspondingly, the SV fusion rate depends on the [Ca 2+ ]i to the 4 th -5 th power (Bollmann et al., 2000;42 Burgalossi et al., 2010;Heidelberger et al., 1994;Schneggenburger and Neher, 2000). Accordingly, 43 previous models of NT release have assumed the successive binding of five Ca 2+ ions to a sensor that 44 regulates release (Bollmann et al., 2000;Lou et al., 2005;Schneggenburger and Neher, 2000). 45 However, how these macroscopic properties arise from the molecular components involved in SV 46 fusion is still unknown. 47 The energy for SV fusion is provided by the assembly of the neuronal SNARE complex, which 48 consists of vesicular synaptobrevin/VAMP and plasma membrane bound SNAP25 and syntaxin proteins 49 (Jahn and Fasshauer, 2012;Sudhof, 2013). Ca 2+  isoforms are expressed in synapses. Depending on the synapse type (e.g. mouse hippocampal 53 pyramidal neurons or the Calyx of Held), syt1 or syt2 is required for synchronous, Ca 2+ -induced fusion 54 (Geppert et al., 1994;Kochubey et al., 2016;Kochubey and Schneggenburger, 2011;Sudhof, 2013). 55 These two syt isoforms are highly homologous and contain two cytosolic, Ca 2+ -binding domains, C2A 56 and C2B (Sudhof, 2002), of which the C2B domain has been shown to be essential, and in some cases 57 even sufficient, for synchronous NT release (Bacaj et

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The factor A<1 on the dissociation rates (β and δ) from the dual-bound state represents the positive allosteric 134 effect of simultaneous PI(4,5)P2 and Ca 2+ binding and leads to stabilization of the dual-bound state. The ratio 135 between dissociation rate and association rate constants (β/α and δ/γ) is equal to the respective dissociation 136 constants of syt1 determined in vitro (KD,2Ca2+ =221 2 µM 2 and KD,PIP2 =20 µM, (van den Bogaart et al., 2012)). An 137 alternative reaction scheme where Ca 2+ binding leads to association of the C2B domain with the plasma 138 membrane is shown in Figure 1 -figure supplement 1. Our model is not influenced by the assumptions on 139 whether Ca 2+ binding to syt leads to plasma membrane or vesicle association. B) The stoichiometry at the SV 140 fusion site. We assume 15 syts per SV (Takamori et al., 2006), and that the association of the syt C2B domain to 141 PI(4,5)P2 is limited to a finite number of slots (here illustrated for Mslots=3). C) The effect of formation of multiple 142 dual bindings on the energy barrier for SV fusion and the SV fusion rate. We assume that each dual-binding C2B The best fit parameters for three slots revealed rapid association rate constants for Ca 2+ and PI(4,5)P2 238 to the C2B domain and PI(4,5)P2 levels corresponding to a concentration of ~1 µM in an in vitro setting 239 (Table 2). Predicted responses obtained using the best-fit parameters were sensitive to changes of 240 either of these parameters (Figure 2 -figure supplement 5). For instance, higher levels of PI(4,5)P2 241 decreased the release latencies and increased the rate of fusion, and changing the Ca 2+ association 242 rate constant () affected the release latencies much more than changing the PI(4,5)P2 association rate 243 constant (). We verified that these parameters represent unique solutions by systematically exploring 244 the parameter space with f (which relates to the lowering of the fusion barrier for each syt dual-binding 245 Ca 2+ /PI(4,5)P2) fixed to the best fit value (f=128), which revealed a clear minimum at the best fit 246 parameters ( Figure 2G, darkest ball). We furthermore confirmed that this f value was optimal by 247 systematically varying f and fitting all other parameters ( Figure 2H). 248 249 Figure 3: Syts binding to PI(4,5)P2 prior to Ca 2+ stimulus underlies very fast SV fusion. A) PI(4,5)P2 binding status 250 of SVs at steady state. At resting [Ca 2+ ]i of 50 nM, more than 40 % of SVs have bound a single PI(4,5)P2 molecule, 251 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 252 dual bindings at steady state. B) Cumulative fusion of SVs after 50 µM step Ca 2+ at t=0, grouped according to their 253 initial PI(4,5)P2 binding state. During the first ~0.5 ms, release is dominated by SVs having two or three syts bound 254 to PI(4,5)P2 prior to the stimulus. The insert shows that the SVs having prebound three PI(4,5)P2 constitute the 255 majority of the first five SVs that fuse in response to the Ca 2+ step and therefore have largely impacted the release 256 latency. C) Cumulative release probability of SVs over time after 50 µM step Ca 2+ at t=0, grouped according to 257 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 258 B is explained by their high release probability compared to SVs with no or only one PI(4,5)P2 bound.

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The number of syt proteins pre-associated to PI(4,5)P2 at rest influences the SV's Ca 2+ responsiveness 262 The steady state concentration of PI(4,5)P2 determines the probability of syts associating to PI(4,5)P2 263 at rest. With the best fit parameters, our model predicts that at rest ([Ca 2+ ]i=50 nM) most SVs associate 264 to PI(4,5)P2 by engaging one (~42%), two (~33%) or three (~8%) syts ( Figure 3A, see Figure 3 - figure  265 supplement 1 for behavior in the model with Mslots=6). With a step-like Ca 2+ stimulus to 50 µM, SVs with 266 two or three pre-associated syts mediated most of the fastest (<0.5 ms) SV fusions ( Figure 3B). 267 Consequently, changing the steady state PI(4,5)P2 concentration (which changes the number of pre-268 associated syts/SVs) largely impacted the release latencies (defined as the timing of the fifth SV that coupling, the Ca 2+ affinities of syts prebound to PI(4,5)P2 are increased and SVs with more PI(4,5)P2 271 interactions are more responsive to the Ca 2+ stimulus ( Figure 3C). Thus, at the single SV level, the 272 number of pre-associated syts to PI(4,5)P2 at rest plays a role in very fast (submillisecond) SV release 273 and causes heterogeneity in release probability among RRP SVs (Wolfel et al., 2007).   We then explored what would happen without the allosteric stabilization of Ca 2+ /PI(4,5)P2 dual 323 binding (by setting A=1; Figure 4E). In this case, the C2B domains still quickly associated Ca 2+ and 324 PI(4,5)P2, but without the allosteric slowing of Ca 2+ /PI(4,5)P2 dissociation the lifetime of dual-bound 325 C2B domains was dramatically reduced (to an average of ~0.0003 ms). This made it very improbable 326 to engage multiple C2B domains in dual Ca 2+ /PI(4,5)P2 binding ( Figure 4E). In turn, without the 327 simultaneous engagement of multiple syts dual-binding Ca 2+ /PI(4,5)P2, NT release became very 328 unlikely. In fact, none of the randomly chosen four RRP SVs fused within 4 ms ( Figure 4E). Inspection 329 of the average behavior of the entire RRP revealed that only few SVs engaged more than one syt C2B 330 domain in dual Ca 2+ /PI(4,5)P2 binding, resulting in a very low fusion rate ( Figure 4F). Correspondingly, 331 postsynaptic EPSCs were severely disrupted, and most release events were ill-synchronized single SV 332 fusion events ( Figure 4G Our model strongly suggests that no more than three syts simultaneously binding Ca 2+ and PI(4,5)P2 339 are required to promote fast SV fusion ( Figure 2). Yet, a total of 15 copies are expressed per SV on 340 average (Takamori et al., 2006), which raises the question why SVs carry such excess and whether and 341 how the additional syt copies contribute to the characteristics of Ca 2+ -induced synaptic transmission. 342 To investigate this, we simulated Ca 2+ uncaging experiments with reduced numbers of syts per SV while 343 keeping all other parameters in the model constant. With fewer syts, release latencies increased and 344 peak release rates reduced. Defects were particularly prominent for reductions to less than three 345 copies per SV ( Figure 5A). Further exploration indicated that this was because it took SVs longer to 346 simultaneously engage three C2B domains in dual Ca 2+ /PI(4,5)P2 binding and that fewer SVs reached 347 this state ( Figure 5B synchronous, but reducing their number decreased response amplitudes ( Figure 5C). Removal of one 355 syt already reduced the average EPSC amplitude by ~10% and removal of half (7/15) of its copies 356 reduced it by ~72% ( Figure 5 -figure supplement 2, for representative example traces see Figure 5C). 357 Note, however, that our model only describes the functioning of syt1/ syt2 and therefore does not 358 include other Ca 2+ -sensors, like syt7 and Doc2B, which may mediate release in case of syt1/ syt2 loss 359   Figure 5D2,E). This shows 391 that although release kinetics strongly depend on the average number of syts per SV, the system is 392 rather insensitive to fluctuations around this number between individual SVs. Taken together, our data 393 show that although only a subset of syts are required to simultaneously bind Ca 2+ and PI(4,5)P2 to 394 induce fusion, all SV syts contribute to the high rates of NT release by increasing the probability that 395 several (i.e. three) syts simultaneously engage in dual Ca 2+ /PI(4,5)P2 binding. 396 Besides the number of syts, the PI(4,5)P2 levels also determine how likely it is for syts to engage 397 in dual Ca 2+ /PI(4,5)P2 binding at an SV (see Figure 3 and data indicate that upregulating [PI(4,5)P2] is a potential, powerful compensatory mechanism to rescue 408 reductions of NT release in case the number of (functional) syts per SV is reduced to no less than three. 409 We note that this compensatory mechanism may complicate experimentally observed effects of 410 stoichiometric changes.  The second hypothetical mutation was designed to not only abolish Ca 2+ binding, but to also 444 mimic the Ca 2+ -bound state. Thereby this mutant featured a high PI(4,5)P2 affinity as if the allosteric 445 interaction between Ca 2+ and PI(4,5)P2 was permanently 'on'. This might represent an extreme 446 example of a mutation electrostatically reducing/inverting the negative charges of the Ca 2+ binding 447 pocket (e.g. 'DN', 'DK'). We termed this mutant the "no Ca 2+ binding, A-on" mutant ( Figure 6A). This 448 mutant showed no NT release in response to the Ca 2+ transient in a homozygous condition ( Figure 6C2-449 D, top), which is explained by its inability to bind Ca 2+ . A major detrimental effect of the mutant was 450 observed when co-expressed with the wildtype protein: When half of the syts on the SV were mutated 451 (heterozygote), the amplitude of simulated eEPSCs was strongly reduced ( Figure 6C2-D, bottom). 452 Merely four mutant proteins expressed together with 11 WT proteins already decreased eEPSC 453 amplitudes by ~70% ( Figure 6D, bottom), indicating a strong dominant negative effect. The strong 454 inhibition is a result of the mutant's increased PI(4,5)P2 affinity leading to occupation of PI(4,5)P2 455 binding slots on the membrane with this Ca 2+ -insensitive mutant which blocks the association of the 456 Ca 2+ sensitive-and SV fusion promoting WT proteins. In comparison, a mutant not able to bind Ca 2+ 457 but having a normal PI(4,5)P2 affinity ("no Ca 2+  WT syt and two mutant syts. The "Ca 2+ -binding" mutant has a lower affinity for Ca 2+ (KD,2Ca2+ 10x increased, i.e. β 465 10x increased). The "no-Ca 2+ binding, A-on" mutant is not able to bind Ca 2+ and has a high binding affinity for 466 PI(4,5)P2, which is equal to the affinity for PI(4,5)P2 when the allostericity between Ca 2+ and PI(4,5)P2 is "active" Strikingly, SV docking in these mutants was rapidly restored within milliseconds after an AP which also 501 led to enhanced synaptic transmission in response to a second AP given 10 ms after the first (Chang et 502 al., 2018). We explored such a situation in the context of our model by driving exocytosis with two 503 successive AP-induced Ca 2+ transients and assuming either constant PI(4,5)P2 levels for syts in wildtype 504 synapses (i.e. all RRP SVs similarly docked) or initially reduced and activity-dependent increasing 505 PI(4,5)P2 levels for syts in mutant synapses (where SVs docked after the first AP) ( Figure 7A). We 506 studied the consequence of a mutation that would only affect SV docking at steady state (as may be 507 the case upon mutation of the arginines 398 and 399 of mouse syt 1, 'R398,399Q') in (Figure 7). This 508 resulted in a markedly decreased initial response ( Figure 7B,C), but repeated activation induced a large 509 facilitation of responses (indicated by a large paired pulse ratio: quotient of the second EPSC 510 amplitudes divided by the first) ( Figure 7D). Mutations of the C2B domain that reduce its PI(4,5)P2 511 affinity (as is likely the case upon mutation of the lysine residues 325 and 327 in syt1 or 327, 328 and 512 332 in syt2) may be more detrimental because even when the effective PI(4,5)P2 concentration 513 accessible to syts is restored upon activity-dependent SV redocking, syt association to PI(4,5)P2 will still 514 be less probable. We conclude that dynamic changes in the PI(4,5)P2 levels accessible to syts -which 515 may be caused by activity dependent SV relocation -strongly impact synaptic short-term plasticity. Exocytosis is a highly energy-demanding reaction, for which the formation of the neuronal SNARE 554 complex provides the energy (Jahn and Fasshauer, 2012). In our model we assume that syts regulate 555 this process by lowering the activation energy barrier for exocytosis when they engage in Ca 2+ /PI(4,5)P2 556 dual binding. However, how Ca 2+ /PI(4,5)P2 dual binding to syt exactly reduces this energy barrier is not 557 known. One possibility is that the energy is provided by the SNAREs themselves and that Ca 2+ /PI(4,5)P2 558 dual binding to syt relieves a clamping function, which syt itself or the auxiliary protein complexin 559 can simultaneously reduce the energy barrier for fusion. We here assumed that all syts exert the same 573 effect on this energy barrier for fusion and that the effects of more dual-bound syts are additive. 574 Whether or not this is the case will depend on the precise mechanism by which they shape the energy 575 landscape. We show here that the simplest model (constant and independent contribution) is 576 sufficient to reproduce the biological response. means that the allosteric effect may either be due to speeding up the association or slowing down the 595 dissociation of Ca 2+ /PI(4,5)P2 ( Figure 1A). We here implemented the latter, a reduction of the 596 unbinding rates of both Ca 2+ and PI(4,5)P2 when both species were bound to the C2B domain, which 597 leads to a stabilization of the dual-bound state. A stabilization of the Ca 2+ -bound state, which increases 598 the lifetime of the state, was also essential to reproduce the Ca 2+ dependence of release in the 599 previously proposed five-site binding model (Heidelberger et al., 1994;Schneggenburger and Neher, 600 2000). We here show in the context of our model that increasing the lifetime of Ca 2+ /PI(4,5)P2 dual 601 binding is particularly important to achieve fast fusion rates as it allows several C2B domains to 602 simultaneously engage to lower the fusion barrier (Figure 4). The drawback of the strong allosteric 603 interaction between the Ca 2+ and PI(4,5)P2 bindings sites might be its potential involvement in the 604 strong dominant-negative effects of some C2B domain mutations (Figure 6). Our model predicts that most RRP SVs have prebound PI(4,5)P2 via one syt at rest (Figure 3A), 640 but it is the Ca 2+ -induced, allosteric PI(4,5)P2 affinity-increase that induces the dynamic assembly of 641 three C2B domains in Ca 2+ /PI(4,5)P2 dual binding. This is fundamentally different from studies 642 suggesting that 12-20 syts need to preassemble in higher-order complexes (rings) to execute their 643 function in fusion (Rothman et al., 2017). A testable property to distinguish these possibilities is the 644 sensitivity to reducing the number of syts per SV. If transmitter release relied on preassembled syt-645 rings, it would immediately break down if the number of syts was reduced to one preventing ring 646 assembly, whereas our model predicts gradual effects (even for titration below nsyt =3) ( Figure 5). 647 648

Heterogeneity in PI(4,5)P2 concentration between different RRP SVs 649
The interaction between syt and PI(4,5)P2 has been shown to be essential in SV exocytosis (Bai et al., closer to the plasma membrane will have increased access to PI(4,5)P2 ("see a higher PI(4,5)P2 664 concentration") compared to those located further away. Taken together, this indicates that the 665 PI(4,5)P2 concentration is likely to vary between RRP SVs and also between individual syts on the SV. 666 Furthermore, this implies that once a syt has engaged in PI(4,5)P2 binding the successive engagement 667 of additional syts might be favored for some (those facing towards the PM) and disfavored for others 668 (those facing from the PM). While knowledge of these details could be helpful to construct a more 669 realistic version of our molecular model, we currently do not possess the methodology to measure 670 these properties. We therefore in our model simulated the simplest scenario where all syts have an 671 equal probability of engaging in PI(4,5)P2 binding. 672 As the localization of syts with respect to the PM influences the accessibility of syt to PI(4,5)P2, 673 mutations in synaptic proteins and stimulation protocols that alter SV docking will affect the PI(4,5)P2 674 concentration as it is implemented in our model (Chang et  interactions such as presented here should allow for the recapitulation of more complex synaptic 683 activity patterns relevant for neural processing. Particularly the molecular resolution of such models 684 will be useful to conceptualize the importance of specific molecular interactions for physiological and 685 pathological processes at the synapse. 686

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Computation of peak release rates 810 The peak of the fusion rate can be computed by multiplying the maximum value of the single SV fusion 811 rate function, (2), with nves. To allow for a variable RRP size, a set of 1000 nves values were drawn 812 according to the RRP size distribution, the peak release rates were determined, and the mean and 95 813 % prediction interval determined (Figure 2A, 2 supplement 4, 2 supplement 5, 4 supplement 1, 5A, 5 814 supplement 1A) for each Ca 2+ concentration. 815 For parameter exploration ( Figure 2G) and for computing the release rates in the fitting 816 routine, it was not feasible to calculate the fusion rate over 100 ms with high temporal precision. 817 Instead, we implemented a custom search algorithm (scripts can be found in accompanying zip-file 818 "Source_code1.zip"), which was constructed to shorten calculation time by taking advantage of the Since the variance in the experimental data points also contains information on the underlying 845 biological mechanism, we wanted to take the distribution of individual data points into account when 846 obtaining estimates of the unknown parameters. We therefore derived the likelihood function, which 847 describes how well the model captures the distribution of the release latencies. Obtaining this function 848 for the peak release rates was not feasible. The experimental peak release rates were therefore 849 compared to the average model prediction. Both measures of describing the correspondence between 850 model simulations and experimental data were combined in a cost value which was optimized to 851 estimate the best fit parameters (the lower this cost value the better the correspondence between 852 model predictions and experimental data). 853 The best fit was obtained by minimizing the following cost function: The likelihood of release latencies with variable RRP size 901 In our model, the RRP size is assumed to follow a Gamma distribution. Let x denote the RRP size, fRRP(x) 902 the probability density of the Gamma distribution, and u= G,C(t). The probability density of the release 903 latency at Ca 2+ concentration Ci is given by 904 where K is a normalization constant, K=1-P(x<5)≈1. The lower limit of the integral reflects that the 907 release latency is only defined when there are more than 5 SVs in the RRP. In simulations this 908 corresponds to redrawing the RRP size whenever an RRP size < 5 SVs occurs, which happens with 909 probability ~3e-11, and is accounted for in the normalization constant K in the following. Inserting the 910 probability density function of a Gamma distribution with shape parameter k and scale parameter , of an individual syt using a 2-digit coding system; 00 for no species bound to syt, 01 for PI(4,5)P2 bound, 944 10 for two Ca 2+ ions bound, and 11 for both species bound (dual-binding syt). As with the analytical 945 implementation, each syt can undergo in total 8 different (un)binding reactions ( Figure 1A), depending 946 on the binding state of the respective syt. The fusion rate, which depends on the number of dual-947 bound syts per SV, is determined for the entire SV. 948

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Determining the initial state of the system 950 The steady state (initial state, X(0)) was computed using the same method as described above (see 951 section 'The steady state of the system') using [Ca 2+ ]i = 0.05 µM as the resting condition. This resulted 952 in , the probability vector of a single SV to be in the different SV-states at steady state. To 953 stochastically determine X(0), we first determined the binding state for each SV, i.e. how many dual 954 bindings are formed (n) and how many syts have bound Ca 2+ (m) and how many PI(4,5)P2 (k). For that 955 we drew pj(0,1), j = 1…,nves, from the uniform distribution. The state number of the j th SV, s, was 956 determined by: 957 Via the ordering of states explained above, s can be linked to the state triplet (ns,ms,ks). As the order 959 of syts is irrelevant for model simulation, this information on the state of SVj was transferred to the j th 960 column of the X(0) matrix in a systematic way: The first ns elements were labeled with '11'; elements 961 ns+1 to ns+ms were labeled with '10'; and elements ns+ms+1 to ns+ms+ks were labeled with '01', and 962 the remaining elements (ns+ms+ks+1):nsyt were set to '00'.