The neuronal calcium sensor Synaptotagmin-1 and SNARE proteins cooperate to dilate fusion pores

Zhenyong Wu; Nadiv Dharan; Zachary A McDargh; Sathish Thiyagarajan; Ben O'Shaughnessy; Erdem Karatekin

doi:10.7554/eLife.68215

. 2021 Jun 30;10:e68215. doi: 10.7554/eLife.68215

The neuronal calcium sensor Synaptotagmin-1 and SNARE proteins cooperate to dilate fusion pores

Zhenyong Wu ^1,², Nadiv Dharan ^3,^†, Zachary A McDargh ^3,^†, Sathish Thiyagarajan ^3,^†, Ben O'Shaughnessy ^3,^✉, Erdem Karatekin ^1,^2,^4,^5,^✉

Editors: Felix Campelo⁶, Vivek Malhotra⁷

PMCID: PMC8294851 PMID: 34190041

Abstract

All membrane fusion reactions proceed through an initial fusion pore, including calcium-triggered release of neurotransmitters and hormones. Expansion of this small pore to release cargo is energetically costly and regulated by cells, but the mechanisms are poorly understood. Here, we show that the neuronal/exocytic calcium sensor Synaptotagmin-1 (Syt1) promotes expansion of fusion pores induced by SNARE proteins. Pore dilation relied on calcium-induced insertion of the tandem C2 domain hydrophobic loops of Syt1 into the membrane, previously shown to reorient the C2 domain. Mathematical modelling suggests that C2B reorientation rotates a bound SNARE complex so that it exerts force on the membranes in a mechanical lever action that increases the height of the fusion pore, provoking pore dilation to offset the bending energy penalty. We conclude that Syt1 exerts novel non-local calcium-dependent mechanical forces on fusion pores that dilate pores and assist neurotransmitter and hormone release.

Research organism: None

Introduction

Release of neurotransmitters and hormones occurs through exocytosis in which neurotransmitter-filled synaptic vesicles or hormone-laden secretory vesicles fuse with the plasma membrane to release their cargo to the extracellular space (Brunger et al., 2018a). The initial merger of the vesicular and plasma membranes results in a narrow fusion pore only ~1 nm in diameter (Karatekin, 2018; Sharma and Lindau, 2018; Chang et al., 2017; Alabi and Tsien, 2013). Dynamics of this key intermediate determine release kinetics and the mode of vesicle recycling. The fusion pore can fluctuate in size, flicker open-closed multiple times and either reseal after partial release of contents or dilate for full cargo release. Because many endocrine cells co-package small and large cargoes, the pore can additionally act as a molecular sieve, controlling the type of cargo released. In pancreatic β-cells, fusion pores that fail to dilate release only small cargo such as ATP, but not insulin, a process that occurs more commonly in type 2 diabetes (Collins et al., 2016). Adrenal chromaffin cells release small catecholamines through flickering small pores, or release additional, larger cargo, in an activity-dependent manner (Fulop et al., 2005). Fusion pore dynamics also affect release of neurotransmitters and the mode of endocytosis during synaptic vesicle fusion (Alabi and Tsien, 2013; He et al., 2006; Pawlu et al., 2004; Staal et al., 2004; Chapochnikov et al., 2014; Gandhi and Stevens, 2003; Lisman et al., 2007; Verstreken et al., 2002).

Little is known about the molecular mechanisms that control pore dilation. SNARE proteins, a core component of the release machinery, are known to influence fusion pore dynamics (Bao et al., 2018; Wu et al., 2016; Wu et al., 2017b; Wu et al., 2017a; Han et al., 2004; Bretou et al., 2008; Kesavan et al., 2007; Dhara et al., 2016; Ngatchou et al., 2010). Formation of complexes between the vesicular v-SNARE VAMP2/Syb2 and plasma membrane t-SNAREs Syntaxin-1/SNAP25 is required for fusion (Weber et al., 1998). Insertion of flexible linkers between the SNARE domain and the transmembrane domain in VAMP2, or truncation of the last nine residues of SNAP25, retard fusion pore expansion in adrenal chromaffin cells (Bretou et al., 2008; Kesavan et al., 2007; Fang et al., 2008). Mutations in SNARE TMDs also affect fusion pores (Wu et al., 2017a). Increasing the number of SNAREs at the fusion site accelerated fusion pore expansion in neurons (Bao et al., 2018; Acuna et al., 2014), astrocytes (Guček et al., 2016), and chromaffin cells (Zhao et al., 2013) and led to larger pores in nanodisc-based single-pore fusion assays (Bao et al., 2018; Wu et al., 2017b). This was interpreted as due to increased molecular crowding at the waist of the pore with increasing SNARE copy numbers (Wu et al., 2017b).

Although they are best known for their role as calcium sensors for exocytosis at most synapses and endocrine cells, Synaptotagmins are another component of the release machinery known to affect fusion pore properties (Segovia et al., 2010; Zhang et al., 2010a; Zhang et al., 2010b; Wang et al., 2006; Wang et al., 2003a; Wang et al., 2003b; Wang et al., 2001; Bai et al., 2004a; Lynch et al., 2008; Rao et al., 2014; Lai et al., 2013). They couple membrane fusion driven by neuronal/exocytic SNAREs to calcium influx (Geppert et al., 1994; Chapman, 2008). Synaptotagmins are integral membrane proteins possessing two cytosolic C2 domains (C2A and C2B) which can bind Ca²⁺, acidic lipids, SNAREs, and other effectors, but affinities vary widely among the 17 mammalian isoforms (Chapman, 2008; Bhalla et al., 2005; Bhalla et al., 2008; Pinheiro et al., 2016; Volynski and Krishnakumar, 2018; Craxton, 2010; Sugita et al., 2002; Hui et al., 2005). Synaptotagmin-1 (Syt1) is the major neuronal isoform that mediates fast, synchronous neurotransmitter release (Chapman, 2008; Volynski and Krishnakumar, 2018; Xu et al., 2007). It resides in synaptic vesicles in neurons and secretory granules in neuroendocrine cells and interacts with SNAREs, acidic phospholipids, and calcium (Brunger et al., 2018a; Chapman, 2008; Brunger et al., 2018b; Südhof, 2013). How calcium binding to Syt1 leads to the opening of a fusion pore is an area of active research and debate (Lynch et al., 2008; Brunger et al., 2018b; Martens et al., 2007; Hui et al., 2009; Rothman et al., 2017; Chang et al., 2018; van den Bogaart et al., 2011; Seven et al., 2013; Lin et al., 2014; Bello et al., 2018; Tagliatti et al., 2020). In addition to its role in triggering the opening of a fusion pore, Syt1 also affects the expansion of the fusion pore after it has formed (Segovia et al., 2010; Zhang et al., 2010a; Zhang et al., 2010b; Wang et al., 2006; Wang et al., 2003a; Wang et al., 2003b; Wang et al., 2001; Bai et al., 2004a; Lynch et al., 2008; Rao et al., 2014; Lai et al., 2013), but mechanisms are even less clear.

Calcium-binding to Syt1 causes hydrophobic residues at the tips of the Ca²⁺-binding loops to insert into the membrane, generating curvature, which may be important for triggering fusion (Lynch et al., 2008; Martens et al., 2007; Hui et al., 2009). Membrane bending has been proposed to facilitate opening of the initial fusion pore by helping to bring the two membranes into close proximity, reducing the repulsive hydration forces by reducing the contact area, and exposing the hydrophobic interior of the two membranes to initiate lipid exchange (Chernomordik and Kozlov, 2008; Kozlov et al., 2010). After fusion pore opening, Syt1 was suggested to contribute to fusion pore expansion through membrane curvature generation as well, based on the observation that in PC12 cells, membrane-insertion deficient mutants reduced exocytosis, whereas mutants with enhanced insertion led to larger fusion pores (Lynch et al., 2008). However, once the initial fusion pore is formed it is not clear whether and how much curvature generation by Syt1 contributes to fusion pore expansion. First, in PC12 cells multiple Syt isoforms reside on the same secretory granule and potentially compete for fusion activity (Zhang et al., 2011; Lynch and Martin, 2007). Disrupting Syt1 function may allow another isoform to dominate fusion pore dynamics. In adrenal chromaffin cells where Syt1 and Syt7 are sorted to distinct granule populations, fusion pores of Syt7 granules dilate more slowly (Rao et al., 2014). Second, compared to Syt1 C2 domains, the higher calcium-affinity Syt7 C2 domains penetrate more avidly and deeply into membranes (Osterberg et al., 2015; Voleti et al., 2017), which should lead to more efficient membrane bending (Martens et al., 2007; Hui et al., 2009). This would appear to be inconsistent with the slower dilation of fusion pores by Syt7. Finally, most previous reconstitutions could not probe the role of Syt1 in fusion pore regulation, as they lacked the required sensitivity and time resolution to detect single pores.

Here, we investigated the mechanism by which Syt1 contributes to fusion pore dynamics, using a single-pore conductance assay (Wu et al., 2016; Wu et al., 2017b). Compared to SNAREs alone, addition of Syt1 increased the mean pore conductance three-fold. This effect required binding of Syt1 to calcium, the acidic phospholipid PI(4,5)P₂, and likely to the SNAREs. In addition, both pore opening and dilation are promoted by insertion of Syt1 C2AB top loops into the membrane in a Ca²⁺-dependent manner, but we propose that membrane curvature generation is not needed to explain fusion pore expansion by Syt1. Mathematical modeling suggests that pore dilation relies on regulation of the intermembrane distance by Syt1. Syt1 penetration into the target membrane upon calcium binding re-orients the C2AB domains and SNARE complexes, forcing the membranes apart in a lever-like action that concomitantly expands the pore.

Results

Co-reconstitution of Synaptotagmin-1 and v-SNAREs into nanolipoprotein particles

Previously, using a nanodisc-cell fusion assay, we characterized single, SNARE-induced fusion pores connecting a nanodisc and an engineered cell expressing neuronal ‘flipped’ t-SNAREs ectopically (Wu et al., 2016; Wu et al., 2017b). In this assay, a flipped t-SNARE cell is voltage-clamped in the cell-attached configuration. Nanodiscs reconstituted with the neuronal/exocytotic v-SNARE VAMP2 are included in the pipette solution. Fusion of a nanodisc with the cell surface creates a nanometer size pore that connects the cytosol to the exterior, allowing passage of ions under voltage clamp. Direct currents report pore size with sub-millisecond time resolution (Wu et al., 2016; Wu et al., 2017b). Fusion pore currents fluctuate and may return to baseline transiently multiple times, evidently reflecting pore flickering (Karatekin, 2018; Wu et al., 2016; Wu et al., 2017b; Dudzinski et al., 2019). Pore conductance is eventually lost (5–20 s on average after initial appearance), evidently reflecting pore closure (Karatekin, 2018; Wu et al., 2016; Wu et al., 2017b; Dudzinski et al., 2019). The mechanism of pore closure is not known, but because pore expansion beyond a maximum size is prevented by the nanodisc scaffold, pore closure is one of the few possible outcomes (Wu et al., 2016; Shi et al., 2012). To ensure single-pore detection, the rate at which pore currents appear (reported in pores/min, also referred to as the ‘fusion rate’) is made low by recording from a small area of the cell surface and by tuning the nanodisc concentration (Karatekin, 2018; Wu et al., 2016; Wu et al., 2017b; Dudzinski et al., 2019) (see Materials and methods and Appendix 1 for details).

To test whether Syt1 affected fusion pores in this system, we co-reconstituted ~4 copies of recombinant full-length Syt1 together with ~4 copies of VAMP2 (per disc face) into large nanodiscs called nanolipoprotein particles (Wu et al., 2017b; Bello et al., 2016) (vsNLPs, ~25 nm in diameter, see Appendix 1—figure 1). We reasoned that, under these conditions, potential modification of pore properties by Syt1 should be detectable. In the absence of Syt1, we previously found that only ~2 SNARE complexes are sufficient to open a small fusion pore (150-200 pS conductance), but dilation of the pore beyond ~1 nS conductance (~1.7 nm in radius, assuming the pore is a 15 nm long cylinder [Hille, 2001]) required the cooperative action of more than ~10 SNARE complexes (Wu et al., 2017b). The increase in pore size was heterogeneous with increasing SNARE load; most pores remained small (mean conductance ≲ 1 nS), but an increasing fraction had much larger conductances of a few nS. With ~4 v-SNAREs per NLP face, fusion driven by SNAREs alone results in relatively small pores with ~200 pS average conductance, corresponding to a pore radius of ~0.76 nm (Wu et al., 2017b). Larger pores (mean conductance > 1 nS) were rare (< 5%, [Wu et al., 2017b]). With ~25 nm NLPs, a fusion pore can in principle grow to > 10 nm diameter (~9 nS conductance) before the scaffold protein stabilizing the edges of the NLP becomes a limitation for further pore dilation (Wu et al., 2017b; Bello et al., 2016). Thus, at this v-SNARE density, there is a large latitude in pore sizes that can be accommodated, if introduction of Syt1 were to lead to any modification.

We tuned NLP size by varying the lipid-to-scaffold protein (ApoE422k) ratio and adjusted copy numbers of VAMP2 and Syt1 until we obtained the target value of ~4 copies of each per NLP face, similar to previous work with SNAREs alone (Wu et al., 2017b; Bello et al., 2016). vsNLPs were purified by size exclusion chromatography and characterized by SDS-PAGE and transmission electron microscopy (see Appendix 1—figure 1B-D). The distribution of NLP diameters was fairly narrow, with mean diameter 25 nm (±5.6 nm SD, see Appendix 1—figure 1E), and did not change significantly compared to the distribution when v-SNAREs alone were incorporated at ~4 copies per face (mean diameter = 25 ± 4 nm) (see Appendix 1—figure 1F-H, and Wu et al., 2017b).

Syt1 promotes fusion pore expansion

To probe fusion pores, we voltage-clamped a flipped t-SNARE cell in the cell-attached configuration and included NLPs co-loaded with Syt1 and VAMP2 in the pipette solution as shown in Figure 1 (100 nM vsNLPs, 120 μM lipid). Even in the presence of 100 μM free calcium, a level that elicits robust release in neurons and chromaffin cells (Pinheiro et al., 2016; Schneggenburger and Neher, 2000; Schneggenburger and Neher, 2005; Voets, 2000; Chanaday and Kavalali, 2018), pore properties were affected only slightly compared to the case when Syt1 was omitted from the NLPs. For example, pore currents (Figure 1D) appeared at similar frequency (Figure 2A) and the mean single-pore conductance, $⟨ G_{p o} ⟩$ , was only slightly elevated in the presence of Syt1 (See Appendix 1—figure 1J, Appendix 1—figure 2, and Appendix 1 Supplementary Materials and methods for definitions and other pore parameters). We wondered whether the lack of acidic lipids in the outer leaflet of the cell membrane could be a limitation for Syt1’s ability to modulate fusion pores. Syt1 is known to interact with acidic lipids, in particular with PI(4,5)P₂, in both calcium-dependent and independent manners, and these interactions are required for Syt1’s ability to trigger membrane fusion (Zhang et al., 2010a; Chang et al., 2018; Ma et al., 2017; Pérez-Lara et al., 2016; Honigmann et al., 2013; Bai et al., 2004b). However, the outer leaflet of the plasma membrane which is seen by Syt1 in our assay is poor in such lipids. To test for a requirement for PI(4,5)P₂, we incubated flipped t-SNARE cells with 20 μM diC₈PI(4,5)P₂ for 20 min and rinsed excess exogenous lipid. At different time points after rinsing, we probed incorporation of the short-chain PI(4,5)P₂ into the outer leaflet of the cell membrane by immunofluorescence, using a mouse monoclonal anti-PI(4,5)P₂ primary antibody, without permeabilizing the cells (Figure 1B). The signal decreased slightly as a function of time but persisted for at least 80 min. To compare the level of short-chain PI(4,5)P₂ incorporated into the outer leaflet in this manner with endogenous PI(4,5)P₂ levels in the inner leaflet, we measured immunofluorescence from permeabilized cells that were not incubated with diC₈PI(4,5)P₂. Outer leaflet diC₈PI(4,5)P₂ levels were within 25% of the endogenous inner-leaflet PI(4,5)P₂ levels (Figure 1B).

Figure 1. — (A) Domain structures of the constructs used in this study. The structure of the soluble C2AB domains was rendered using PyMol, from PDB: 5kj7 (Lyubimov et al., 2016). The orientations of the C2A and C2B domains relative to each other are not known in the presence of SNAREs and membranes. Conserved aspartate residues coordinating calcium ions are depicted in orange. Calcium ions are shown as orange spheres. A poly-lysine motif on the side of C2B (K324,K325,K326,K327 in the rat sequence) that preferentially interacts with PI(4,5)P₂ (Radhakrishnan et al., 2009) is highlighted in cyan. (B) Incorporation of exogenous PI(4,5)P₂ into the outer leaflet of flipped t-SNARE cells. Top: cells were incubated with diC8-PI(4,5)P₂ for 20 min, rinsed, and immunolabeled for PI(4,5)P₂ at the indicated time points. Only control cells that were permeabilized with saponin showed immunostaining, confirming absence of PI(4,5)P₂ in the outer leaflet, and providing a reference value for inner-leaflet PI(4,5)P₂ levels (**a and b**). Cells incubated with diC8-PI(4,5)P₂ showed immunofluorescence in the absence of permeabilization, indicating successful incorporation of PI(4,5)P₂ into the outer leaflet of the cell membrane (**c–e**). The signal was comparable to endogenous inner-leaflet PI(4,5)P₂ levels, and persisted at least for 80 min (lower panel). Cells processed similarly, but not treated with saponin or diC8-PI(4,5)P₂ served as negative controls (a). One-way analysis of variance (ANOVA) followed by multiple comparison test was used to compare the signals from the endogenous PI(4,5)P₂ sample (b) with all others. *, **, *** indicate p<0.05, 0.01, and 0.001, respectively. (C) Schematic of the single-pore nanodisc-cell fusion assay. A glass micropipette forms a tight seal on a patch of the plasma membrane of a cell expressing ‘flipped’ t-SNARE proteins on its surface. NLPs co-reconstituted with Syt1 and VAMP2 are included in the pipette solution (left). NLP-cell fusion results in a fusion pore connecting the cytosol to the cell’s exterior (right). Under voltage clamp, direct-currents passing through the pore report pore dynamics. With ~25 nm NLPs, the scaffolding ring does not hinder pore expansion up to at least 10 nm diameter. Exogenous PI(4,5)P₂ can be added to the cell’s outer leaflet as in B, and calcium in the pipette is controlled using calcium buffers. (D) Representative currents that were recorded during vsNLP-tCell fusion, for the indicated conditions. PI(4,5)P₂ indicates cells were pre-treated with diC8-PI(4,5)P₂. Tetanus neurotoxin (TeNT) light chain cleaves VAMP2 and blocks exocytosis. Currents were larger when all components were present (SNAREs, Syt1, exogenous PI(4,5)P₂ and calcium). (E) Similar to D, but instead of full-length Syt1, 10 μM soluble Syt1 C2AB domains were used together with NLPs carrying ~4 copies of VAMP2 per face.

When we repeated vsNLP-flipped t-SNARE cell fusion experiments with cells pre-incubated with diC₈PI(4,5)P₂, the rate of fusion in the absence of calcium was unchanged compared to fusion with SNAREs alone, but increased three- to fourfold when 100 μM calcium was present (Figure 2A). Note that our fusion rate estimates throughout should be interpreted with caution, because they are inherently noisy and they systematically underestimate fusion rates when the rates are high. Both effects are due to the fact that in the assay only a few fusion pores can be analyzed per patch (see Appendix 1- Materials and methods and Karatekin, 2018). Compared to SNARE-alone fusion, the mean single-pore conductance increased only slightly in the absence of calcium but was three-fold larger in the presence of 100 μM calcium (Figure 2B). Conductance fluctuations around the mean value were larger and flicker frequency lower when Syt1, calcium and PI(4,5)P₂ were all present, but no major differences emerged for burst lifetimes, $T_{o}$ , or pore open probability during a burst (the fraction of time the pore was open during a burst), $P_{o}$ (see Appendix 1—figure 3). For all cases tested, the distributions of the number of pore flickers ( $N_{f l i c k e r s}$ ) and burst durations ( $T_{o}$ ) were well-described by geometric and exponential distributions, respectively (see Appendix 1—figure 3), as would be expected for discrete transitions between open, transiently blocked, and closed states (Colquhoun and Hawkes, 1995). Fusion was SNARE-dependent, as treatment with the tetanus neurotoxin TeNT, which cleaves VAMP2 at position 76Q-77F and blocks exocytosis (Schiavo et al., 2000), dramatically reduced the fusion rate of vsNLPs even in the presence of calcium and exogenous PI(4,5)P₂ (Figure 1D and Figure 2A). Thus, Syt1 increases the fusion rate and promotes pore dilation during SNARE-induced fusion, in a calcium- and PI(4,5)P₂-dependent manner.

We pooled individual current bursts to obtain the distributions for fusion pore conductances and pore radii as shown in Figure 2C,D, and Appendix 1—figure 4. The distributions were similar for SNAREs alone, whether calcium or PI(4,5)P₂ were added, and with Syt1 when calcium was omitted (Figure 2C,D, and see Appendix 1—figure 4). By contrast, in the presence of 100 μM free calcium and exogenous PI(4,5)P₂, larger conductance values (and corresponding pore radii) became more likely (Figure 2C,D).

Even when pores were maximally dilated by Syt1, the mean conductance and pore radius, $G_{p o} = 595$ pS (S.E.M. = 51 pS), and $r_{p o} = 1.13$ nm (S.E.M = 0.04 nm) were significantly less than the maximum possible value predicted from NLP dimensions (Wu et al., 2017b). That is, the geometric constraints imposed by the NLP dimensions were not limiting pore expansion. Instead, there is inherent resistance to pore dilation, independent of NLP scaffolding (Wu et al., 2017b) as predicted and observed in other systems (Jackson, 2009; Cohen and Melikyan, 2004; D'Agostino et al., 2018). To quantify the resistance, we computed (Wu et al., 2017b) the apparent pore free energy $U (r_{p o})$ from the distribution of pore radii, $P (r_{p o}) ~ e^{- U (r_{p o}) / k T}$ for fusion with both SNAREs alone and with Syt1 under optimal conditions (with exogenous PI(4,5)P₂ and 100 μM free calcium). Invoking the Boltzmann distribution amounts to assuming the membrane-protein system is approximately in equilibrium, that is conductance measurements are approximately passive and only weakly perturb the fusion pore. We cannot exclude substantial non-equilibrium effects, as application of a potential difference may in itself promote pore formation and affect the structure and dynamics of the pores that result, as seen in lipid bilayer electroporation studies (Melikov et al., 2001), although the potential difference used in our studies is much lower (<20 mV). Generally, the profiles we report should be interpreted as effective free energies. With SNAREs alone, or with Syt1 but in the absence of calcium, the free energy profile suggested that ~6-7 kT energy was required to expand the pore from 1 to ~2.5 nm radius, whereas calcium-bound Syt1 reduced this resistance to ~2 kT (Figure 2E). That is, the force opposing pore expansion decreased from 16-19 pN in the absence of calcium to ~5 pN in the presence of 100 μM calcium.

We tested if the soluble C2AB domains of Syt1 could recapitulate these results. We included 10 μM C2AB together with NLPs reconstituted with ~4 copies per face of VAMP2 in the patch pipette and monitored fusion with flipped t-SNARE cells in the cell attached configuration under voltage clamp. Similar to the results with full-length Syt1, there was little change in the fusion rate compared to the SNARE-alone case if either calcium or exogenous PI(4,5)P₂ was omitted (Figure 2A). When both calcium (100 μM) and PI(4,5)P₂ were present, the fusion rate was higher, but we are not as confident about this increase as in the case of Syt1. The mean conductance was significantly above the SNARE-only value in the presence of calcium and PI(4,5)P₂, but not when either was omitted (Figure 2B). The distributions of average single pore conductances (Figure 2F), conductance fluctuations, and other pore parameters were similar whether full-length Syt1 or soluble C2AB were used, except $P_{0}$ was higher for the +Ca²⁺/+PI(4,5)P₂ case and $T_{0}$ lower for +Ca²⁺/-PI(4,5)P₂ case for C2AB compared to Syt1 (Figs. S3 and S4). The apparent free energy profile calculated from the pore size distribution was indistinguishable from that of full-length Syt1 (Figure 2E). We conclude that soluble Syt1 C2AB largely recapitulates the effect of full-length Syt1 on promoting dilation of SNARE-mediated fusion pores. As they were far easier to manipulate, we used soluble Syt1 C2AB domains for the remainder of this work.

In some cases, a peak at ~200 pS is apparent in open-pore conductance distributions, corresponding to a peak at $r_{p o} \approx 0.7$ nm in pore size distributions (e.g. see Appendix 1—figure 4). This is manifested as a small dip in the energy profiles (Figure 2E). We do not know the underlying mechanisms, as we have not identified a clear correlation between the peak's amplitude or location and the parameters we varied, such as calcium concentration.

Pore dilation by Synaptotagmin-1 C2AB requires binding to calcium, PI(4,5)P₂, and likely SNAREs

We further tested the requirement for Syt1 C2AB binding to calcium, PI(4,5)P₂, and SNAREs for promoting pore dilation, using mutagenesis (Figure 3). Binding of calcium to the second C2 domain of Syt1 is known to be essential for evoked release (Chapman, 2008; Mackler et al., 2002; Shin et al., 2009). When calcium binding to the C2B domain was impaired by mutating a highly conserved aspartate to asparagine (Syt1 C2AB D309N Nishiki and Augustine, 2004), mean single pore conductance returned to the value obtained in the presence of SNAREs alone (Figure 3C). The rate at which current bursts appeared also returned to the SNARE-alone level (Figure 3B). Other pore properties were also indistinguishable from the SNARE-alone case (see Appendix 1—figure 5). We conclude that calcium binding to Syt1 C2B is essential for fusion pore dilation, in addition to its well-known role for triggering the opening of a fusion pore (Wang et al., 2006).

The C2B domain of Syt1 possesses a polybasic patch (K324-327) that interacts with acidic phospholipids (Figure 3A) and is important for synchronous evoked release (Chang et al., 2018). Although this interaction occurs in the absence of calcium (Chapman, 2008), it contributes to the membrane binding energy of C2AB in the presence of calcium (Ma et al., 2017), presumably because multivalent interactions increase the bound lifetime of C2AB. Partially neutralizing the polybasic patch in C2B (K326A, K327A) reduced the fusion rate, and resulted in single pore conductances that were indistinguishable from those for SNARE-alone pores (Figure 3). Similarly, the burst lifetime and the flicker rate were comparable to the SNARE-alone level, but conductance fluctuations were reduced, while there was an increase in the pore open probability during a burst, $P_{o}$ (see Appendix 1—figure 5), as would be expected for pores that fluctuate less. Thus, in addition to its established role in evoked release (Chang et al., 2018; Borden et al., 2005), the polybasic patch in Syt1 C2B is also required for fusion pore dilation.

Two recent crystal structures identified a ‘primary’ interaction interface between Syt1 C2B and the four-helical SNARE complex (Zhou et al., 2015; Zhou et al., 2017; Figure 3A). Specifically, two arginines (R398 and R399) form salt bridges with glutamates and aspartates in a groove between SNAP25 and Syntaxin-1 (Zhou et al., 2015). Mutation of these arginines to glutamines (R398Q, R399Q) was shown to largely abolish evoked release from hippocampal neurons (Chang et al., 2018; Zhou et al., 2015; Xue et al., 2008), possibly by disrupting the interaction of Syt1 C2B with SNAREs (Chang et al., 2018; Zhou et al., 2015). When we used purified C2AB bearing the same mutations (C2AB^{R398Q, R399Q}) both the fusion rate and the mean pore conductance decreased significantly, close to SNARE-alone levels (Figure 3B,C). Burst lifetimes, conductance fluctuations, and the pore open probability were not significantly different than for pores induced by SNAREs alone, but the flicker rate was lower (see Appendix 1—figure 5).

Together, these results indicate that binding of Syt1 to calcium, PI(4,5)P₂, and likely SNAREs, which are all crucial for Syt1’s role in evoked neurotransmitter release (Brunger et al., 2018a; Chapman, 2008), are also essential for its function in dilating SNARE-induced fusion pores.

Calcium-dependence of pore dilation by Syt1 C2AB

To determine whether pore properties are altered by calcium, we varied the free calcium concentration in the pipette solution and repeated the fusion experiments. Mean open-pore conductance $⟨ G_{p o} ⟩$ increased with increasing calcium (Figure 4A), consistent with a mathematical model (see below). Conductance fluctuations and burst lifetimes also increased, while the flicker rate decreased slightly and the pore open probability during a burst did not change significantly as [Ca²⁺] was increased (see Appendix 1—figure 6). That is, pores tended to last longer with higher calcium, and the open state conductance increased. The rate at which pore currents appeared also increased with calcium (Appendix 1—figure 6F).

The conductances in the open-state and the corresponding pore radii ( $r_{p o}$ ) were broadly distributed at all calcium concentrations tested, but the distributions did not shift uniformly as calcium increased (see Appendix 1—figure 6). The apparent free energy profiles, estimated from the pore size distributions, are plotted in Figure 4B. With increasing calcium, the well around the most likely radius (~0.5-0.7 nm) became wider, and the slopes of the energy profiles for radii above the well’s upper boundary, reflecting the force needed to dilate the pore, decreased as calcium increased. The calcium concentration at which this transition occurs (~20 μM) is consistent with the known calcium binding affinity of Syt1 (Ma et al., 2017; Pérez-Lara et al., 2016; Bai et al., 2004b; Radhakrishnan et al., 2009; Davis et al., 1999).

We also examined the kinetics of pore dilation as a function of calcium (Figure 4C,D). To this end, we averaged pore conductances after aligning them to the initial pore opening, in the presence of Syt1 C2AB at different Ca²⁺ levels. The average conductance rapidly increased after initial pore opening for all traces, but reached larger values for larger calcium concentrations (Figure 4C). We estimated the pore expansion rate as the 10–90% rise time from the baseline to the level of conductance reached within the first 100 ms after pore opening, divided by the time it took for this rise (Figure 4D). With low amounts of calcium (0–30 μM), the expansion rate is ~3–12 nS/s, which increases rapidly to 20–25 nS/s for 40–100 μM Ca²⁺.

Both the increase in mean open-pore conductance (Figure 4A) and the pore expansion rate (Figure 4D) with increasing free calcium were fit to a Hill equation, using parameters describing cooperative binding and loop-insertion of Syt1 C2AB to lipid bilayers containing PI(4,5)P₂ (Bai et al., 2004b).

Calcium-dependent membrane-insertion of Syt1 C2AB is necessary for pore dilation

Calcium binds simultaneously to acidic phospholipids and highly conserved aspartate residues in a pocket formed by loops at the top of the beta-sandwich structure of the Syt1 C2 domains (Chapman, 2008; Shin et al., 2009; Martens and McMahon, 2008). Hydrophobic residues at the tips of the loops flanking the calcium-binding residues in Syt1 C2A (M173 and F234) and C2B (V304 and I367) insert into the membrane as a result of these interactions, strengthening membrane binding of C2 domains (Chapman, 2008; Ma et al., 2017; Chapman and Davis, 1998) while causing a reorientation of the C2 domains (Kuo et al., 2011; Herrick et al., 2006; Figure 5A). The membrane insertion of these hydrophobic residues contributes to the triggering of release (Lynch et al., 2008; Martens et al., 2007; Hui et al., 2009). We wondered whether membrane-insertion of hydrophobic loops also played any role in pore dilation. To test this, we introduced mutations that made the loops insertion-deficient (M173A, F234A, V304A, and I367A, the ‘4A’ mutant [Lynch et al., 2008; Martens et al., 2007]) or that increased membrane affinity (M173W, F234W, V304W and I367W, the ‘4W’ mutant [Lynch et al., 2008; Martens et al., 2007]).

Figure 5. — (A) Schematic depiction of Syt1 C2B domain’s calcium-dependent interactions with membranes. Calcium-free C2B interacts with acidic lipids through its poly-lysine motif (highlighted in cyan as in Figure 1). Upon binding to calcium, hydrophobic residues (V304 and I367 on C2B) insert into the membrane, causing C2B to reorient (Chapman, 2008) and inducing membrane curvature (Martens et al., 2007; Hui et al., 2009). In the presence of PI(4,5)P₂, the calcium-bound C2B assumes a tilted conformation with respect to the membrane (Kuo et al., 2011). M173 and F234 on C2A top loops similarly insert into membranes in a calcium-dependent manner, with similar effect on orientation and curvature generation (Chapman, 2008) (not shown). A mutant with the membrane-inserting residues replaced with tryptophans (M173W, F234W, V304W, and I367W, ‘4W’) binds membranes more avidly, resulting in more membrane tubulation activity, whereas alanine substitution of the same residues (‘4A’) abolishes membrane penetration and curvature induction (Martens et al., 2007). (B) Pore nucleation rate (mean ± S.E.M) in the presence of wildtype, 4W and 4A mutants. Student's t-test was used to assess significant differences between the ‘no C2AB’ group and the rest. (C) Mean open-pore conductance (± S.E.M) for the conditions indicated. Two-sample Kolmogorov-Smirnov test was used to assess significant differences between the ‘no C2AB’ group and the rest. (D) Cumulative density functions for mean open-pore conductances for wild-type Syt1 C2AB, 4W and 4A mutants. In A, calcium-free C2B was rendered from PDB 5w5d (Zhou et al., 2017) and calcium-bound C2B was rendered from 5kj7 (Lyubimov et al., 2016). *, **, *** indicate p<0.05, 0.01, and 0.001, respectively.

In the nanodisc-cell fusion assay, the membrane penetration deficient 4A mutant was non-functional, having no discernible effect on pore dilation or fusion rate when compared to the assay without Syt1, other than a slight reduction in the fusion rate in the absence of PI(4,5)P₂ (Figure 5B–D). By contrast, the 4W mutant which binds the membrane more avidly essentially behaved like the wild-type C2AB, with the exception that the pore dilation ability of the 4W mutant was less dependent on the presence of PI(4,5)P₂ (Figure 5C and see Appendix 1—figure 7). Thus, calcium-induced membrane penetration of Syt1 C2 domains is required for pore expansion by Syt1.

Mathematical modeling suggests that Syt1 and SNARE proteins cooperatively dilate fusion pores in a mechanical lever action

How do Syt1 and SNAREs cooperate to expand the pore in the presence of calcium? To help elucidate the mechanism, we developed a detailed mathematical model of the membrane fusion pore and the ApoE scaffold of the NLP in the presence of SNARE proteins and the C2AB domain of Syt1 (see Appendix 1 for model details and parameters). The energetics of the fusion pore membrane are described in the classic Helfrich framework, with contributions from bending energy and membrane tension (Helfrich, 1973), while the ApoE scaffold is modelled by adapting the theory of elasticity (Landau and Lifshitz, 1986a) (see Appendix 1—figure 8A). We obtained the minimum energy shape of the fusion pore with a given height and radius by solving the membrane shape equation (Zhong-can and Helfrich, 1989), assuming that the membrane has zero slope where it joins the tCell, taken as a remote location (see Appendix 1). We found there was very little change in the shape of the fusion pore when either this location was changed or freely hinged boundary conditions were used instead at this location, demonstrating that the model is insensitive to these assumptions. To compare directly with the present experiments, we incorporate four SNARE complexes, each of which can either be in the trans configuration and free to roam the fusion pore, or else fully zippered in the cis configuration near the waist, Figure 6A (Wu et al., 2017b). The model accounts for the SNARE zippering energy which favors full zippering (Gao et al., 2012; Ma et al., 2015), and for crowding interactions among zippered SNAREs which favor partial unzippering into the trans state, an entropic effect (Wu et al., 2017b; Mostafavi et al., 2017).

Figure 6. — (A) Schematic of model. The membrane free energy has contributions from membrane tension and bending energy. SNARE complexes may be unzippered and free to roam laterally, or zippered and confined to the pore waist. Crowding among zippered SNARE complexes generates entropic forces that tend to enlarge the pore (top view, shown lower right). The Syt1 C2B domain (green ellipsoid) has a SNARE-binding region, a polybasic patch and Ca²⁺-binding loops. (B) Free energy-minimizing fusion pore shapes determined by solving the membrane shape equation in the presence and absence of constraints applied by the SNARE-C2B complex (see Appendix 1). The C2B calcium-binding loops may either be unburied (top panel) or buried (lower panel) in the membrane. In the buried state the SNARE complex tilts upwards, expanding the fusion pore. The membrane shape constraint is evaluated using the SNARE-C2B complex crystal structure in a space filling representation. Both upper and lower panels depict situations in the presence of Ca²⁺. The model predicts the tilted configuration is strongly favored at high $[C a^{2 +}]$ following equilibration, while the untilted configuration is relevant to the kinetics that establish this equilibrium, and to experiments using low $[C a^{2 +}]$ . VAMP2, syntaxin, SNAP25 and the C2B domain are shown blue, red, yellow, and green, respectively. The C2B hydrophobic membrane-inserting residues (V304, I367), polybasic patch (K326, K327) and SNARE-binding region (R398, R399) are shown orange, cyan, and purple, respectively. The protein structure was generated with PyMOL (Schrodinger, LLC, 2015) using the SNARE-C2B crystal structure (PDB ID 5ccg) (Zhou et al., 2015). The TMD of the SNARE complex (PDB ID 3hd7) (Stein et al., 2009) was incorporated using UCSF chimera software (Pettersen et al., 2004). (C) Model-predicted free energy and experimental apparent free energy versus pore radius without calcium and in the presence of excess calcium. (D) Model-predicted normalized conductances shown with experimentally measured values for comparison. Experimental data taken from Figure 2B experiments including Ca²⁺ and PI(4,5)P₂. (E) Pore dilation mechanism emerging from the model. Under conditions of low calcium concentration, the C2B domain is unburied, the SNARE complex lies parallel to the membrane and the membrane separation is set by the maximum thickness of the SNARE-C2B complex. At high calcium concentrations, the calcium binding loops penetrate the plasma membrane, rotating the C2B domain and the entire SNARE-C2B complex which exerts force (red arrows) on the upper and lower membranes of the fusion pore in a lever-like action. These forces increase the fusion pore height, which is coupled by membrane energetics to fusion pore dilation.

Syt1 C2B domains are assumed bound to each SNARE complex at the so-called primary interface identified in recent crystal structures (Zhou et al., 2015; Zhou et al., 2017; Wang et al., 2016; Figure 3A). For simplicity, we first consider only the C2B domain in our model. When Ca²⁺ is bound to the C2B domain loops, the loops may be buried or unburied in the membrane with a relative probability that depends on the calcium concentration according to the Hill equation (Bai et al., 2004a; Radhakrishnan et al., 2009). We use a Hill coefficient of 2.3, and the measured affinity of calcium for Syt1 in the presence of PI(4, 5)P₂-containing membranes (Bai et al., 2004b). Without calcium, the loops are assumed unburied.

Thus, in the presence of calcium, the model permits two configurations of the SNARE-C2B complex, implemented according to the crystal structure (PDB ID 5ccg [Zhou et al., 2015]), Figure 6B. (1) With bound Ca²⁺, the C2B complex can be in the buried state, in which the C2B polybasic patch lies ~ 0.5 nm from the membrane (Kuo et al., 2011) and the C2B domain is anchored to the membrane by its calcium-binding loops, reported to penetrate ~ 1 nm deep (Herrick et al., 2006). With these constraints, the SNAREpin is forced to tilt its C-terminus 'upwards', see Figure 6B; precise implementation of the constraints shows that the C2B anchoring tilts the SNAREpin upwards at ~15° to the plasma membrane, imposing a significant constraint on the shape of the fusion pore. We determined whether a given fusion pore geometry satisfied these constraints by directly comparing the structure of the SNARE-C2B complex with the shape of the fusion pore (see Appendix 1). Only fusion pores satisfying the shape constraints were accepted as possible pores. (2) With no bound calcium, the C2B polybasic patch (Kuo et al., 2009) and the SNAREpins orient parallel to the plasma membrane. In this configuration, the SNARE-C2B complex imposes no constraints on the shape of the fusion pore. This unanchored state is also accessible when calcium is bound, with a probability that decreases with increasing calcium concentration.

Given the microscopically long pore lifetimes of seconds, we assumed the fusion pore-SNARE-Syt1 system has sufficient time to equilibrate. For a given pore radius, $r_{p o}$ , we calculated the free energy by summing over all allowed SNARE-C2B configurations and all possible numbers of zippered SNAREs. Each state in this sum is weighted by its Boltzmann factor, yielding the free energy $U (r_{p o})$ and pore size distribution $\sim \exp [- U (r_{p o}) / k_{B} T]$ . We assumed that the pore height is equal to the value that minimizes the free energy at a given radius $r_{p o}$ , since other heights have small probability as the free energy increases rapidly as a function of pore height. The predicted free energy profiles with and without calcium are close to the experimental profiles, as shown in Figure 6C. We compared model and experimental free energies up to a maximum pore size of 4 nm, since sampling for larger pores was limited in the experiments. In agreement with experiment, introduction of calcium is predicted to increase the pore size fluctuations, as reflected by the broader distribution. From these pore size statistics, we calculated mean pore sizes and conductances. In the absence of calcium, the model predicts a mean fusion pore radius ~0.9 nm and a mean height ~9.0 nm, due to entropic crowding effects among cis SNARE complexes (Wu et al., 2017b), Appendix 1—figure 8. These crowding effects expand the pore relative to the SNARE-free case, since a bigger pore increases the entropy of cis-SNAREs at the waist by providing more space.

When Ca²⁺ is introduced at high saturating concentrations, the model predicts a ~1.4-fold increase of pore radius to ~1.3 nm, or a ~2.3-fold increase in conductance, close to the experimentally measured ~2.2-fold increase (Figure 6D). The pore expansion mechanism is the constraint on the pore shape imposed by the SNARE-C2B complex. At low pore radii, the SNARE-C2B complex acts as a membrane inclusion that increases the height of the fusion pore, forcing the pore to adopt energetically unfavorable shapes, biasing the system toward large pore radii (Figure 6B,E, Figure S8C). Due to membrane bending and tension, the fusion pore resists the lever action tending to increase its height and enlarge the pore. However, these resistance forces are insufficient to rotate the SNARE-C2B lever complex and undo its pore-enlarging action, since this would require unanchoring of the Ca-binding loops from the membrane or dissociation of the SNARE-C2B domain binding interface. Both of these are sufficiently energetically unfavorable (Ma et al., 2017; Zhou et al., 2017) to overcome the fusion pore resistance forces (see Appendix 1 for a detailed discussion). Figure 6D shows the predicted increase of normalized pore conductance in elevated Ca²⁺ concentrations, compared with the experimental values. In summary, our model suggests a mechanism in which the SNARE-C2B complex is a calcium-triggered mechanical lever that enlarges the fusion pore in cooperation with entropic forces generated by SNARE complexes (Figure 6E). On addition of Ca²⁺, the C2B domain rotates and inserts its calcium binding loops into the membrane, tilting the SNARE complex so that it pushes the membrane surfaces further apart in a lever action. Since this increase in pore height would otherwise increase the net membrane bending energy, the pore diameter increases to offset this penalty (see Appendix 1).

Discussion

Membrane fusion occurs in stages. First, membranes are brought into close apposition to overcome repulsive hydration forces. Second, a small, nascent fusion pore forms, connecting the fusing membranes. Third, the initial small pore expands to allow passage of cargo molecules (Karatekin, 2018; Sharma and Lindau, 2018; Chang et al., 2017). Among different stages of membrane fusion, pore expansion can be energetically one of the costliest (Jackson, 2009; Cohen and Melikyan, 2004; Chizmadzhev et al., 1995; Ryham et al., 2013; Nanavati et al., 1992). Consistent with this notion, fusion pores connecting protein-free lipid bilayers fluctuate, flicker open-closed, and eventually reseal unless external energy is supplied in the form of membrane tension (Chanturiya et al., 1997), while the initial fusion pore during biological membrane fusion is a metastable structure whose dynamics are regulated by cellular processes (Sharma and Lindau, 2018; Chang et al., 2017; Alabi and Tsien, 2013; Collins et al., 2016; Fulop et al., 2005; Staal et al., 2004; D'Agostino et al., 2018; Doreian et al., 2009; Barg et al., 2002; Hanna et al., 2009; MacDonald et al., 2006).

Syt1 is involved in both the pore opening and pore expansion stages during calcium-triggered exocytosis. Before membrane fusion, Syt1 was proposed to regulate membrane apposition (Rothman et al., 2017; Chang et al., 2018; van den Bogaart et al., 2011; Seven et al., 2013; Lin et al., 2014), preventing fusion pore opening at low calcium by maintaining the membranes >5–8 nm apart, halting complete SNARE zippering. Upon calcium binding to Syt1, this distance is reduced to <5 nm (Chang et al., 2018), sufficient for SNAREs to complete their zippering and initiate fusion. Other mechanisms, such as calcium-dependent release of an inhibition of complete SNARE assembly by Syt1 (Brunger et al., 2018b), or concerted action of an oligomeric complex containing Syt1, SNAREs, and additional proteins (Bello et al., 2018; Tagliatti et al., 2020), have also been proposed for the pore opening stage. It has also been proposed that during this stage, curvature generation by insertion of Syt1’s hydrophobic loops into the membranes may contribute to pore opening (Lynch et al., 2008; Martens et al., 2007; Hui et al., 2009).

After fusion pore opening, Syt1 contributes to the dilation of the nascent fusion pore (Wang et al., 2006; Lynch et al., 2008), but the mechanisms for this regulation have remained even less clear. Several Syt1-independent mechanisms regulating fusion pore dynamics have recently emerged. First, membrane tension promotes fusion pore dilation during exocytosis, often through cytoskeleton-plasma membrane interactions (Bretou et al., 2014; Kozlov and Chernomordik, 2015; Wen et al., 2016). Second, neuronal/exocytic SNARE proteins promote fusion pore dilation by providing entropic forces due to molecular crowding at the pore’s waist (Wu et al., 2017b), consistent with the observation that increased SNARE availability results in larger, or faster expanding pores (Bao et al., 2018; Wu et al., 2017b; Acuna et al., 2014; Guček et al., 2016; Zhao et al., 2013). Third, during yeast vacuole-vacuole fusion, increased fusogen volume has been suggested as a mechanism that stabilizes fusion pores (D'Agostino et al., 2018; D'Agostino et al., 2017). However, these mechanisms cannot explain fusion pore dilation during exocytosis, because none are calcium-dependent, in contrast to exocytic fusion pore expansion (Wang et al., 2006; Hartmann and Lindau, 1995; Fernández-Chacón and Alvarez de Toledo, 1995; Scepek, 1998). Previous reconstituted single-pore measurements by Lai et al., 2013 and Das et al., 2020 found Syt1 and calcium promoted expansion of SNARE-mediated fusion pores. In the former study, pores were detected indirectly through passage of large probe molecules (Lai et al., 2013), while the latter study reported that the larger, stable pores formed in the presence of Syt1, calcium and PI(4,5)P₂ could be closed by dissociation of the SNARE complexes by the ATPase NSF, but not by a soluble cytoplasmic fragment of the v-SNARE VAMP2 (Das et al., 2020). However, the mechanism of fusion pore dilation remained unclear.

Here, we found that Syt1 has roles in both fusion pore formation and dilation, consistent with studies in secretory cells (Wang et al., 2006; Lynch et al., 2008) and in previous reconstitutions (Lai et al., 2013; Das et al., 2020), and we focused on pore dilation mechanisms. Syt1 promotes expansion of SNARE-induced fusion pores in a calcium- and acidic lipid-dependent manner. When PI(4,5)P₂ is present, increasing free Ca²⁺ leads to pores with larger mean open-pore conductance. Fusion pore expansion by Syt1 also likely relies on Syt1's interactions with the neuronal SNARE complex, because when we used C2AB domains with mutations (R398Q,R399Q) designed to disrupt the 'primary' interaction interface with the SNARE complex (Zhou et al., 2015; Zhou et al., 2017), the pore dilation function of Syt1 C2AB was largely reduced (Figure 3). The same mutations were previously shown to greatly reduce evoked release from hippocampal neurons (Chang et al., 2018; Zhou et al., 2015; Xue et al., 2008), possibly by disrupting the interaction of Syt1 C2B with SNAREs (Chang et al., 2018; Zhou et al., 2015). The most relevant interactions in which these residues engage is however not completely resolved, so results of mutagenesis of these residues must be interpreted with caution. For example, this mutation did not have a significant effect in the co-IP experiments of Syt1 with SNAREs (Zhou et al., 2015), but it did have substantial effects on the ability of Syt1 C2B to bridge two membranes (Xue et al., 2008). In addition, in the presence of polyvalent ions such as Mg²⁺ and ATP, Syt1 was found not to bind to SNAREs (Park et al., 2015), but ATP did not have any effect in a tethered-liposome fusion assay (89). Later work by Wang et al., 2016 examined these interactions in the presence of membranes and SNARE complexes, and suggested that the C2B (R398 R399)–SNARE complex interaction is Ca²⁺ independent ( $K_{d} < 1$ μM in the presence of PI(4,5)P₂ in the membranes), stronger than the C2B (R398 R399)–acidic lipid interactions, persists during insertion of the Ca²⁺-binding loops into the membrane, and occurs simultaneously with the calcium-independent interactions of the C2B polybasic patch with PI(4,5)P₂ containing membranes. Wang et al. showed ATP/Mg²⁺ does not disrupt Syt1-SNARE complex interactions in the absence of Ca²⁺, but the effect was not tested in the presence of Ca²⁺ (Wang et al., 2016). Thus, although the most likely interpretation is that mutation of R398,R399 disrupts Syt1 C2B-SNARE complex binding through the primary interface, other possibilities cannot be excluded.

A mathematical model suggests the major contribution of Syt1 to pore dilation is through its mechanical modulation of the fusion pore shape. Syt-SNARE complexes introduce non-local constraints on the fusion pore shape, making larger pores more energetically favorable. How does the non-local constraint come about? Previous work showed calcium binding to isolated Syt1 C2 domains leads to insertion of the hydrophobic residues at the tips of both of the the calcium-binding loops into the membrane (Chapman, 2008; Herrick et al., 2006; Kuo et al., 2009; Bradberry et al., 2019) (however, see Bykhovskaia, 2021). In the presence of PI(4,5)P₂, calcium-bound C2B assumes a conformation in which its long axis is tilted with respect to the membrane normal, as it interacts with the membrane simultaneously through its calcium binding loops and the polybasic patch (K324-327) bound to PI(4,5)P₂ (Kuo et al., 2011; Pérez-Lara et al., 2016). When present, C2B also binds the t-SNAREs Stx1 and SNAP25, with its long axis parallel to the SNARE bundle, in a calcium-independent manner (Zhou et al., 2015; Wang et al., 2016). In this orientation, the polybasic patch on C2B (K324-327) is free to interact with acidic lipids on the target membrane (Zhou et al., 2015). At low, resting amounts of calcium, the calcium-free SNARE-C2B complex is therefore expected to lie parallel to the membrane, with the C2B domain simultaneously interacting with target membrane acidic lipids and the SNARE complex (Zhou et al., 2015; Figure 6). By contrast, in the presence of high calcium, the calcium-bound C2B domain will tend to reorient such that its hydrophobic top loops insert into the target membrane, resulting in a tilting of the SNARE complex of ~15 degrees, which alters the pore shape (Figure 6). The resultant pore size increase quantitatively accounts for the conductance increase in the presence of Syt1, and its requirements for intact calcium- and SNARE-binding regions on C2B. At intermediate calcium levels, the mean pore radius is expected to have an intermediate value, as the Syt1 molecules would be activated by calcium for a fraction of the time only. Thus, our results may explain why initial fusion pore size and its expansion rate increase as intracellular calcium increases (Wang et al., 2006; Lynch et al., 2008; Hartmann and Lindau, 1995; Fernández-Chacón and Alvarez de Toledo, 1995; Scepek, 1998). In addition, regulation of the fusion pore shape including interbilayer distance may be a general mechanism to stabilize fusion pores against re-closure, as a similar mechanism was observed during yeast vacuole-vacuole fusion (D'Agostino et al., 2018; D'Agostino et al., 2017).

Mutations of the hydrophobic residues at the tips of the calcium-binding loops of the C2 domains (M173, F234, V304, and I367) designed to increase or decrease the affinity of Syt1 for calcium-induced membrane binding were previously interpreted largely in terms of the ability of these mutants to generate membrane curvature. Indeed, the rates of fusion between liposomes (Martens et al., 2007; Hui et al., 2009) and exocytosis (Lynch et al., 2008; Rhee et al., 2005) correlate well with the curvature-generation ability of the Syt1 mutants. By contrast, here the correlation between the curvature-generation ability of the mutants and pore expansion was not strong, with the 4W mutant with enhanced membrane tubulation activity (Lynch et al., 2008; Martens et al., 2007) having a similar effect as wild-type C2AB. Modeling supported the idea that curvature-generation by Syt1 membrane penetration is not needed to explain how Syt1 promotes pore expansion.

We also explored how Syt1 affects pore dilation kinetics as a function of calcium. We found pore expansion rate increases with increasing [Ca²⁺]_free, with a similar dependence on calcium as the mean open-pore conductance (Figure 4A,D), from ~3–12 nS/s at low calcium (0–30 μM), to 20–25 nS/s at high calcium (40–100 μM). Modeling suggests the C2A domain of Syt1 is critical for rapid expansion of the fusion pore, by contributing to the total binding energy of Syt1 C2 domains to acidic membranes. By comparison, in secretory cells the pore opens suddenly (Breckenridge and Almers, 1987) before continuing to expand at a slower rate. In horse eosinophils stimulated by intracellular application of GTP-γ-S, pores were found to expand, on average, at 19 nS/s, 40 nS/s, and 89 nS/s at low (<10 nM), 1.5 μM, and 10 μM Ca²⁺, respectively (Hartmann and Lindau, 1995), consistent with a later study (Scepek, 1998). Pore expansion rates were 5–10 nS/s for rat mast cells, with higher rates at high calcium (Fernández-Chacón and Alvarez de Toledo, 1995), and varied from 15 to 50 nS/s for bovine chromaffin cells (Fang et al., 2008; Berberian et al., 2009; Dernick et al., 2005). Lower rates (~7 nS/s) were observed in excised patch recordings (Dernick et al., 2005). A rate of ~98 nS/s was reported for rat chromaffin cells overexpressing myosinII (Neco et al., 2008). These pore expansion rates, and the increasing rates with increasing calcium, are remarkably consistent with our findings.

Our findings also recapitulate the observation that during exocytosis, fusion pore fluctuations increase with intracellular calcium (Zhou et al., 1996). A mathematical model suggests that this originates in the cooperative mechanical effects of Syt1 and SNAREs which exert outward expansive forces on the fusion pore. These forces oppose the inward force that results from the intrinsic tendency of the protein-free fusion pore to close down due to membrane bending and tension effects (Wu et al., 2017b). The net inward force is thus lowered, leading to a broader distribution of pore sizes and bigger fluctuations.

In several neuronal preparations, the maximal rate of secretion scales as ${[C a^{2 +}]}_{i}^{n}$ with $n \approx 4$ (Schneggenburger and Neher, 2000; Schneggenburger and Neher, 2005; Dodge and Rahamimoff, 1967; Sun et al., 2007; Kochubey et al., 2011; Heidelberger et al., 1994), while in our system the mean open pore conductance or the rate of fusion pore expansion (Figure 4A,D) are consistent with a Hill relationship with cooperativity ~2 and calcium affinity ~20 μM, taken from studies of purified recombinant Syt1 C2AB binding to lipid bilayers (Bai et al., 2004b). There are several reasons for these differences. Most importantly, the maximal rates of secretion measured in neurons or neuroendocrine chromaffin cells is due to the rapid fusion of a pool of docked and primed vesicles called the readily releasable pool (RRP) (Kaeser and Regehr, 2017; Sørensen, 2004; Rizzoli and Betz, 2005). Vesicles acquire fusion-competence at low, resting calcium levels (≲0.1 μM). When the calcium concentration near release sites increases rapidly in response to stimulation, fusion from the RRP ensues within milliseconds. Docking (~30 s) and priming (~10 s) are much slower events (Kaeser and Regehr, 2017; Sørensen, 2004) and require tethering and priming factors such as Munc13 and Munc18 (Brunger et al., 2018a; Rizo, 2018). There is no RRP or its equivalent in our assay: nanodiscs dock and fuse with the target cell membrane under a constant calcium level throughout the measurement and key components of the docking and priming machinery such as Munc13 and Munc18 are absent in our minimalistic reconstitution. Thus, the steep calcium-dependence of the maximal rate of RRP secretion observed in neurons is not directly comparable to the fusion pore opening or expansion kinetics in our assay in which discs fuse with the target membrane under conditions of constant calcium levels, very low fusion rates, and absence of docking and priming factors.

The nanodisc-cell fusion assay is tuned for sensitivity to post-fusion stages. Unfortunately, like other electrical or electrochemical methods that generate a signal only after fusion pore opening, our assay cannot directly detect pre-fusion stages. In particular, the delay between docking and fusion of nanodiscs, and the molecular configurations leading to the opening of the initial fusion pore are currently not known. Until a better understanding of such pre-fusion stages is achieved, our post-fusion studies should be interpreted with care. Another, possibly related, limitation is that due to the small numbers of proteins that can be incorporated into nanodiscs, large fluctuations are expected in the actual copy numbers from disc-to-disc. Such fluctuations likely contribute to the variability observed in our single-pore measurements, for example, of mean conductance values. A detailed discussion of the relevance and limitations of nanodisc-based single pore measurements in relation to exocytotic fusion pores monitored in secretory cells can be found in Karatekin, 2018.

In neurons and many neuroendocrine cells, fusion is triggered by a brief calcium transient. The finding that fusion pore dilation is calcium sensitive suggests that the pore size, expansion rate, and duration can be modulated by calcium dynamics. Thus, weak stimulations that result in brief calcium transients would be more likely to lead to small fusion pores and slow release, and strong stimulations would conversely result in larger and faster dilating pores. This behavior is indeed observed in neurons (Pawlu et al., 2004), and in neuroendocrine cells (Fulop et al., 2005; Cárdenas and Marengo, 2016). In this framework, different Syt isoforms would affect fusion pore dynamics differently, depending on their ability to reorient with respect to the membranes, their interactions with the SNAREs, and their calcium affinities.

Materials and methods

Recombinant protein expression and purification

Expression and purification of the constructs used are described in Appendix 1, Supplementary Materials and methods.

Reconstitution of synaptotagmin-1 and VAMP2 into nanodiscs

Eight copies of VAMP2 (~four per face) were incorporated into nanolipoprotein particles (vNLP8) as previously described (Wu et al., 2016; Wu et al., 2017b; Bello et al., 2016). The protocol was modified to produce nanolipoprotein particles co-reconstituted with full-length Syt1 and VAMP2 (vsNLP), as detailed in Appendix 1, Supplementary Materials and methods.

Stable flipped SNARE cell lines

Single fusion pore conductance assay

All recordings were done as previously described (Wu et al., 2016; Wu et al., 2017b), and detailed in Appendix 1, Supplementary Materials and methods. Estimations of fusion rates and pore properties are explained in Appendix 1, Supplementary Materials and methods, along with evidence that ATP-dependent channel activity is absent and that cell membrane potential changes are negligible during recordings.

Statistical analysis

Details are given in Appendix 1, Supplementary Materials and methods, and in figure legends.

Acknowledgements

We thank Ekaterina Stroeva and Shyam Krishnakumar (Rothman Laboratory, Yale University) for help with reconstitution of full-length Syt1 into nanodiscs. This work was supported by National Institute of General Medical Sciences, National Institute of Neurological Disorders and Stroke, and the National Eye Institute of the National Institutes of Health under award numbers R01NS113236 and R01EY010542 (to EK) and R01GM117046 (to BOS). The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health. We acknowledge computing resources from Columbia University’s Shared Research Computing Facility project. We thank Rui Su and members of the Karatekin lab for helpful discussions.

Appendix 1

Recombinant protein expression and purification

All SNARE and Synaptotagmin-1 constructs used were generous gifts from James E. Rothman, unless noted otherwise. Plasmid pET32a-Trx-His6X-ApoE422K, used to express the N-terminal 22 kDa fragment of apolipoprotein E4 (residues 1–199, ApoE422K), was kindly provided by Dr. Nicholas Fischer, Lawrence Livermore National Laboratory, CA (Morrow et al., 1999; Blanchette et al., 2008). Full-length VAMP2 (residues x1-116 in plasmid pET-SUMO-VAMP2) and ApoE422K were expressed and purified as previously described (Wu et al., 2016; Wu et al., 2017b). Rat Syt1 residues 96–421 corresponding to cytoplasmic C2AB domains were expressed from a pET28a-SUMO-synaptotagmin1 vector. C2AB^R398,399Q, C2AB^D309N and C2AB^K326,327A were generated from the wild-type sequence using the QuickChange site-directed mutagenesis kit (Stratagene, La Jolla, CA). C2AB^4W and C2AB^4A were prepared using QuikChange Multi Site-Directed Mutagenesis Kit (Stratagene, La Jolla, CA). Wild-type C2AB and all mutated versions of C2AB were expressed in BL21 (DE3) and purified as previously reported (Ma et al., 2017). Full-length Syt1 (pET28a-SUMO-synaptotagmin 1, residues 57–421) was expressed in BL2 (DE3) at 37°C to optical density 0.8 (at 600 nm) and induced with 1 mM isopropyl β-D-thiogalactoside (IPTG) for 4 hr. Cells were then lysed by a cell disruptor (Avestin, Ottawa, CA) and lysates were clarified by centrifugation (35,000 rpm at 4°C for 30 min using a Beckman-Coulter Ti45 rotor and 70 ml polycarbonate tubes, corresponding to 142,160 × g). The supernatant was incubated with Ni-NTA agarose (Qiagen, Valencia, CA) overnight at 4°C. Protein-bound beads were washed by buffer A (25 mM HEPES, pH 7.4, 400 mM KCl, 0.5 mM tris-2-carboxyethyl phosphine [TCEP]) supplemented with 50 mM imidazole and 1% Octylglucoside (OG). The protein was first separated from beads using buffer A supplemented with 400 mM Imidazole and 4% OG. Then the His-SUMO tag was cleaved by SUMO proteinase at 4°C for 2 hr. The protein was diluted four times by dilution buffer (25 mM HEPES, 0.5 mM TCEP and 4% OG) and then immediately loaded into Mono S5/50G column (GE Healthcare Bio-Sciences, Pittsburgh, PA). The full-length Syt1 was washed out by high-salt buffer (25 mM HEPES, 1 M KCl, 0.5 mM TCEP and 1% OG). After concentration determination using the Bradford assay (Bio Rad, Hercules, CA), the samples were aliquoted, flash frozen by plunging into liquid nitrogen, and stored at −80°C for future use.

Co-reconstitution of Synaptotagmin-1 and VAMP2 into nanolipoprotein particles (NLPs)

Eight copies each of VAMP2 and full-length Synaptotagmin-1 (Syt1) (~four per face each) were incorporated into nanolipoprotein particles (vsNLP8) following previous protocols for reconstitution of VAMP2 alone (Wu et al., 2016; Wu et al., 2017b; Bello et al., 2016). A mixture of palmitoyl-2-oleoylphosphatidylcholine (POPC) and 1,2-dioleoyl phosphatidylserine (DOPS) (85:15 molar ratio) dissolved in a chloroform-methanol mixture (2:1 by volume) was dried under nitrogen flow, then placed under vacuum for 2 hr. All lipids were purchased from Avanti Polar Lipids (Alabaster, AL). The lipid film was re-suspended in 25 mM HEPES, pH 7.4, 140 mM KCl, 1 mM TCEP buffer with 1% OG supplemented by the desired amount of full length syt1 and VAMP2. The mixture was vortexed for 1 hr at room temperature followed by the addition of ApoE422K and vortexed for another half hour at room temperature and then 3 hr at cold room. The ApoE422K:VAMP2: syt1: lipid ratio for vsNLPs was 1:2:2:180. Excess detergent was removed using SM-2 bio-beads (Bio-Rad) overnight at 4°C with gentle shaking. The assembled vsNLPs were purified using size-exclusion chromatography using a Superose 6, 10/300 GL column (GE Healthcare Bio-Sciences, Pittsburgh, PA). Collected samples were concentrated using Amicon Ultra (30 KDa cutoff) centrifugal filter units, and analyzed by SDS-PAGE with Coomassie staining. The size distribution of the NLPs was determined for every batch of production using transmission electron microscopy (JEM-1400, JEOL, MA, USA). This allowed estimating the average number of ApoE copies per disc as before (Wu et al., 2017b; Bello et al., 2016), using previously published information about the number of ApoE copies as a function of disc size (Blanchette et al., 2008). The copy numbers of Syt1 and VAMP2 per disc were then estimated from the quantification of Syt1- or VAMP2-to-ApoE ratio using densitometry (ImageJ, NIH).

Stable flipped SNARE cell lines

Stable ‘tCell’ HeLa cell lines expressing flipped t-SNAREs (rat Syntaxin-1, residues 186–288, and rat SNAP-25, residues 2–206) and the nuclear marker CFP-nls (cyan fluorescent protein fused to nuclear localization signal) were a generous gift from the Rothman laboratory (Giraudo et al., 2006) and cultured as previously reported (Wu et al., 2016; Wu et al., 2017b). Mycoplasma contamination was reported and tested not to affect the results in Wu et al., 2017b. Note that the as long as the cells express flipped t-SNAREs on their surfaces (which was quantified in the references above), they fuse with membranes harboring the cognate v-SNAREs. In fact, fusion was reported with other cell lines (e.g. CHO or HEK under transient expression of flipped SNARE constructs. e.g. see Hu, 2003). The flipped SNARE constructs used in the generation of these lines, pBI-flipped Syntaxin-1 (186–288)-flipped SNAP-25-IRES-CFP-nls, are schematically shown in Appendix 1—figure 1I (Giraudo et al., 2006; Giraudo et al., 2005). The pBI expression vector is a bidirectional mammalian expression vector of the Tet-Off gene expression system that allows co-regulation of the synthesis of two gene products in stoichiometric amounts (Baron et al., 1995). The cells were cultured in DMEM (4500 mg/L glucose, L-glutamine, sodium pyruvate, and sodium bicarbonate) and 10% (v/v) fetal calf serum at 37°C.

PI(4,5)P₂ incorporation and immunostaining

Where indicated, short-chain diC8-PI(4,5)P₂ (Echelon Biosciences Inc, Salt Lake City, UT) (1 mM stock solution, dissolved in water), was added to the cell culture medium to a final concentration of 20 μM and incubated 20 min at 37°C. Cells were then washed three times using extracellular buffer (ECS: 125 mM NaCl, 4 mM KCl, 2 mM CaCl₂, 1 mM MgCl₂, and 10 mM HEPES, pH adjusted to 7.2 with NaOH and 10 mM glucose added freshly).

For assessing diC8-PI(4,5)P₂ incorporation into the outer leaflet of the plasma membrane and lifetime, after 20 min incubation with the lipid, cells were rinsed thoroughly with phosphate buffered saline (PBS) supplemented with 10% goat serum, and kept at 37 °C with the same solution for different durations. Mouse monoclonal anti-PI(4,5)P₂ primary antibodies (Echelon Biosciences Inc, Utah) were added to the cells at time points of 0, 40, and 80 min and incubated 1 hr at 37°C. Then cells were fixed with 4% paraformaldehyde (Electron Microscopy Sciences, PA) for 20 min at room temperature before addition of goat anti-mouse IgM heavy chain secondary antibody conjugated with Alexa Fluor 647. Control cells that were not incubated with diC8-PI(4,5)P₂ were treated similarly and fixed by 4% paraformaldehyde. Some cells were then permeabilized by 0.5% saponin (Sigma, MO) to allow access of the antibody to the inner leaflet of the plasma membrane where endogenous PI(4,5)P₂ resides. Cells were blocked for 30 min with PBS supplemented with 10% goat serum, followed by incubation with anti-PI(4,5)P₂ primary antibody for 1 hr at 37°C. After three successive washes in PBS, cells were incubated with the secondary antibody as above. All groups of cells were washed three times with PBS and mounted on a glass slide with mounting medium (ProLong Gold Antifade Mountant with DAPI, Molecular Probes, OR). Fluorescence images were collected using a spinning disk confocal microscope (model TiE, Nikon, Japan, equipped with a Yokogawa CSU-W1 spinning disc head and CFI Plan Apochromat Lambda 60x/1.4 oil immersion objective). Images were analyzed using ImageJ software. We drew a region of interest (ROI) around cells using the freehand ROI tool and measured the mean pixel intensity in the ROI. We then subtracted the intensity from a nearby region not containing any cells to define the background subtracted pixel intensity to define $Δ F$ in Figure 1B. For each condition, 10 regions of interest encompassing cells were analyzed from three to six independent preparations.

Whole-cell conductance of flipped t-SNARE cells

We measured whole-cell current responses to step changes in membrane potential under voltage-clamp, from HeLa cells stably expressing flipped t-SNAREs (Figure S11A). Currents were averaged for 27 cells and plotted against voltage (Figure S11B). Pipettes were filled with intracellular solution (in mM): 134 KCl, 2 MgCl₂, 1 CaCl₂, 10 HEPES and 10 EGTA (pH is adjusted to 7.2 by KOH).

Single fusion pore conductance assay

All recordings were done as previously described (Wu et al., 2016; Wu et al., 2017b). Briefly, a dish with cultured tCells was rinsed using ECS, then mounted on a Thermo-Plate (Tokai Hit, Shizuoka-ken, Japan) pre-set to 37°C. tCells were visualized with an inverted Olympus IX71 microscope (Olympus Corp., Waltham, MA) using a ThorLabs USB3.0 digital camera (UI-3240CP-NIR-GL-TI) controlled by ThorCam software (ThorLabs, Newton, NJ). Recording pipettes (borosilicate glass, BF 150-86-10, Sutter Instruments, Novato, CA) were pulled using a model P-1000 pipette puller (Sutter Instruments, Novato, CA) and polished using a micro-forge (MF-830, Narishige, Tokyo, Japan). The pipette solution (PipSol) contained: 125 mM NaCl, 4 mM KCl, 1 mM MgCl2, 10 mM HEPES, 26 mM TEA-Cl, 2 mM ATP (freshly added), 0.5 mM EGTA, pH adjusted to 7.2 by NaOH and the indicated free calcium (0–500 μM) was adjusted by 0.1 M Calcium Standard Solutions (Thermo Fisher Scientific, Waltham, MA). Free calcium was calculated using MaxChelator (https://somapp.ucdmc.ucdavis.edu/pharmacology/bers/maxchelator/CaMgATPEGTA-TS.htm) taking into account ATP, Mg²⁺, ionic strength, temperature, and pH. The pipette was pre-filled by PipSol and then back filled with PipSol supplemented with nanodiscs with or without additional C2AB. All voltage-clamp recordings were made using a HEKA EPC10 Double USB amplifier (HEKA Elektronik Dr. Schulze GmbH, Lambrecht/Pfalz, Germany), controlled by Patchmaster software (HEKA). Current signals were digitized at 20 kHz and filtered at 3 kHz. The recording traces were exported to MatLab (MathWorks, Natick, MA) and analyzed as previously described in detail (Wu et al., 2016; Wu et al., 2017b).

Detection of fusion pore currents

As described previously (Wu et al., 2016; Wu et al., 2017b; Dudzinski et al., 2019), the pipette tip was initially filled with ~1 μl of disc-free buffer and back-filled with NLPs suspended in the same buffer (final [NLP] ≈ 100 nM, 120 μM lipids). This allowed establishing a tight seal ( $R_{s e a l} > 10$ GOhm) with high success rate and recording a stable baseline before the NLPs diffused to the membrane patch and started fusing with it a few to several min later. All cell-attached recordings were performed using a holding potential of $V_{p} = - 40$ mV relative to bath. With a cell resting membrane potential of 56±7 mV (mean ± S.D., n=36 Wu et al., 2016), this provided 16 mV driving force across the patch membrane. The pipette solution had resistivity 0.60 Ohm.m, measured using a conductivity cell (DuraProbe, Orion Versa Star, Thermo Scientific).

After a good seal was established on a cell, currents were recorded under voltage-clamp for 800 s, in 40 s sweeps, with a sampling rate of 20 kHz using a HEKA EPC10 Double USB amplifier (HEKA Elektronik), controlled by Patchmaster software (HEKA). The analysis pipeline started with initial off-line inspection of the traces in PatchMaster. Traces with activity were exported to Matlab (Mathworks, Natick, MA) where they were analyzed in more detail using an interactive graphical user interface we developed to help identify, crop and process single fusion pore currents (Wu et al., 2016; Wu et al., 2017b; Dudzinski et al., 2019). Traces with excessive noise or unstable baseline were excluded from analysis. Exported traces were low-pass filtered (280 Hz cutoff) and frequencies due to line voltage were removed using notch filtering. Zero phase shift digital filtering algorithms (Matlab Signal Processing Toolbox function filtfilt) were employed to prevent signal distortion. Filtered traces were averaged in blocks of 80 points (125 Hz final bandwidth) to achieve rms baseline noise ≲ 0.2 pA. Currents $I$ for which $| I |$ > 2.0 pA for at least 250 ms were accepted as fusion pore current bursts. During a burst, rapidly fluctuating currents often returned to baseline multiple times, i.e. pores flickered. To quantify pore flickering, we defined currents ≲0.2 pA and lasting ≥60 ms (15 points) as open pores and currents not meeting these criteria as closed. For a given burst, the number of open periods was equal to the number of flickers, $N_{f l i c k e r s}$ . The burst lifetime is defined as the time from the initial to the final point detected using the criteria above. Current bursts spaced >5 s apart by a quiet baseline were assigned to separate bursts, since the typical lifetime of well-isolated bursts is 5-10 s. An example of a current burst is shown in Appendix 1—figure 1J with the threshold current, detected open sub-periods, and the burst lifetime indicated. Examples of entire 800 s recordings are shown in Fig. S2. The MatLab programs used in analysis and the data are available upon request.

Estimation of fusion rate

To estimate the fusion rate for each recording (i.e. the rate at which current bursts appeared), we counted the number of current bursts that fit the set criteria (current amplitude >2 pA for at least 250 ms) and divided this number by the duration of the recording. Examples are shown in Appendix 1—figure 2A, B. These per-cell rates were averaged over all cells to estimate the average rate of fusion (‘pores/min’) and its standard deviation for a given condition. Standard error of the mean was calculated as the standard deviation divided by the square root of the number of cells. Periods during which the baseline was not stable were excluded from this analysis. For individual cells, the number of well-isolated pores varied from 0 to 22. Many recordings ended with what seemed to be currents from overlapping fusion pores (Appendix 1—figure 2B). Such end-of-record currents were also excluded, since they could also be attributed to a loose seal. Thus, the fusion rates we report may underestimate the true rates, especially for conditions where fusion activity was high.

We checked that increasing or decreasing the concentration of v-SNARE NLPs in the pipette solution increased or decreased the fusion rate, respectively. Indeed, we found there is good linear correlation between the v-SNARE NLP concentration and the fusion rate, as shown in Appendix 1—figure 2C.

As an alternative estimate of the fusion rate, for every condition, we summed all detected pores, $N_{t o t}$ , and the analysis time $τ_{t o t}$ over all cells (excluding portions with noisy/unstable baseline), and calculated the total number of pores divided by the total analysis time, ${\dot{F}}_{t o t} = N_{t o t} / τ_{t o t}$ . The results of this estimate were close to the ones described above, as shown in Appendix 1—figure 2D.

Estimation of fusion pore parameters

The number of flickers, $N_{f l i c k e r s}$ , and the burst lifetime, $T_{o}$ , were defined as explained above. The flicker rate was defined as the number of flickers divided by the burst lifetime for individual pores. The pore open probability, $P_{o}$ , is defined as the total time the pore was in the 'open' state divided by the burst lifetime, $T_{o}$ , for individual pores. We converted current to conductance by dividing every point in a current trace by the transmembrane voltage $V_{m} = V_{c e l l} {- V}_{p} = - 16$ mV, where $V_{p}$ is the pipette potential (-40 mV) and $V_{c e l l} = - 56$ mV as indicated above. To calculate the open-pore conductance, $G_{p o}$ , and its statistics, we used pore open-state values, denoted by the subscript 'po'. Similarly, we used pore open-state values to calculate the distributions of open-pore conductance values and radii. For the distributions in Figure 2C,D, S4, S6, and S7, we first computed the probability density functions (PDFs) for individual pores using a fixed bin width for all, then averaged these to give equal weight to all pores. All distribution fits (e.g. Figure S3E, F) were performed using Matlab Statistics Toolbox functions fitdist or mle, using maximum likelihood estimation. Open-pore conductance values were used point-by-point to estimate the open-pore radii, by approximating the pore as a cylinder and using the expression (Hille, 2001) $r_{p o} = {(ρ λ G_{p o} / π)}^{1 / 2}$ , where $ρ$ is the resistivity of the solution, $λ = 15$ nm is the length of the cylinder, and $G_{p o}$ is the open-pore conductance.

For assessing statistical significance when comparing sample means, we used the student's t-test when the parameters were normally distributed, or the nonparametric two-sample Kolmogorov-Smirnov test otherwise (ttest2 or kstest2, Matlab Statistics Toolbox), as indicated in figure legends. We considered each single-pore measurement a biological replicate.

Estimation of fusion pore expansion rates

For aligning and averaging conductance traces in Figure 4C, we shifted the time axis such that $t = 0$ corresponded to the first data point in a burst. We estimated pore expansion rate as the 10-90% rise time from the baseline to the level of conductance reached within the first 100 ms after pore opening, divided by the time it took for this rise using the Matlab function 'slewrate'.

As an alternative, we also fit a straight line to each of the aligned and averaged conductance rise, for the initial 16 ms of the rise, and used the slope of the line as an estimate of the pore expansion rate. Pore expansion rates estimated from these slopes as a function of [Ca²⁺] resulted is a plot very similar to the one in Figure 4D obtained using the slew rate estimate above. The differences in the slopes can be largely explained by differences in the conductance level reached within ~16 ms. After filtering and block averaging, the spacing between successive points is 4 ms in individual traces, corresponding to a Nyquist frequency of 125 Hz. That is, we should be able to faithfully reconstruct signals varying on a time scale of 8 ms or slower. However, slopes calculated over a 16 ms span are still likely to be limited by our resolution to some degree, because we cannot detect finer kinetic details during this period. Thus, the pore expansion rates we averaged over 16 ms may be underestimates of the true rates and finer details of the kinetics cannot be resolved.

No evidence for ATP-dependent channel activity in flipped t-SNARE cells

For cell-attached single-pore measurements, ATP was included in the pipette solutions. HeLa cells were reported to express ATP-dependent P2 receptors (Welter-Stahl et al., 2009). To test whether ATP-dependent channel activation is present in the flipped t-SNARE cells, we recorded currents from cell-attached, voltage-clamped patches from these cells in the absence and presence of ATP (nanodiscs were absent). Pipette solutions were the same as for single fusion pore measurements with 100 μM free calcium, except for ATP as noted. Both in the absence and presence of ATP (2 mM), we occasionally had patches that displayed channel-like activity (Figure S9). We conclude that the activity of these channels is not regulated by ATP, consistent with an earlier report (Welter-Stahl et al., 2009).

In addition, we note that the vast majority of channel-like currents as in Figure S9 are excluded from our analysis of fusion pore currents, because their lifetime is too short ( $< 250$ ms), their amplitude is too low (<-2 pA), or both, and therefore do not significantly affect our results.

Cell membrane potential changes do not significantly distort cell-attached fusion pore recordings

It has been reported that cell membrane potential may change under some conditions during cell-attached recordings (e.g. see Fenwick et al., 1982). In such recordings, the single-channel conductance $g$ is underestimated (compared to its true value $G$ ), unless $G_{c e l l} ≫ G_{p a t c h}$ , where $G_{c e l l}$ is the cell membrane conductance, and $G_{p a t c h}$ is the patch conductance (Fischmeister et al., 1986). Given that the ratio of the cell area to patch area is typically $A_{c e l l} / A_{p a t c h} > 100$ or 1000, and that membrane capacitance is proportional to membrane area, one would expect the requirement for $G_{c e l l} ≫ G_{p a t c h}$ is easily satisfied. However, for some small cells, sometimes it is found that ions passing through single channels can change the cell membrane potential, hence the potential across the patch (Fenwick et al., 1982; Hamill, 1983). The effect was found only occasionally for some cells from the same preparation, and for small cells. Fenwick et al., 1982 suggested that some local damage to the membrane patch during the formation of the gigaseal may occur in some cases.

Several lines of evidence suggest cell membrane potential changes do not significantly distort our cell-attached recordings:

If the cell membrane potential changed due to currents passing through fusion pores, such currents would depolarize the cell membrane and reduce the transmembrane voltage across the patch ( $V_{m} = V_{c e l l} - V_{p}$ ). Indeed a 15–20 mV depolarization of the cell membrane from its starting value of -56 mV would bring it close to $V_{p}$ and largely abolish the driving force $V_{m}$ for current flow across the patch. This would result in larger currents at the beginning of a pore event compared to its end, and this effect would be strongest for the condition producing the largest pores, that is, in the presence of full-length Syt1 (with calcium and PI(4,5)P₂). To test this idea, we aligned pore currents to the beginning or end of events, and averaged them, as shown in Fig. S10. We do not find large differences between averaged traces aligned either way.
The hallmark of cell membrane potential changes in single-channel recordings is ‘relaxation’ of single-channel currents when the channels open and close (Fenwick et al., 1982). In our recordings, we do not see such relaxation, even after aligning pore current to their moment of closure and averaging them as shown in Figure S10.
In whole-cell voltage-clamp recordings, we found $G_{c e l l} = 5 - 6$ nS for flipped t-SNARE cells (Fig. S11). Thus, the condition $G_{c e l l} ≫ G_{p a t c h}$ is satisfied in most of our recordings. Even in the presence of Syt1, $G_{m}$ is nearly 10 times larger than the average conductance ( $G_{p a t c h} \approx 600$ pS). The range of mean open-pore currents and transmembrane voltages comprising 95% of the data values for C2AB in the presence of PI(4,5)P₂ and 100 μM calcium are indicated as a red-colored box on Figure S11B.

Statistical analysis

For fusion rates and other parameters that were expected to follow a normal distribution, the two-sample t-test was used. For open-pore conductance, or other parameter distributions which do not follow a normal distribution, the two-sample Kolmogorov-Smirnov test was used for pair-wise comparisons. In Figure 1B we used one-way ANOVA, followed by a multiple comparison test (using the Tukey-Kramer criterion). For all statistical analyses, we used Matlab Statistics and Machine Learning Toolbox (MathWorks). Details are provided in figure legends.

Mathematical model of the fusion pore with snares and synaptotagmin-1

The shape of the fusion pore between the nanolipoprotein particle (NLP) and the tCell membrane is determined by minimizing the Helfrich energy (Helfrich, 1973); this is achieved by numerically solving the membrane shape equation with constraints fixing the pore radius $r_{p o}$ and height $h$ , defined to be the separation between the NLP and tCell membrane (see subsection Numerical method for solving the membrane shape equation). We assume that each side of the NLP contains $N$ v-SNAREs and that all are available to associate with the t-SNAREs in the tCell membrane and contribute to pore expansion. Out of $N$ SNAREs, $N_{Z}$ denotes the number of fully zippered SNAREs. For a given set of values $(r_{p o}, h, N, N_{Z})$ the total free energy of the fusion pore is

U_{t o t} (r_{p o}, h, N, N_{Z}) = U_{m b} + U_{h y d} + U_{S N A R E} + U_{s c a f f o l d},

(1)

where $U_{m b}$ , $U_{h y d}$ , $U_{S N A R E}$ , and $U_{s c a f f o l d}$ stand for the membrane energy of the pore, the energy due to hydration forces between the NLP and tCell membranes, the free energy associated with the SNAREpins, and the free energy of the deformed NLP scaffold, respectively.

Each SNARE is bound to a Syt1 C2AB domain at the primary interface between the SNARE and the C2B domain (Zhou et al., 2015). The C2AB domain calcium binding loops can be unburied or buried in the membrane with a probability that depends on calcium concentration (see 'Calcium dependent pore conductance' below). In the unburied state, the C2B polybasic patch is facing the tCell membrane and parallel to it (Kuo et al., 2009). In this orientation the C2B-attached SNARE is also roughly parallel to the membrane. In the buried state, the C2B domain anchors to the membrane by insertion of its calcium binding loops $~ 1 n m$ into the membrane (Herrick et al., 2006), and the polybasic patch is distanced $~ 0.5 n m$ from the membrane (Kuo et al., 2011). With respect to the unburied state, this configuration has a rotated C2B domain, which is attached to the SNARE complex at the primary interface, such that the SNARE complex is somewhat raised above the membrane and is concomitantly tilted by ∼15° with respect to the membrane plane (Figure 6B, main text). This tilt angle is measured by taking the inverse sine of the ratio between the SNARE motif length projected on the vertical axis of the pore and the length of the SNARE motif. Thus, the C2B domain acts as a fulcrum about which the SNARE lever pivots. This configuration imposes a geometric constraint on the pore, leading to increased pore radius and height.

We calculate the pore conductance in the absence of calcium where C2B domains are unburied and in saturating calcium levels when all C2B domain are buried, and use these values to predict the mean pore conductance as described in the subsubsection Model- predicted pore conductance below. The expressions for the different energy terms in Equation (1) are described below.

Membrane free energy

The NLP and tCell membranes are modelled as a planar bilayer with diameter $D$ and an infinite planar bilayer, respectively, and both are at a constant surface tension. The membrane free energy of the fusion pore is given by Helfrich, 1973,

U_{m b} (r_{p o}, h) = min {\int_{A_{m b}} [\frac{κ}{2} (2 C)^{2} + γ] d A}

(2)

where $κ$ is the membrane’s bending modulus, $γ$ is the membrane tension, $C$ is the local mean curvature, and the integration is taken over the area of the membrane mid plane of the pore, $A_{m b}$ . The shape of the fusion pore is determined by solving a set of differential equations whose solutions minimize the membrane energy subject to the constraints of a fixed pore height $h$ and pore radius $r_{p o}$ (see Appendix 1 subection 'Numerical method of solving the membrane shape equation'). A term associated with the Gaussian curvature is omitted throughout our analysis because it depends only on the membrane topology. We set the bending modulus to a typical value of $κ = 20 k_{B} T$ . We set the value of $γ$ to $0.1 p N {n m}^{- 1}$ , which was obtained as a best fit parameter by comparing model-predicted pore energies with results from a similar experimental setup where fusion between the tCell and the NLP was induced by SNAREs alone (4), Appendix 1—figure 8B.

Numerical method of solving the membrane shape equation

We used the MATLAB differential equation solver 'bvp4c' with an absolute tolerance of 10⁻⁶ and a relative tolerance of 10⁻⁴ to solve the membrane shape equation (MathWorks, Natick, MA). This method requires that the equation be rendered as a set of first order ordinary differential equations. The process by which we determined these differential equations is described here.

For simplicity, the fusion pore is assumed to be axisymmetric in our calculations, that is, symmetric under rotations about the $z$ -axis. Given this assumption, the membrane energy can be written

U_{m b} = \int_{0}^{2 π} d θ \int_{0}^{L} d s r (s) [\frac{κ}{2} {(2 C)}^{2} + γ] = 2 π \int_{0}^{L} d s r (s) [\frac{κ}{2} {(2 C)}^{2} + γ],

(3)

where $θ$ is the azimuthal angle, $s$ measures the arclength along a meridian of the fusion pore (i.e., a curve of constant $θ$ ), $r (s)$ is the distance of a given point on the fusion pore from the z-axis, and $L$ is the total arclength of the meridian. We add to this expression two Lagrange multiplier terms which fix the definition of $s$ as the arclength,

\begin{array}{ll} U_{m b} = 2 π \int_{0}^{L} d s & {r (s) [\frac{κ}{2} {(2 C)}^{2} + γ] + f_{r} (s) (r^{'} (s) - \cos (ϕ (s))) \\ + f_{z} (s) (z^{'} (s) - \sin (ϕ (s)))} \end{array}

(4)

where $ϕ (s)$ gives the angle between the local tangent vector to the meridian and the radially outward direction. The Lagrange multipliers $f_{r}$ and $f_{z}$ can be interpreted as the radial and vertical components, respectively, of the force exerted on a curve of constant $z$ due to membrane stress. With this parametrization, the mean curvature can be written

C = \frac{1}{2} (ϕ^{'} (s) + \frac{\sin (ϕ (s))}{r (s)}) .

(5)

Inserting this expression for the mean curvature into the membrane energy and taking the functional derivative of the membrane energy with respect to $r (s), z (s), ϕ (s), f_{r} (s),$ and $f_{z} (s)$ , we find a set of differential equations characterizing fusion pore shapes that minimize the membrane energy,

\begin{array}{cc} r^{'} (s) = \cos (ϕ (s)) \\ z^{'} (s) = \sin (ϕ (s)) \\ ϕ^{'} (s) = 2 C - \frac{\sin (ϕ (s))}{r (s)} \\ C^{'} (s) = \frac{f_{r} (s) \sin (ϕ (s)) - f_{z} (s) \cos (ϕ (s))}{2 κ r (s)} \\ f_{r}^{'} (s) = γ + 2 κ C (C - \frac{\sin (ϕ (s))}{r (s)}) \\ f_{z}^{'} (s) = 0. \end{array}

(6)

These are the Hamilton’s equations corresponding to the Lagrangian given by $U_{m b}$ , and are equivalent to the membrane shape equation. The last equation indicates that $f_{z}$ is a constant; this is associated with the assumed symmetry of the fusion pore. We therefore have five first order differential equations, and two unknown parameters ( $f_{z}$ and $L$ ), requiring seven boundary conditions.

At the end of the meridian corresponding to the perimeter of the NLP (defined as $s = 0$ ), the boundary conditions are

\begin{array}{cc} r (0) = R_{N L P}, \\ 2 κ C (0) = k \sin (ϕ (s)) \end{array}

(7)

where $R_{N L P}$ is the radius of the NLP, and $k$ is the twisting stiffness of the ApoE scaffold. The latter equation guarantees torque equilibrium between the membrane and the NLP scaffold, described in the Appendix 1 'Mathematical Model of the ApoE scaffold'. At the opposite end of the meridian, where the fusion pore meets the tCell membrane, the boundary conditions are

\begin{aligned} r (L) & = R_{\infty}, \\ z (L) & = 0, \\ ϕ (L) & = 0. \end{aligned}

(8)

where $R_{\infty} = 30 n m$ is chosen to be much larger than the length scale of the fusion pore. We found that the shape of the fusion pore was not significantly changed by increasing $R_{\infty}$ to 50 nm or by imposing freely hinged boundary conditions at the tCell interface (i.e. taking $C (L) = 0$ ), showing that the model is insensitive to these boundary conditions, Figure S8E. The choice $z (L) = 0$ is arbitrary, and is only used to set a reference point for the $z$ coordinate.

We fix the vertical force on the fusion pore $f_{z}$ in order to vary the height of the pore. The membrane energy is minimized when $f_{z} = 0$ . However, forces created by the Syt-SNARE complex can alter the height of the fusion pore. We therefore scan the parameter $f_{z}$ from $- 6 p N$ to $+ 6 p N$ to find fusion pores that satisfy the geometric constraint imposed by the Syt-SNARE complex. We assume that the selected height is that which minimizes the free energy subject to the constraints of the Syt-SNARE complex.

Lastly, the contour length of the meridian $L$ is unknown. The selected contour length is the one that minimizes the membrane energy. The condition that $L$ minimizes the membrane energy is given by Jülicher and Seifert, 1994:

0 = \cos (ϕ (L)) + \sin (ϕ (L)) f_{z} + r (L) (2 κ C (L) [C (L) - \frac{\sin (ϕ (L))}{r (L)}] - γ) .

(9)

In order to find the shape of a fusion pore with a given radius $R_{p o r e}$ , we additionally impose boundary conditions

\begin{array}{cc} r (x) = R_{p o r e} \\ ϕ (x) = \frac{π}{2} \end{array}

(10)

at the waist of the fusion pore, between the NLP and the tCell membrane. Note that this is measured from the membrane midplane, and related to the pore radius by $R_{p o r e} = r_{p o} + δ / 2$ , where $δ$ is the membrane thickness. Since the location of the waist is not known in advance, this procedure is mathematically equivalent to solving the shape equation twice, once from the NLP to the waist, and once from the waist to the point where the fusion pore joins the tCell membrane.

Mathematical Model of the ApoE scaffold

We modelled the ApoE scaffold of the NLPs as an elastic rod with rectangular cross-section, a simple representation of the two parallel alpha helices comprising the scaffold. The elastic bending energy of the rod is

U_{s c a f f o l d} = \int d L (\frac{K_{s o f t}}{2} C_{s o f t}^{2} + \frac{K_{h a r d}}{2} C_{h a r d}^{2}),

(11)

where $K_{s o f t}$ and $K_{h a r d}$ are the bending moduli of the rod in the material directions across its narrow and wide faces, respectively, $C_{s o f t}$ and $C_{h a r d}$ are the respective material curvatures, and $L$ measures the arclength around the scaffold. The material curvatures represent the curvature of the scaffold projected onto the basis vectors of the material cross section. Because of the rectangular shape of the cross section, the rod is more difficult to bend across its wide face than across its narrower face. For a homogeneous scaffold with a rectangular cross-section of width $w$ (across the wider face) and thickness $t$ (across the narrower face), this is quantified by a classical result from elasticity theory, which states $K_{s o f t} = E t^{3} w / 12, K_{h a r d} = E t w^{3} / 12,$ where $E$ is the Young’s modulus of the scaffold (Landau and Lifshitz, 1986b). From these scaling relations, we infer that the scaffold should have twice the bending modulus of a single alpha helix in the soft direction, and 8 times the bending modulus of a single alpha helix in the hard direction, as the scaffold comprises two parallel alpha helices. Given the typical persistence length of an alpha helix of ~ $100 n m$ and the well-known relation between bending modulus and persistence length $K = k_{B} T L_{p}$ (Choe and Sun, 2005), we conclude $K_{s o f t} \approx 200 k T n m$ and $K_{h a r d} \approx 800 k T n m$ .

Suppose the cross section of the scaffold is rotated such that the long axis of the cross section makes an angle $ϕ$ with the vertical direction (as in Figure S8A), while maintaining the shape of the scaffold as a ring of radius $R_{N L P} = 12 n m$ . Then, the material curvatures are

C_{1} = \frac{\cos ϕ}{R_{N L P}} C_{2} = \frac{\sin ϕ}{R_{N L P}},

(12)

This gives an elastic bending energy

U_{s c a f f o l d} = 2 π R_{N L P} (\frac{K_{s o f t}}{2} \frac{\cos^{2} ϕ}{R_{N L P}^{2}} + \frac{K_{h a r d}}{2} \frac{\sin^{2} ϕ}{R_{N L P}^{2}}) .

(13)

The torque per unit length to twist the scaffold through an angle $ϕ$ is thus

τ = \frac{1}{2 π R_{N L P}} \frac{\partial U_{s c a f f o l d}}{\partial ϕ} = \frac{K_{h a r d} - K_{s o f t}}{2 R_{N L P}^{2}} \sin 2 ϕ = k \sin 2 ϕ,

(14)

where $k$ is the apparent twisting rigidity of the scaffold. Using the parameter values above, we find $k = 2.1 k_{B} T / n m$ . The model predicts that a torque per unit length $~ 2 k T / n m$ twists the rod ~30 degrees.

We incorporated these effects in our calculation of the fusion pore shape by imposing a torque equilibrium condition at the NLP edge, so that membrane torque is resisted by the ND scaffold. The membrane bending torque per unit length about the local tangent vector to the NLP boundary is given by $τ = 2 κ C$ , where $C$ is the local mean curvature, neglecting terms associated with the Gaussian curvature modulus (Deserno, 2015). Thus, equilibrium is attained when

2 κ C = k \sin 2 ϕ

(15)

at the boundary of the NLP.

Geometric constraints imposed by the Syt-SNARE complex

In order to determine whether a fusion pore determined by solving the membrane shape equation satisfied the constraints imposed by the Syt-SNARE complex, we directly compared the geometry of the fusion pore with that of the Syt-SNARE complex. First, we measured the dimensions of the Syt-SNARE complex and the orientation of the SNARE complex relative to the membrane using PyMol. The long axis of the SNARE formed a ~15° angle with the membrane when docked via the primary interface to the Syt C2B domain in the orientation measured using electron paramagnetic resonance (Zhou et al., 2015; Kuo et al., 2011). The point where the SNARE complex would contact the membrane (determined by the Syntaxin and VAMP TMDs) was located $d = 8.0 n m$ from the point where the C2B domain inserted into the PM, and the line connecting the two contact points made a $ψ = 39 °$ angle with the PM.

To determine if the fusion pore satisfied the relevant constraints, we represented the Syt-SNARE complex as a wedge, with one segment of length 10 nm approximately perpendicular to the membrane, representing the long axis of the SNARE complex. Another segment of length 8 nm at a 17.7° angle to the first represented the line between the two points where the Syt-SNARE complex inserts into the membrane. We scanned this wedge along the meridian of the fusion pore seeking two points $r_{1}$ and $r_{2}$ representing the membrane contact points of the Syt-SNARE complex satisfying the following criteria:

The distance between $r_{1}$ and $r_{2}$ is within 10% of the measured distance between the membrane contact points, $\frac{| r_{1} - r_{2} |}{d} < 0.1.$ This 10% error range is roughly comparable with the depth of insertion of the C2B domain Ca-binding loops beyond the phosphate plane (Kuo et al., 2009; Kuo et al., 2011; Pérez-Lara et al., 2016).
The line connecting $r_{1}$ and $r_{2}$ makes an angle with the membrane tangent vector at $r_{2}$ within 0.1 radians of the measured value, $ψ - 0.1 < \arccos (\frac{r_{1} - r_{2}}{| r_{1} - r_{2} |} \cdot t_{2}) < ψ + 0.1$ , where $t_{2}$ is the membrane tangent vector (pointing along the meridian) at $r_{2}$ , representing the point where Syt contacts the membrane.
The long axis of the SNARE complex makes an angle with the membrane normal vector at $r_{1}$ of less than 0.1 radians.

If all three conditions were satisfied, the pore was assumed to satisfy the constraint imposed by the Syt-SNARE complex.

Short-ranged steric hydration free energy

The pressure due to short-ranged hydration forces between membranes with separation $d$ follows the form $P_{0} \exp (- d / λ)$ , where $λ$ is the characteristic length scale over which the hydration forces decay and $P_{0}$ is a pressure pre-factor (Rand and Parsegian, 1989). The steric hydration free energy was evaluated in our previous work by calculating the work done by the hydration pressure to increase the pore size of a toroidal pore (Wu et al., 2017b). The expression for the hydration free energy is given by

U_{h y d} = P_{0} λ π l \exp (- \frac{2 r_{p o}}{γ}) (r_{p o} + \frac{γ}{2}),

(16)

where $l = \sqrt{2 λ (h + 2 δ)}$ is the effective pore height that substantially contributes to the steric hydration interaction. For purposes of determining the hydration energy, we used this expression, approximating the fusion pore as a toroid. Another term giving the work done by the hydration forces to bring two distant planar membranes to a separation $h$ was omitted because it contributed negligibly. The second term is the work done to separate the membranes to form a pore of radius $r_{p o}$ . Values for $P_{0}$ and $λ$ are obtained from previous studies and are set to $P_{0} = 5 \times 10^{11} d y n / {c m}^{2}$ and $λ = 0.1 n m$ (see Appendix 1—table 1).

Free energy of SNAREs

We assume that each side of the NLP contains $N$ v-SNAREs that are all available to associate with the t-SNAREs in the tCell membrane and contribute to pore expansion. SNAREs can be fully zippered, where their TMDs are circularly arranged near the fusion pore waist. Alternatively, they can adopt a partially zippered configuration, where the TMD and linker domain are unzippered, and the v-SNARE and t-SNARE TMDs are located on the NLP and tCell membranes, respectively, but on the same side of the fusion pore. We denote the number of fully and partially zippered as $N_{Z}$ and $N_{U Z}$ , respectively. The SNARE free energy in the fully zippered state reads

U_{Z} (r_{p o}, N_{Z}) = - N_{Z} k_{B} T [\ln \frac{2 π r_{p o} - N_{Z} b}{N_{Z} b} + 1] - N_{Z} k_{B} T I n Ω_{Z} - N_{Z} ϵ_{Z},

(17)

where $k_{B}$ is the Boltzmann constant, $T$ is the temperature and $b = 2 n m$ is the thickness of a single SNARE (Wu et al., 2017b). The first term in Equation (17) is the positional entropy of the zippered SNAREs TMDs. The second term is the orientational entropy associated with the zippered SNAREs. We assume that these are stiff rods that can explore a small solid angle of $Ω_{Z} = 0.05 s r,$ based on molecular dynamics studies of t-SNARE TMDs showing that these domains explore angles of 10° around their equilibrium position (Knecht and Grubmüller, 2003). We assume that for the zippered SNAREs the equilibrium orientation is the local normal to the fusion pore membrane.

The last term is the total energy released when the TMDs and the adjacent linker regions of $N_{Z}$ SNAREs are fully zippered, where $ϵ_{Z}$ is the zippering energy per SNARE. This zippering energy was obtained as a best-fit parameter in a previous study where fusion was induced between NLPs and tCells with only SNAREs (Fulop et al., 2005). The best-fit value of 9.6 $k_{B} T$ (Appendix 1—table 1) is higher than the ~5 $k_{B} T$ that we estimated from a previous study as the zippering energy of the linker domains (Gao et al., 2012), as explained in the following paragraph.

The linker domain (LD) has ~10 residues (Stein et al., 2009), and is thus ~ 3 nm in length, assuming an unfolded contour length 0.3 nm per residue. Previous measurements show the free energy to unzip the SNAREs has slope ~1.5 k_BT per nm when the LDs are being unzippered (Gao et al., 2012). Thus, we estimate the LD unzippering energy from Gao et al. is ~ 5 k_BT.

The SNARE free energy in the partially zippered state reads

U_{U Z} (r_{p o}, N_{U Z}) = - N_{U Z} k_{B} T \ln \frac{2 π D}{b} - N_{U Z} k_{B} T I n Ω_{U Z} .

(18)

The first term in Equation (18) is the positional entropy of the TMDs, while the second term is the orientational entropy associated with a solid angle $Ω_{U Z}$ explored by the SNAREs. In the partially zippered state the SNARE linker domains are assumed to be unstructured, which allows them to adopt all orientations where they are not intersecting with the membranes. Since this orientational freedom is available when the SNAREs are away from the fusion pore, we restrict their position to the edge of the pore and set ${Ω = Ω}_{U Z} = π .$

We assume that, in elevated Ca concentrations, the C2B domains will bind the membrane via their Ca-binding loops. This lifts the C-terminal end of the SNARE complex ~5 nm above the tCell membrane; this has been proposed to drive dissociation of SNARE complexes from Syt in the presence of Ca (Voleti et al., 2020; Grushin et al., 2019). As this dissociation would cost $10 - 12 k_{B} T$ (see subsection Pushing forces from the membranes are insufficient to disrupt the SNARE-Syt primary-interface interaction), we omit this possibility and assume that SNAREs are unable to explore the fusion pore in elevated Ca concentrations. In this case, the positional entropy of SNAREs is unaltered by unzippering, and the free energy difference between the zippered and unzippered state is therefore given by $ϵ_{Z}$ per zippered SNARE.

Total free energy as a function of pore size, minimum membrane separation, and total number of SNAREs

To obtain the free energy of a fusion pore with a radius $r_{p o}$ , we numerically summed all the Boltzmann factors of all possible states according to

\begin{array}{cc} \exp (- \frac{U_{t o t} (r_{p o}, h, N)}{k_{B} T}) = \sum_{N_{Z} = 0}^{N} \exp (- \frac{U_{t o t} (r_{p o}, h, N, N_{Z})}{k_{B} T}) \\ U_{t o t} (r_{p o}, N) = min_{h} {U_{t o t} (r_{p o}, h, N)} \end{array}

(19)

where we set the number of SNAREs to $N = 4$ to match experiment.

Model-predicted pore conductance

Consider an axially symmetric fusion pore whose inner surface is described by a function $r (z)$ which gives the distance from the axis to the luminal surface of the membrane. The resistance of the pore is given by

R_{p o} = ρ \int_{0}^{L} \frac{d z}{π r {(z)}^{2}}

(20)

where ρ is the resistivity of the solution in the pore lumen, and the height of the pore lumen $L = h + 2 δ$ , where δ is the thickness of the bilayer (Nanavati et al., 1992). We numerically evaluated the above integral for fusion pores determined by solving the membrane shape equation. The total resistance of the pore also has a contribution from access resistance given by Nanavati et al., 1992,

R_{a c c} = \frac{ρ}{2 r_{p o} + L} .

(21)

The pore conductance is then given by $G_{p o} = {(R_{p o} + R_{a c c})}^{- 1}$ .

Pushing forces from the membranes are insufficient to disrupt the SNARE-Syt primary-interface interaction

We show here that forces needed to separate the membranes and expand the fusion pore are not large enough to disrupt the SNARE-Syt primary interface.

To calculate the pushing forces shouldered by the SNARE-Syt complexes, we calculated increase in the pore free energy $U_{m b}$ caused by the expansion driven by the SNARE-Syt complexes as a function of pore radius (Fig. S8D). From Fig. S8D, we see that change in height costs ~0-10 k_BT. The forces increasing the height of the pore are $\partial U_{m b} / \partial h \approx 10 p N$ . This force is shared across 4 SNARE-Syt complexes. Thus, an estimate for the force shouldered per complex during pore expansion is ~2.5 pN.

We estimate that 2.5 pN is far less than the force needed to break the primary C2B-SNARE complex interface. Reported dissociation constants for the SNARE-C2B complex are 0.86 μM (Wang et al., 2003b) and 14 μM (Wang et al., 2001). These correspond to binding energies ΔG of 12 k_BT and 10 k_BT, respectively, after estimating a microscopic capture radius of 2 nm (equivalently a reference concentration 0.21M) and using ΔG = -k_BTlnKd/0.21M. Even if we conservatively use a large ‘unbinding distance’ d ~ 3 nm, breaking the interface thus requires a force of order ΔG/d ~14–16 pN, much larger than the ~4 pN force exerted on a lever complex by the fusion pore. Thus, we expect the SNARE-Syt complexes will remain intact.

Appendix 1—table 1. Parameters used in the mathematical model with coarse-grained membranes, SNAREs and Synaptotagmin-1 C2B domains.

(A) Measured in Mitra et al., 2004. (B) Estimated previously as a best fit model parameter to experiments where NLP-tCell fusion pore was induced only by SNAREs (Wu et al., 2017b). (C) Consistent with NLP diameter measurements in this study. (D) Calculated as the weighted average of the hydration pressures of palmitoyl-2-oleoyl phosphatidylcholine (POPC) and 1,2-dioleoyl phosphatidylserine (DOPS) adopted from Rand and Parsegian, 1989, using a (85:15) molar ratio of POPC:DOPS as present in the NLP in the current study. (E) Values for the bending modulus range between $10 - 50 k_{B} T$ (Brochard and Lennon, 1975; Khelashvili et al., 2013; Marsh, 2006; Cohen and Melikyan, 2004). We used a value of $κ = 20 k_{B} T$ . (F) Obtained by fitting the membrane energy as a function of pore radius to measurements from a previous study using a similar method to measure the pore free energy in the absence of SNAREs, see Figure S8B (Wu et al., 2017b). (G) Calculated based on a 10° angle explored by t-SNARE TMDs around the equilibrium configuration, as measured in molecular dynamics simulations (Knecht and Grubmüller, 2003). (H) Estimated here from the $~ 100 n m$ persistence length of typical alpha helices and cross-sectional dimensions of the ApoE scaffold (see Appendix 1 subsection 'Mathematical Model of the ApoE scaffold'). (I) Measured in Syt1-liposome binding assays (Bai et al., 2004a; Bai et al., 2004b)

Symbol	Meaning	Value	Legend
$δ$	Membrane thickness	$5 n m$	(A)
$ϵ_{Z}$	Zippering energy of SNARE’s linker and TMD domains	$9.6 k_{B} T$	(B)
$D$	NLP diameter	$24 n m$	(C)
$λ$	Hydration interactions decay length	$0.1 n m$	(B)
$P_{0}$	Pressure pre-factor for steric hydration interaction	$5 \times 10^{11} d y n / {c m}^{2}$	(D)
$κ$	Membrane bending modulus	$20 k_{B} T$	(E)
$γ$	Membrane tension	$0.1 p N \cdot n m^{- 1}$	(F)
$Ω_{Z}$	Solid angle explored by fully zippered SNAREs	$0.05 s r$	(G)
$k$	Twisting rigidity of ApoE scaffold	$600 k_{B} T \cdot n m$	(H)
${[{C a}^{2 +}]}_{1 / 2}$	Apparent affinity of Syt1 to calcium in the presence of PIP2 containing membranes	$23 μ M$	(I)
$n$	Hill coefficient	2.3	(I)

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Appendix 1—figure 1. — (A) Schematic of an NLP reconstituted with 4 copies per face each with Syt1 and VAMP2. Syt1 C2AB domains are shown in green; VAMP2 is shown in blue and the scaffold protein ApoE protein is shown in cyan. Domain structures of Syt1 and VAMP2 are indicated. (B) Typical size-exclusion chromatography elution profiles of vNLP (NLPs loaded with VAMP2 alone) and vsNLP (NLPs loaded with VAMP2 and Syt1) samples using a Superose 6 Increase 10/300 GL column. Proteins were detected using absorbance at 280 nm. Collected eluted volumes are indicated by horizontal bars above each profile. (C) SDS-PAGE stained with Coomassie Brilliant Blue shows the purified NLPs carried Syt1 and VAMP2 proteins. (D) A representative transmission electron microscopy (TEM) image of a vsNLP sample after purification. Nanodiscs indicated by white stars have their lipid bilayer plane positioned perpendicularly to the imaging plane. (E) Distribution of vsNLP sizes from TEM images. More dilute samples (5-10x) than the example shown in D were used for size quantification, such that most NLPs were lying flat on the grid. A Gaussian fit to the distribution is shown as the red solid line (fitted mean diameter = 25±5.6 nm (± SD), n = 200 NLPs). (**F–H**) Characterization of nanolipoprotein particles reconstituted with VAMP2 alone. (F) SDS-PAGE of purified vNLPs stained with Coomassie Brilliant Blue indicting the NLPs incorporated ApoE and VAMP2 proteins. (G) Negative stain transmission electron microscopy image of a representative vNLP sample. Nanodiscs indicated by white stars are oriented with their disc plane perpendicular to the imaging plane. (H) Size distribution of vNLPs reconstituted with a total of 8 copies of VAMP2 per disc. A Gaussian fit is shown as the red solid line (best fit diameter = 25 ± 4.6 nm (mean ± SD), 171 discs were analyzed). (I) Domain structure of flipped t-SNARE constructs used to generate HeLa cells stably expressing flipped t-SNAREs (Giraudo et al., 2006; Giraudo et al., 2005). (J) Example of a fusion pore current burst and definition of analysis parameters. To be included in the analysis, a current burst must have amplitude >2 pA and last at least 250 ms. Open sub-periods during a burst cross a threshold (-0.25 pA, red dotted line) for at least 60 ms (indicated as the thick colored bars above the current trace). The number of open sub-periods during a burst is equal to the number of pore flickers, $N_{f l i c k e r s}$ . The duration of the burst is the time from the first detected open-pore point until the last one and is denoted $T_{o}$ . The flicker rate is $N_{f l i c k e r s} / T_{o}$ . The pore open probability is the sum of the open-pore sub-periods (the colored bars) divided by the burst lifetime, $T_{o}$ .

Appendix 1—figure 2. — (A) An example of an entire 800 s recording that started shortly after establishing a tight seal. The colored regions correspond to currents that are counted as fusion pore currents because they fit the criteria explained in Appendix 1 *Detection of pore currents* and *Estimation of fusion rate* (also see Fig. S1J). These regions are shown with expanded axes in insets. In this example, 3 pores were counted in 800 s of recording. (B) Another example of an 800 s recording. In this case, large currents appeared starting ~140 s. The baseline did not recover before the end of the recording and the red-colored portion was excluded from analysis. Thus, two current bursts contributed to the fusion rate from this trace (starting ~90 and 130 s, colored in green and teal), from 140 s of recording. (C) Fusion rate increases with increasing NLP concentration. Fusion rates were calculated as described in Appendix 1 *Estimation of fusion rate* and plotted against the concentration of NLPs reconstituted with v-SNAREs (8 copies total). Pores from 12-37 cells were recorded for every condition. Error bars indicate S.E.M. The best fit straight line is shown (slope = 2.3 × 10⁻³ pores/(min•nM), $R^{2} = 0.86$ ). (D) Comparison of per cell and overall fusion rates. As an alternative estimate of the fusion rate, we summed all detected pores, $N_{t o t}$ , and the analysis time $τ_{t o t}$ over all cells (excluding portions with noisy/unstable baseline), and calculated the total number of pores divided by the total analysis time, ${\dot{F}}_{t o t} = N_{t o t} / τ_{t o t}$ for the indicated conditions. This estimate (blue) is compared with the per cell estimate used throughout (red).

Appendix 1—figure 3. — Open-pore conductance fluctuations relative to mean (A), average flicker rate during a burst (B), average open-pore probability, $P_{o}$ , during a current burst (fraction of time pore is in the open state during a burst) (C), and average burst lifetime, $T_{o}$ , (D) for the indicated conditions. (E) Distributions of the number of flickers per burst, $N_{f l i c k e r s}$ , for the indicated conditions. Fits to geometric distributions are shown in red, $y = p {(1 - p)}^{n - 1}, n = 1, 2, 3, \dots$ . Best fit parameters (with ± 95% confidence intervals) are $p = 0.072 (0.053, 0.092)$ (no Syt1, 100 μM Ca²⁺, averaged over 49 individual fusion pores from 10 cells, mean $N_{f l i c k e r s} = 12.8$ ), 0.083(0.051,0115) (Syt1, 0 μM Ca²⁺; averaged over 24 individual fusion pores from 11 cells, mean $N_{f l i c k e r s} = 11.0$ ), 0.053(0.044,0.063) (Syt1, 100 μM Ca²⁺; averaged over 123 individual fusion pores from 20 cells, mean $N_{f l i c k e r s} = 17.7$ ). (F) Distribution of burst lifetimes, $T_{o}$ for the indicated conditions. Best fits to single exponentials are shown as red curves, with means (and 95% confidence intervals) as follows. No Syt1, 100 μM Ca²⁺: 6.1 s (4.7 to 8.3 s, 49 fusion pores from 10 cells), Syt1, 0 μM Ca²⁺: 6.5 s (4.5 to 10.1 s, 24 fusion pores from 11 cells), Syt1, 100 μM Ca²⁺: 16 s (13.5 to 19.3 s, 123 fusion pores from 20 cells). In A-D, the two-sample Kolmogorov-Smirnov test was used to assess significant differences between the "no C2AB" group and the rest. *, **, *** indicate p<0.05, 0.01, and 0.001, respectively. Comparison between Syt1 and C2AB in the presence of Ca²⁺ and PI(4,5)P₂ are also indicated (using the two-sample Kolmogorov-Smirnov test).

Appendix 1—figure 4. — (**A–D**) Probability density function (PDF) for point-by-point open-pore conductance values for the indicated conditions. Substantial density is present for $G_{p o} ≳ 500$ pS only when C2AB, calcium, and PI(4,5)P₂ were all present. (**F–I**) PDFs for open-pore radii corresponding to the conductance distributions in A-D, assuming pores are 15 nm long cylinders. Data were from 49 fusion pores/10 cells (SNARE only), 44 fusion pores/12 cells (0 µM Ca²⁺), 84 fusion pores/19 cells (no PI(4,5)P₂) and 98 fusion pores/17 cells (100 µM Ca²⁺ plus PI(4,5)P₂).

Appendix 1—figure 5. — (A) Open-pore conductance fluctuations relative to mean. Compared with the SNARE-alone (no C2AB) group, fluctuations were larger for wild-type C2AB, and lower for C2AB^K326A,327A. (B) Average flicker rate for the same conditions as in A. Compared with the SNARE alone group (no C2AB), C2AB and C2AB^R398Q,R399Q decreased the flicker rate. (C) Average pore open probability during a burst, $P_{o}$ , for the indicated conditions. Compared with the SNARE alone group (no C2AB), C2AB and C2AB^K326A,K327A had larger pore open probabilities. (D) Average burst lifetimes for the same conditions. Error bars are +/- S.E.M. Data were from no C2AB: 49 pores/10 cells, C2AB: 98 pores/17 cells, C2AB^K326A,327A: 42 pores/14 cells, C2AB^D309N (18 pores/7 cells), C2AB^R398Q,R399Q (42 pores/18 cells). For A-D, two-sample Kolmogorov-Smirnov test was used to assess significant differences between the "no C2AB" group and the rest. *, **, *** indicate p<0.05, 0.01, and 0.001, respectively.

Appendix 1—figure 6. — (**A–D**) Average single-pore conductance fluctuations relative to mean (A), average burst lifetime (B), average flicker rate (C), and the pore open probability $P_{o}$ (D) as a function of [Ca²⁺]_free. Error bars are ± S.E.M. (E). Probability density functions (PDFs) for point-by-point open-pore conductance values at different [Ca²⁺]_free. The probability density for $G_{p o} ≳ 500$ pS increases as a function of calcium. (0 µM Ca²⁺: 44 pores/12 cells; 5 µM Ca²⁺: 54 pores/20 cells; 20 µM Ca²⁺: 114 pores/18 cells; 50 µM Ca²⁺: 88 pores/26 cells; 100 µM Ca²⁺: 98 pores/17 cells). (F) The fusion rate increases as a function of [Ca²⁺]_free. For A-D, two-sample Kolmogorov-Smirnov test was used to assess significant differences between the "no C2AB" group and the rest. *, **, *** indicate p<0.05, 0.01, and 0.001, respectively.

Appendix 1—figure 7. — (**A–D**) Average single-pore conductance fluctuations relative to mean (A), burst lifetime (B), pore open probability during a burst, $P_{o}$ (C), and flicker rate (D) for SNAREs alone (no C2AB), wild-type Syt1 C2AB (C2AB), the 4W mutant with enhanced membrane-penetration ability (M173W, F234W, V304W and I367W), and the 4A mutant which cannot penetrate membranes in response to calcium (M173A, F234A, V304A and I367A). Error bars are ± S.E.M. (E) Probability density functions (PDFs) for point-by-point open-pore conductance values for wild-type C2AB, and the membrane penetration mutants 4A and 4W. (4W: 115 pores/20 cells, 4A: 31 pores/9 cells). For A-D, two-sample Kolmogorov-Smirnov test was used to assess significant differences between the "no C2AB" group and the rest. *, **, *** indicate p<0.05, 0.01, and 0.001, respectively.

Appendix 1—figure 8. — Data in (C) and (D) was smoothed using a moving average with width 0.5 nm. (A) Schematic illustrating a fusion pore with buried SNARE-Syt1 levers. $ϕ$ represents the angle of twisting of the ApoE proteins. (B) Pore free energy as a function of radius predicted by the model and measured in a previous study (Wu et al., 2017b); the membrane tension was tuned to reproduce the experimental curve here. (C) Pore height, defined as the maximal separation between the NLP and the tCell membranes, as a function of pore radius with and without Ca²⁺. (D) Free energy difference between pores in the expanded state and those in the unexpanded state. Syt-SNARE complex-driven pore expansion costs a maximum of $~ 10 - 12 k_{B} T$ at low pore radii. (E) Fusion pores determined from the model using varying boundary conditions at the location where the fusion pore membrane joins the tCell (lower edge). The blue curve shows the boundary conditions used throughout the paper, while the orange curve uses $R_{\infty} = 50 n m$ (instead of 30 nm), and the purple curve imposes freely hinged boundary conditions at this location. These changes have very little effect, especially in the region close to the fusion pore (zoom in, right).

Appendix 1—figure 9. — Top: Schematic of the cell-attached recordings to test for ATP-regulated channel activity. Pipette solutions were the same as for single-pore measurements with 100 μM free calcium, but adjusted to contain either 0 or 2 mM ATP. Pipette potential was −40 mV. Middle: Current recordings under voltage clamp from three different patches (out of 21 total) in the absence of ATP. Bottom: Current recordings as in the middle panels, but in the presence of 2 mM freshly prepared ATP (26 cells were recorded). Occasionally, channel activity is recorded both with and without ATP.

Appendix 1—figure 10. — Data for full-length Syt1, in the presence of 100 μM free Ca²⁺ and PI(4,5)P₂. Other conditions also failed to yield large differences between pore opening or closure.

Appendix 1—figure 11. — (A) Whole-cell current responses to step changes in membrane potential under voltage-clamp, from a HeLa cell line expressing flipped t-SNAREs. (B) Current-voltage relationship. Currents were averaged for 27 cells. The average slope is $G_{c e l l} = 5.04 \pm 0.32$ nS (95% confidence interval), excluding the five highest voltages (red crosses). If all points are included, $G_{c e l l} = 6.20 \pm 0.51$ nS (95 % confidence interval). The range of mean open-pore currents and transmembrane voltages comprising 95% of the data values for C2AB in the presence of PI(4,5)P₂ and 100 μM calcium are indicated as a red-colored box.

Funding Statement

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

Contributor Information

Ben O'Shaughnessy, Email: bo8@columbia.edu.

Erdem Karatekin, Email: erdem.karatekin@yale.edu.

Felix Campelo, The Barcelona Institute of Science and Technology, Spain.

Vivek Malhotra, The Barcelona Institute of Science and Technology, Spain.

Funding Information

This paper was supported by the following grants:

National Institute of Neurological Disorders and Stroke R01NS113236 to Erdem Karatekin.
National Eye Institute R01EY010542 to Erdem Karatekin.
National Institute of General Medical Sciences R01GM117046 to Ben O'Shaughnessy.
Columbia University Shared Research Computing Facility to Ben O'Shaughnessy.

Additional information

Competing interests

No competing interests declared.

Author contributions

Conceptualization, Data curation, Formal analysis, Investigation, Writing - original draft, Writing - review and editing.

Software, Formal analysis, Validation, Investigation, Visualization, Writing - review and editing.

Conceptualization, Software, Formal analysis, Validation, Investigation, Visualization, Writing - review and editing.

Conceptualization, Formal analysis, Supervision, Funding acquisition, Validation, Writing - original draft, Project administration, Writing - review and editing.

Conceptualization, Resources, Software, Formal analysis, Supervision, Funding acquisition, Validation, Investigation, Writing - original draft, Project administration, Writing - review and editing.

Additional files

Transparent reporting form

elife-68215-transrepform.pdf^{(229.7KB, pdf)}

Data availability

All data associated with the plots shown in this study are included in the manuscript and supporting files. Source data files have been provided for all figures, in the form of a. zip file containing mostly matlab .fig and/or .mat files corresponding to the data presented in the manuscript and the Appendix. The raw data can be extracted for every plot from the .fig file. In a few cases, we included Excel or Igor Pro files.

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eLife. doi: 10.7554/eLife.68215.sa1

Decision letter

Editor: Felix Campelo¹

Reviewed by: Felix Campelo², Patricia Bassereau³

In the interests of transparency, eLife publishes the most substantive revision requests and the accompanying author responses.

Acceptance summary:

This paper will be of interest to neuroscientists, and more broadly to scientists working on membrane fusion. A combination of experiments fusing an elegant nanodisc-cell fusion assay and of mechanical models reveals a new mechanism by which Synaptotagmin-1 mechanically promotes the opening of the fusion pore induced by SNARE proteins.

Decision letter after peer review:

[Editors’ note: the authors submitted for reconsideration following the decision after peer review. What follows is the decision letter after the first round of review.]

Thank you for submitting your work entitled "The neuronal calcium sensor Synaptotagmin-1 and SNARE proteins cooperate to dilate fusion pores" for consideration by eLife. Your article has been reviewed by 3 peer reviewers, one of whom is a member of our Board of Reviewing Editors, and the evaluation has been overseen by a Senior Editor.

Having considered your revision plan. our decision has been reached after consultation between the reviewers. Based on these discussions and the individual reviews below, we regret to inform you that your work will not be considered further for publication in eLife.

Two reviewers read the author response. Their comments are presented below. In brief, the reviewers and the reviewing editor understand that the additional experiments, which are necessary for revision of the experimental part of the article, could be hard to perform in the near future because of the pandemic. At the same time, the author replies to the reviewer comments on the theoretical part of the work, do not appear satisfactory.

Computational part

"In cell-attached recordings, the patch of membrane that is under study is under high tension due to adhesion to the walls of the pipette. Strong adhesion of the membrane to the walls of the glass pipette is needed to obtain a high-resistance seal (the so-called "Gigaseal") for low-noise recordings. Previous measurements show the membrane tension in the patch is ~1 pN/nm [37]. This is consistent with our model that obtained a tension of 0.66 pN nm-1 as a best-fit parameter by comparing the model-predicted slope of the free energy of pore dilation for pores of size ~ 1 nm between the model prediction and the experimental measurement when only SNAREs were present in a previous study of ours [3].

Forces that oppose membrane tension at the nanodisc boundary arise presumably from the bending rigidity of the ApoE proteins, and from their interactions with the lipids. A radially inward force per unit length equal to the membrane tension acts on the ApoE scaffold. Assuming only the bending rigidity opposes this inward force, we can compare the membrane tension to the threshold force per unit length where a circular ring buckles, kT Lp /d2 , where : and d and Lp are the radius of the cross-section of the circular ring and its persistence length respectively. As the scaffold proteins consist of a series of α-helical regions interspersed with unstructured regions [38], and a typical persistence length of α-helices is ~ 100 nm [39], the buckling threshold is ~400 pN nm-1 assuming a thickness : d~ 1 nm, much larger than the membrane tension of 0.66 pN nm-1"

The should be a misunderstanding here. According to the classical literature on the buckling instability of a ring, the radial force per unit length of the ring (the membrane tension in the present case) leading to the instability is, approximately, γ~(kT L_p)/r³ , where r is the ring radius. Taking Lp = 100nm, as suggested by the authors, and r~10"nm" , according to the dimension of nanodiscs used in the work, one gets, practically, a vanishing critical tension. This must mean that, as a result of the pore nucleation, the tension drops to zero.

This means that the model is inconsistent with the reality in this essential point.

"We agree that the toroidal shape is not an exact fusion pore solution, but we use this shape for simplicity, and we believe it captures all the important features of a more exact solution. It has the advantage that the biophysical aspects are clearly articulated. For this reason, toroidal pores have been assumed in many previous theoretical studies (e.g. [40-42])."

This is not a convincing argument. In the previous studies the toroidal pore approximation was used for the cases of two infinitely large membranes connected by a fusion pore. In the present study, the dimension of the nanodisk is of the same order of magnitude as the pore radius so that the deviation from the toroidal shape may have essential consequences for the results.

One of the consequences of the toroidal pore assumption is the conclusion that SNARE reorientation results in the expansion of the pore waist, which is one of the central conclusions of the model. An alternative outcome could be an increase of the tangent angle to the membrane profile at the ND rim without the waist expansion. A detailed computational analysis avoiding the toroidal shape assumption is needed to resolve this issue.

"Regarding the torque at the nanodisc edge, the question raised by the reviewer, it can be shown that the downward bending is small, so that the flat annulus approximation at the outer nanodisc edge does not deviate by a large amount from the exact solution. The argument is as follows. (1) The angle made by an annular piece of membrane of width : at the nanodisc edge is ? ~ @:!/A, where @ is the downward force per unit length at the nanodisc edge and A is the membrane bending modulus. (2) The net downward force is the same at any cross section of the pore. At the pore waist net downward force is ~ 2C(D + F/2)H, assuming the mean curvature of the waist *+,- is negligible. Here, D , F and H refer to the radius of the pore, the membrane thickness, and *+,- tension respectively. Thus, for pores of radii similar to the membrane thickness, the force per unit length at the ND edge is @ ~ FH/J./ where J./ is the radius of the ND. (3) This force per unit length gives an angle ? ~ FH:!/AJ./. Using : ~ 5 ->, and other values as in Table S1, we get an angle ? ~ 4. Thus, the bending of the membrane is negligible near the nanodisc"

This reasoning is very hard to follow. (i) For some reason, the expressions include the membrane thickness, while the latter is already accounted for by the bending rigidity, which is also a part of the same expressions. (ii) Further, the authors estimate the angle of 4o at the ND edge, while the question is about the curvature (mean curvature) there rather than the angle. The expression for the curvature includes the angle derivative along the contour length, not just the angle itself. (iii) Moreover, the origin of the constant downforce, used by the authors for their argumentation, is unclear. Indeed, the cell membrane is, practically, horizontally oriented so that the downforce at the bottom of the pore should vanish. (iv) The suggestion of an almost vanishing mean curvature in the pore waist is incompatible with the assumption of a considerable lateral tension.

"The protein scaffold around the nanodisc can be formed by various configurations of the apolipoprotein E variant containing the N-terminal 22 kDa fragment (ApoE422K) [38]. In all cases, it is thought that two rows of stacked α-helical segments form a belt at the boundary of the nanodisc. The α-helical segments interact laterally and are connected by short linkers [38]. The torque contribution could arise either from the twisting rigidity of the α-helices or from the interactions between the proteins and the lipid molecules.

As the reviewer says, we assumed constant torque. We found a potential quadratic in the twisting angle could not reproduce the energetics of large pores of radii ~ 3 – 6 nm when ~15 SNARE complexes are present at the fusion pore without Synaptotagmin-1 [3].

In fact, we did consider the effect of the torque for pores of smaller radii. The proteins are twisted only when the radius or the height of the pore are large enough so that the rim of the toroidal pore where it joins with the flat membranes reaches the boundary of the nanodisc. Such radii or heights are larger than the equilibrium values predicted by the model, so it costs energy to access them. Thus, such states do not contribute much to the statistical average at the equilibrium values of radius and height."

A proposal about a specific mechanism of a constant (independent of deformation) torque generation should enable quantitative estimation of this factor. Otherwise, this energy contribution appears too speculative to be published.

Experimental part

The reviewers were disappointed to learn that the authors chose not to do an additional experiment, in particular, of determining the binding kinetics of nanodiscs to the cell membranes. The reviewers believe this experiment would yield an important piece of data showing what constitutes the rate-limiting step in the fusion pore assay the authors have developed. Moreover, the technical difficulties stated in the rebuttal, mainly high fluorescence backgrounds, may be bypassed using techniques such as FRET.

However, the senior author professed difficult situations in his lab midst the current pandemic situation. Therefore, at least regarding Comment 1, the authors need to state these potential issues in their experimental assay-including low rates of fusion pore opening, low cooperativity and unawareness of the rate-limiting step-and discuss the limitations and reservations in interpreting their data sets. It may then be possible to proceed as the authors have suggested (on page 7 of the rebuttal).

Reviewer #1:

The article by Z. Wu et al. addresses experimentally and theoretically the mechanism by which Syt-1 contributes to fusion pore dilation. The system used consists of nanodiscs fused with SNARE-containing cell membranes. The new proposal of the work is that the fusion pore expansion is driven by an intra-membrane reorientation of Syt1 hydrophobic loops, which leads to rotation of SNARE complexes and the resulting increase of the inter-membrane distance. The latter leads to an increase of the fusion pore radius.

In my view the article can not be published in the present form.

The suggested mechanism of the fusion pore dilation is crucially based on the theoretical model which, in its present form, raises questions.

1. The model assumes that the whole membrane is exposed to a constant lateral tension. I am wondering whether any relevant level of tension can exist in this system given that the edge of the nano-disc is free, i.e. is not subjected to any external force. It is true that the apolipoprotein scaffold at the disc edge could sustain some tension due to the scaffold compression and bending/twisting rigidities provided that the latter are sufficiently large.

Estimations of sustainable tensions based on the feasible values of the protein scaffold rigidities are necessary to support the model.

2. It is assumed that for a substantial range of the pore radii the pore can be described by a toroidal shape. This implies that the fragment of the nano-disc membrane between the ND edge and the rim of the pore is flat. This does not seem to be feasible mechanically since it would violate the torque equilibrium at the disc edge. Indeed, the tension in the cell membrane generates a rotational moment with respect to the ND edge (the pore height serving as a lever), which must be counteracted by torque at the edge. On the other hand, the existence of the edge torque necessarily means generation of the membrane curvature next to the disc edge.

Consideration and estimation of this torque and the related shape of the ND membrane, including their dependence on the pore radius are absolutely necessary to justify the model and its major prediction on the increase of the pore radius upon increasing of the pore height. Also, in case the scaffold is too soft to develop large enough torques to equilibrate the rotational moment of the membrane tension, the whole description becomes questionable.

3. Considering the partially toroidal shapes of the pore, the authors assume the torque at ND edge to be constant since the related energy contribution is linear in the angle. I am wondering about the physical origin of such a constant torque and why its effect was not considered for smaller pore radii.

Reviewer #2:

The authors have done a remarkable job of creating an assay for the fusion pore that does not require capacitance measurements or amperometry, but detects a transient in the DC current through a cell membrane , interpreted as the fusion pore, when a nanodisc is applied to the cell surface.

I do not understand why the conductance is limited in time, and what the meaning of the time course is. If the conductance rises and then falls, does it mean that competing factors are changing in time? In that case, what does the mean pore conductance mean for this complex time course?

While this system shows an effect of Syt1, it only explains a very small part of the biological effect of Syt1. The effect of calcium on synaptic exocytosis follows a fourth-power continuously increasing curve with presynaptic [Ca²⁺]free, this is a large effect by 20 uM, and not in keeping with the rather modest (3 fold) increase in activity in the author's model with [Ca²⁺]free in an S-shaped curve that saturates rapidly. An explanation for the saturation of the Ca effect is needed.

The section, "Calcium-dependent membrane-insertion of Syt1 C2AB, but not curvature generation, is necessary for pore dilation" did not seem particularly convincing. I did not follow this explanation: "Membrane insertion of these hydrophobic residues expands the membrane in one leaflet, creating an area mismatch, which relaxes as the membrane curves away from the wedge-like insertion. This membrane buckling is thought to contribute to the triggering of release (37, 52, 53). Nor was I convinced that "Thus, membrane penetration is required for pore expansion by Syt1, but curvature generation is not." Or that " It is well known that calcium induced loop insertion causes a reorientation of the C2 domains (86, 87)."

Reviewer #3:

This manuscript by Wu et al. reports on use of in vitro assays to study opening of fusion pores catalyzed by SNAREs and syanptotagmin1 (Syt1). One of the persisting questions in Ca²⁺-triggered exocytosis is how these machineries catalyze fusion pore opening, which is allegedly energetically-expensive, on millisecond scales as in the case of central nerve systems.

Recent incorporation of the electrophysiology tools is a welcoming addition to the field because it makes characterization of the fusion pores more quantitative, to the extent that would be likely unattainable with other methods. The authors formed nanodiscs reconstituted with 8 copies of R-SNAREs and Syt1 each (~25 nm diameter), and expressed Q-SNARE proteins in a flipped orientation on HeLa cell membranes. Fusion events between the nanodiscs and the cell membranes led to conductance of ions through fusion pores, which was monitored via the electrophysiology tool. The authors carried out detailed and quantitative analysis on the various physical properties of fusion pores including the average conductance and fluctuation rates. The authors took one step further to introduce various mutations to the C2B domain and studied their effects on the fusion pore properties.

These observations convincingly showed that in the in vitro assay the authors developed, SNAREs and Syt1 work in a concerted manner to open fusion pores with larger diameters and increased fluctuations with Ca²⁺ and PI(4,5)P2 working as important cofactors. The authors propose a model where enhanced membrane penetration of the C2B domains in the presence of these cofactors tilts up the SNARE complexes. This increases height of the pore structure, which in turn leads to dilation of fusion pores.

Although these results provide some interesting insights into the molecular mechanisms underlying fusion pore opening, there are issues that need to be addressed before recommendation of this manuscript for publication in eLife.

Comment 1. One concern is the rate of fusion pore opening is still low, a few times within 10 minutes, which is orders of magnitude slower than what is observed and Ca²⁺-evoked exocytosis in physiological milieu. Although it would be too demanding to expect reconstitution of ms-scale Ca²⁺-triggered pore opening in the current work, it is still important to identify the rate-limiting step for fusion pore opening in the in vitro assay the authors have developed.

The authors may want to study of binding kinetics of the nanodiscs to cell membranes under the reaction conditions used in this study probably using single-particle fluorescence microscopy or capacity measurement. If the binding latency is only a small fraction of the observed long latency, the priming step after binding could define the rate-limiting step. This priming may involve many molecular re-arrangement between two fusing membranes, such as formation of SNARE complexes (in trans or cis forms) and inter-SNARE complex arrangement (shown in Figure 6E) and recently reported interactions between SNARE complexes and the C2B domains (Ref. 76, 77). To sum up, the authors need to characterize the binding kinetics of nanodiscs and cell membranes and specify the rate-limiting step of the current in vitro fusion pore assay in the manuscript.

In this vein, it is also important to see how the pore open frequency is modulated as a function of Ca²⁺ concentration, which is currently missing in Figures 4 and S5. This is because the binding between fusing membranes is known to be substantially accelerated in the presence of Ca²⁺.

Comment 2. In the model shown in Figure 6, the authors suggest that enhanced binding and penetration of the C2B domain mechanically tilt up the SNARE complexes, thereby catalyzing larger fusion pores. The authors further suggest that this levering action can withstand restoring force of the fusion pore up to 14-16 pN.

This estimation, however, appears to be at odds with the observations made in previous single-molecule force spectroscopy studies. For example, the single neuronal SNARE complex is stabilized by a huge free energy of 65 kBT, but even the SNARE complexes are fully unzipped upon application of 16 pN tension (Ref. 92, 93). In addition, binding between the negatively charged membranes (with 5 mol% PI(4,5)P2) and C2B already shows repetitive binding and unbinding under 3 to 4 pN tension (Ref 62). Thus, although the model proposed by the authors is interesting, it may be more realistic to expect that membrane penetration of multiple C2B domains has a moderate steering effects for the SNARE complexes lining the fusion pores, rather than working as strong mechanical supports maintaining the suggested elongated pore structure.

[Editors’ note: further revisions were suggested prior to acceptance, as described below.]

Thank you for submitting your article "The neuronal calcium sensor Synaptotagmin-1 and SNARE proteins cooperate to dilate fusion pores" for consideration by eLife. Your article has been reviewed by 3 peer reviewers, including Felix Campelo as the Reviewing Editor and Reviewer #1, and the evaluation has been overseen by Vivek Malhotra as the Senior Editor. The following individual involved in review of your submission has agreed to reveal their identity: Patricia Bassereau (Reviewer #2).

The reviewers have discussed their reviews with one another, and the Reviewing Editor has drafted this to help you prepare a revised submission.

Essential Revisions:

We request no additional experiments. We are only asking for some revisions that are mostly aimed at improving the clarity the manuscript as well as some extra computations regarding the model's assumptions. These additional computations should be relatively straight-forward for the authors. For these required revisions, see the detailed reports from Reviewer #1 and Reviewer #3. In particular, we'd like to emphasize on the following:

1. About the BCs used for the computations (see e.g. Eq. (8) of the SI Appendix): the authors should study (or provide a solid argumentation on why this might not be necessary) the shape and energies when the tCell membrane does not relax to a perfectly flat state but to a catenoidal shape.

2. The final section of Results presents some modeling work with C2A. There are no relevant experiments and the results are not discussed in the Discussion section. It is not clear how this section fits into this paper, so unless the authors can adapt it to provide a logical explanation in the context of this paper, this section should probably be removed.

Reviewer 1:

The calcium sensor Synaptotagmin-1 (Syt1) is known to be a key element for neuronal SNARE-mediated fusion, but how fusion proceeds is still debated and many different scenarios and physical models have been proposed. In this work, Z. Wu and collaborators use an interesting assay for measuring single fusion event with a very good time resolution (ms): v-SNARE proteins are reconstituted in large nanodiscs and fuse with "flipped cells" expressing t-SNAREs facing the extracellular media. Syt1 interacts either as a full length protein co-reconstituted in the nanodisc or as a truncated soluble version (C2A+C2B domains, or mutants) added in the patch pipette. Single fusion events are followed by electrophysiology using voltage-clamp in the cell-attached mode, as a function of PIP2 in the cell membrane or calcium in the medium. The authors focus mostly on the effect of Syt1 on pore expansion. In parallel, they have developed a mathematical model for fusion of nanodisc and cells based on Helfrich energy for the membrane fusion part and theory of elasticity for the scaffolding by ApoE around the nanodisc. The experiments clearly show that Syt1 promotes the growth of the fusion pore in a way dependent on binding to PiP2 and calcium concentration. Its interaction with SNAREs also contributes to pore expansion. The C2B+C2A domain (C2AB) is sufficient to induce this effect and Ca²⁺-dependent penetration of the hydrophobic loop is essential. These dependences and the pore growth rates are nicely reproduced by a model where at low calcium, the C2B domain binds to t-SNARES and to PiP2, remaining parallel to the membrane and keeping the pore small or closed. When calcium increases, the membrane insertion of the hydrophobic loop while being connected to SNAREs produces a tilt of about 15{degree sign} of the SNARE-Syt1 complex. SNARE-Syt1 acts as a mechanical lever on the pore edge, which changes the pore shape and tends to open it more. The C2A domain's loop strongly boosts the kinetics of the opening process. Altogether, the lever model accounts well for the experiments presented in the study, in contrast with different models previously published.

With this work, we can expect conceptual advances on the contribution of Syt1 to neuronal membrane fusion. In addition, the modelling of the mechanical deformation of a nanodisc and of its scaffold in the presence of a pore should be more generally relevant to experiments involving mechanosensitive membrane proteins or other pore forming structures.

I was not a reviewer in the initial version of the manuscript, but I have now read carefully both the current revised manuscript and the rebuttal letter including the detailed responses to the reviewers of the previous submission.

In general, I think that this manuscript deals with an interesting topic (fusion pore expansion by Syt and SNARES) using a variety of tools (experimental study of pore size and dynamics using nanodisks, as well as detailed modeling of the pore shape).

Regarding the experimental part, and following the discussion from the previous submission, although I agree that the ND binding kinetic measurements would have been an important piece to be added, I accept the statements made by the authors in this revised manuscript.

Regarding the modeling part, I do appreciate the effort made by the authors in implementing and solving the shape of the pore without the toroidal pore assumption. The finding that the tension required to open up the pore is different in the exact solution as compared to the toroidal pore is interesting and important. It also helps the authors discuss why they think that the scaffold is not buckling as a response to tension (and bending) of the ND membrane.

That being said, I have some specific comments about the model, and about some of the assumptions made there:

1. Perhaps to me the most important one is the BCs shown in Eq. (8) of the SI Appendix. There the authors assume that the membrane (on the tCell side) is flat (phi(L)=0) at a certain distance (R_inf=30nm) from the pore axis. A couple of thoughts.

– R_inf is chosen somehow arbitrarily.

– Why does the membrane need to relax to a flat state far away from the pore and not a catenoidal geometry (which also has zero bending energy)? This latter condition could be implemented by assuming phi(L)≠0. To me, intuitively (so maths might proof me wrong of course), such a geometry could make that zipping does not lead to pore expansion but maybe to a change in the catenoidal angle? I think that the authors should discuss if this makes sense or not.

2. I've noticed some inconsistencies in the "Mathematical Model of the ApoE scaffold" in the SI Appendix. In particular:

– some references are missing in the appendix.

– Eq. (14) in the app. please use U_scaffold and not F.

– Two AHs per ApoE scaffold are assumed to estimate K_soft and K_hard, is that correct? This should be explained and reasoned in the text as the readers are left to deduce that from the numbers.

– pg. 11 appendix: with the definition given in Eq. (14) of k=(K_hard-K_soft)/(2 R_NLP²), and using the values in the text just above that, I get k=2.1 kBT/nm and not 4.2 kBT/nm as the authors wrote. Please verify. And then the evaluation of the twist angle for a 2 pN torque, in my hands, appears to be phi=7.5 degrees and not 30 degrees. If this is correct, how does it alter the results of the model?

3. What's the relative importance of the hydration energy to the overall free energy of the pore? I'm asking because the pore is assumed toroidal for Eq. (16) in the SI appendix, but the shape is not toroidal anymore. Could the authors elaborate on that?

4. Figure 1B: Is it fair to compare IF signal of PIP2 in permeabilized cells to the signal in non-permeabilized cells?

5. Figure 2A: Did the authors considered a multiple comparison test when inferring the statistical significance, or just performed one-to-one Student's t-test between the different conditions? If the answer is the latter, then caution should be taken in interpreting the observed differences (see e.g. PMID: 31596231)

Reviewer #2:

The calcium sensor Synaptotagmin-1 (Syt1) is known to be a key element for neuronal SNARE-mediated fusion, but how it proceeds is still debated and many different scenarios and physical models have been proposed. In this work, Z. Wu and collaborators use an interesting assay for measuring single fusion events with a very good time resolution (ms): v-SNARE proteins are reconstituted in large nanodiscs and fuse with "flipped cells" expressing t-SNAREs facing the extracellular media. Syt1 interacts either as a full length protein co-reconstituted in the nanodisc or as a truncated soluble version (C2A+C2B domains, or mutants) added in the patch pipette. Single fusion events are followed by electrophysiology using voltage-clamp in the cell-attached mode, as a function of PIP2 in the cell membrane or calcium in the medium. The authors focus mostly on the effect of Syt1 on pore expansion. In parallel, they have developed a mathematical model for fusion of nanodisc and cells based on Helfrich energy for the membrane fusion part and theory of elasticity for the scaffolding by ApoE around the nanodisc. The experiments clearly show that Syt1 promotes the growth of the fusion pore in a way dependent on binding to PiP2 and calcium concentration. Its interaction with SNAREs also contributes to pore expansion. The C2B+C2A domain (C2AB) is sufficient to induce this effect and Ca²⁺-dependent penetration of the hydrophobic loop is essential. These dependences and the pore growth rates are nicely reproduced by a model where at low calcium, the C2B domain binds to t-SNARES and to PiP2, remaining parallel to the membrane and keeping the pore small or closed. When calcium increases, the membrane insertion of the hydrophobic loop while being connected to SNAREs produces a tilt of about 15{degree sign} of the SNARE-Syt1 complex. SNARE-Syt1 acts as a mechanical lever on the pore edge, which changes the pore shape and tends to open it more. The C2A domain's loop strongly boosts the kinetics of the opening process. Altogether, the lever model accounts well for the experiments presented in the study, in contrast with different models previously published.

With this work, we can expect conceptual advances on the contribution of Syt1 to neuronal membrane fusion. But in addition, the modeling of the mechanical deformation of a nanodisc and of its scaffold in the presence of a pore should be more generally relevant to experiments involving mechanosensitive membrane proteins or other pore forming structures.

This manuscript is an extensive revision of a paper that was previously submitted to eLife. The main critics on the previous version were on the mechanical models behind the interpretation of the data, in particular on the mechanical resistance of the ND assembly to pore opening, the toroidal pore model and the torque exerted by the protein scaffold on the nanodisc periphery. It is true that these models are essential for providing a mechanism. As far as I can tell and not being a theoretician myself, I think the authors did a good job at addressing the different issues that were raised by the former editor and reviewers. These new additions reinforce their conclusions and their interpretation of their data. On the experimental side, considering the requests after the previous review and the still difficult situation related to the COVID pandemic, I consider that the new version includes the necessary discussions and precautions, in particular on the limitation of the assay to assess the binding kinetics. Personally, I think that the paper is ready for publication.

Reviewer #3:

This study by Wu et al. presents interesting new results obtained with a very sophisticated experimental system and incorporating very sophisticated modeling into their interpretations. The principal results advance the idea that synaptotagmin promotes fusion pore expansion through its interactions with membranes. The idea of a role for synaptotagmin in pore expansion has been around for quite some time but the present results extend what we know about this process. In particular, Syt1 binding to the lipid bilayer to exert force and change fusion pore shape is novel and interesting. All in all, it is a strong paper but a number of concerns require attention.

1. When the authors state ~4 copies of syt1 and VAMP2 per disc face (page 4 and 5), this is an average and the actual number will have a wide range due to inherent fluctuations when numbers are small. This variation in copy number must be incorporated into the discussion.

2. How do the authors arrive at 10 nm maximum diameter (top of P 5)? There must be a limit in a 25 nm NLP but the actual value is hard to specify, and the 10 nm value seems like a guess.

3. The authors use the Boltzmann distribution to go from the observed pore size distribution to the size dependence of pore energy. This is an impressive leap of insight and creativity. But the Boltzmann distribution applies to systems at equilibrium and the observed conductance time course is probably very far from equilibrium. The underlying process appears to be irreversible. Each pore opening episode looks like a trajectory through a complex energy landscape. Some acknowledgement of these shortcomings must be made.

4. On P 9 the authors discuss changes in pore radius, height, and shape. Doesn't that complicate the relation between diameter and conductance?

5. The last sentence of the Mathematical modeling section on P 10 states that increasing pore height increases membrane bending energy. Ref 109 shows that increasing height reduces bending energy.

6. The final section of Results presents some modeling work with C2A. There are no relevant experiments and the results are not discussed in the Discussion section. I do not see how this section fits into this paper.

eLife. 2021 Jun 30;10:e68215. doi: 10.7554/eLife.68215.sa2

Author response

[Editors’ note: the authors resubmitted a revised version of the paper for consideration. What follows is the authors’ response to the first round of review.]

Computational part

"In cell-attached recordings, the patch of membrane that is under study is under high tension due to adhesion to the walls of the pipette. Strong adhesion of the membrane to the walls of the glass pipette is needed to obtain a high-resistance seal (the so-called "Gigaseal") for low-noise recordings. Previous measurements show the membrane tension in the patch is ~1 pN/nm [37]. This is consistent with our model that obtained a tension of 0.66 pN nm-1 as a best-fit parameter by comparing the model-predicted slope of the free energy of pore dilation for pores of size ~ 1 nm between the model prediction and the experimental measurement when only SNAREs were present in a previous study of ours [3].

Forces that oppose membrane tension at the nanodisc boundary arise presumably from the bending rigidity of the ApoE proteins, and from their interactions with the lipids. A radially inward force per unit length equal to the membrane tension acts on the ApoE scaffold. Assuming only the bending rigidity opposes this inward force, we can compare the membrane tension to the threshold force per unit length where a circular ring buckles, kT Lp /d2 , where : and d and Lp are the radius of the cross-section of the circular ring and its persistence length respectively. As the scaffold proteins consist of a series of α-helical regions interspersed with unstructured regions [38], and a typical persistence length of α-helices is ~ 100 nm [39], the buckling threshold is ~400 pN nm-1 assuming a thickness : d~ 1 nm, much larger than the membrane tension of 0.66 pN nm-1"

The should be a misunderstanding here. According to the classical literature on the buckling instability of a ring, the radial force per unit length of the ring (the membrane tension in the present case) leading to the instability is, approximately, γ~(kT L_p)/r³ , where r is the ring radius. Taking Lp = 100nm, as suggested by the authors, and r~10"nm" , according to the dimension of nanodiscs used in the work, one gets, practically, a vanishing critical tension. This must mean that, as a result of the pore nucleation, the tension drops to zero.

This means that the model is inconsistent with the reality in this essential point.

We apologize for our incorrect and extremely careless response, and we thank the editor for pointing out the error. Our “estimate” of the critical buckling force per unit length for the ND scaffold tension did not even have the correct dimensions. Below, we have done the job carefully. The conclusion is that the ND scaffold is easily strong enough to withstand the forces from the membrane.

In fact, the critical buckling force is not small. As the editor stated, calculation of the stability of an elastic ring gives a buckling threshold ${3 k T L}_{p} / R_{ND}^{3}$ (we include the prefactor; see e.g. S. P. Timoshenko, J. M. Gere, Theory of elastic stability (Courier Corporation, 2009)). Noting that the ND scaffold of radius R_ND ~ 12 nm in fact comprises two α helices, the estimated persistence length is L_p ~ 200nm, giving a substantial critical force per unit length ~1.4 pN/nm. This value is well above the estimated tension ~ 0.1 pN/nm. (Previously we estimated ~ 0.7 pN/nm using the toroidal pore; with our exact calculations of pore shapes – see below – we find a smaller best fit tension).

However, the forces acting on the ND boundary are due not only to tension, but also to bending. The force on the scaffold is determined by the in-plane membrane stress (R. Capovilla et al., J. Phys. A, 2002)

σ^{a} = [2_{k} C (K^{ab} - {Cg}^{AB}) - {γg}^{AB}] e_{b} - 2_{K} \nabla^{a} C n,

whose projection onto the outward pointing membrane tangent vector at the ND boundary 𝝂 = 𝝂_𝒂𝒆^𝒂 and the radial unit vector $\hat{r}$ gives the radial force per unit length acting on the scaffold

f_{r} = \hat{r} • σ^{a} v_{a} = [2_{K} (C_{⊥}^{2} - C_{∥}^{2}) - γ] cos α + 2_{K} \frac{\partial C}{\partial s} sin α

where α is the angle the membrane makes with the “horizontal” direction at the ND boundary, i.e. the angle between the outward pointing membrane tangent vector 𝝂 and the radial direction. Here C_-, C_∥ are the membrane curvatures perpendicular and parallel to the ND boundary, 𝒔 is arclength along the meridian of the membrane (whose rotation about the symmetry axis generates the membrane surface), 𝜿 is the bending stiffness, 𝑪 and K^𝒂𝒃 denote the mean curvature and curvature tensor, 𝒈^𝒂𝒃 the metric tensor, 𝒆_𝒃 the membrane surface tangent vectors, 𝛻^𝒂 the covariant derivative, and 𝒏 the membrane unit normal vector (𝒂, 𝒃 = 𝟏, 𝟐 label directions in the membrane tangent plane, repeated indices summed).

One can get a sense of the magnitude of the force per unit length 𝒇_𝒓 by considering the simple case 𝜶 = 𝟎 (neglecting rotation of the ND boundary). Then 𝑪_∥ = 𝐬𝐢𝐧 𝜶/𝑹_𝑵𝑫 vanishes, so

f_{r} = {2 k C}^{2} - γ

From numerically determined fusion pore shapes (see below) we find a perpendicular radius of curvature $r_{⊥} \equiv C_{⊥}^{- 1} \approx 30 n m$ , weakly dependent on tension in the range 𝟎 < 𝜸 < 𝟏 𝐩𝐍 𝐧𝐦^-𝟏. Using 𝜿 = 𝟐𝟎 𝐤𝐓, this gives an expansive bending contribution ~ 0.18 pN, and a net force per unit length 𝒇_𝒓~𝟎. 𝟏 pN/nm in the outward direction (i.e. a net expansive effect, not contractile). Thus there is no buckling threat to the ND boundary.

These conclusions are qualitatively unchanged when one allows 𝜶 to vary due to rotation of the ND boundary. Solving the membrane shape equation numerically (without toroidal or other variational approximations, see below) and imposing a torque-balance boundary condition at the ND boundary, we find the net inward force per unit length is even smaller in magnitude, 𝒇_𝒓~ −0.01 pN/nm, valid for a range of tensions 𝟎. 𝟏 < 𝜸 < 𝟏 𝐩𝐍/𝐧𝐦. This weak contractile effect is well below the buckling threshold.

"We agree that the toroidal shape is not an exact fusion pore solution, but we use this shape for simplicity, and we believe it captures all the important features of a more exact solution. It has the advantage that the biophysical aspects are clearly articulated. For this reason, toroidal pores have been assumed in many previous theoretical studies (e.g. [40-42])."

This is not a convincing argument. In the previous studies the toroidal pore approximation was used for the cases of two infinitely large membranes connected by a fusion pore. In the present study, the dimension of the nanodisk is of the same order of magnitude as the pore radius so that the deviation from the toroidal shape may have essential consequences for the results.

One of the consequences of the toroidal pore assumption is the conclusion that SNARE reorientation results in the expansion of the pore waist, which is one of the central conclusions of the model. An alternative outcome could be an increase of the tangent angle to the membrane profile at the ND rim without the waist expansion. A detailed computational analysis avoiding the toroidal shape assumption is needed to resolve this issue.

In response to the editor’s suggestion, we performed detailed computational analysis without assuming a toroidal pore (TP). Overall, the exact fusion pore shapes are similar to those predicted by the TP model, and the exact calculations (within the Helfrich framework) show that the pore radius increases when the pore height is increased, as in the TP model (this qualitative effect was central to our model of Syt-mediated pore expansion). The pore free energy versus pore radius is well approximated by the TP model. The biggest failure of the TP model is that the predicted membrane tension, based on fitting the TP model predictions to experiment, is too large. The tension from fitting experiment using the exact solution is lower, because the “exact” pore is more difficult to open up against applied tension than is the TP. Other than this (important) difference, our new numerical calculations have not qualitatively altered our conclusions.

Previous works using the TP approximation typically use infinite planar membranes to obtain solutions, but these solutions are then interpreted in terms of situations with far from infinite membranes. For example, Chizmadzhev et al. and Nanavati et al. (cited in our response above) interpret their results in terms of exocytosis, where vesicles with radii as small as 20 nm (synaptic vesicles) are involved (Chizmadzhev et al. Biophys. J., 2000; Nanavati et al., Biophys. J., 1992). This is clearly inconsistent with the infinite planar membrane boundary condition. Chizmadzhev et al. and Nanavati et al. use the TP to model pores with radii of up to ~30 nm and ~100 nm, respectively, comparable to the size of even large secretory granules. Overall, TP models are widely used to analyze fusion pores between finite sized membranes whose size is of order the fusion pore itself. Given this, it is of interest to note that the TP approximation performs reasonably well.

"Regarding the torque at the nanodisc edge, the question raised by the reviewer, it can be shown that the downward bending is small, so that the flat annulus approximation at the outer nanodisc edge does not deviate by a large amount from the exact solution. The argument is as follows. (1) The angle made by an annular piece of membrane of width : at the nanodisc edge is ? ~ @:!/A, where @ is the downward force per unit length at the nanodisc edge and A is the membrane bending modulus. (2) The net downward force is the same at any cross section of the pore. At the pore waist net downward force is ~ 2C(D + F/2)H, assuming the mean curvature of the waist *+,- is negligible. Here, D , F and H refer to the radius of the pore, the membrane thickness, and *+,- tension respectively. Thus, for pores of radii similar to the membrane thickness, the force per unit length at the ND edge is @ ~ FH/J./ where J./ is the radius of the ND. (3) This force per unit length gives an angle ? ~ FH:!/AJ./. Using : ~ 5 ->, and other values as in Table S1, we get an angle ? ~ 4. Thus, the bending of the membrane is negligible near the nanodisc"

This reasoning is very hard to follow. (i) For some reason, the expressions include the membrane thickness, while the latter is already accounted for by the bending rigidity, which is also a part of the same expressions. (ii) Further, the authors estimate the angle of 4o at the ND edge, while the question is about the curvature (mean curvature) there rather than the angle. The expression for the curvature includes the angle derivative along the contour length, not just the angle itself. (iii) Moreover, the origin of the constant downforce, used by the authors for their argumentation, is unclear. Indeed, the cell membrane is, practically, horizontally oriented so that the downforce at the bottom of the pore should vanish. (iv) The suggestion of an almost vanishing mean curvature in the pore waist is incompatible with the assumption of a considerable lateral tension.

Again, we apologize for our incorrect and confusing previous response, and again we thank the editor for pointing out the errors. We tried to argue that the true fusion pore curvature at the ND boundary is small, so the TP shape (with its assumed flat outer edge) is not dramatically wrong. Roughly we used the tension contribution to the membrane stress to estimate the downward force 𝒇_𝒛 (per unit length) bending the membrane at the edge. In reality 𝒇_𝒛 = 𝟎 as the ND is free, so the tension contribution is balanced by a bending contribution.

Here is the correct argument. Our calculations using the TP model predicted that, with 100 µM Ca, the pore minimizing the membrane free energy has a flat region that extends ~2 nm inward from the ND scaffold. We will argue that the exact solution to the membrane shape equation is not far from flat in this region as well. Using the expression above for the stress tensor, the vertical force per unit length acting on the circle 𝒔 = 𝐜𝐨𝐧𝐬𝐭. of radius 𝑹 lying in the membrane is

f_{z} = \hat{z} \cdot σ^{a} v_{a} = [2_{K} (C_{⊥}^{2} - C_{∥}^{2}) - γ] s i n α - 2_{K} \frac{\partial C}{\partial s} cos α

where 𝑪_⊥ = 𝝏𝜶/𝝏𝒔, 𝑪_∥ = 𝐬𝐢𝐧 𝜶/𝑹 are the curvatures perpendicular and parallel to 𝒔 = 𝐜𝐨𝐧𝐬𝐭. For simplicity, assume 𝜶 = 𝟎 at the ND boundary (clamped boundary conditions), so 𝝏𝑪/𝝏𝒔 = 𝟎 at the boundary. Then for a location close to the ND boundary 𝜶 and 𝝏𝑪/𝝏𝒔 are small so, to leading order,

f_{Z} = [2_{K} • {(\frac{\partial C}{\partial s})}^{2} - γ] α - 2_{K} \frac{\partial C}{\partial s} + 𝓋 (a^{2}) = 0 .

At this point it is not possible to close the perturbative argument, since 𝝏𝑪/𝝏𝒔 is unknown. Thus we used our numerical solutions to calculate this derivative, and we find it contributes negligibly to the vertical force. Hence the square bracket term approximately vanishes, i.e. the curvature 𝝏𝜶/𝝏𝒔 ≈ √(𝜸/𝟐𝜿) ≈. 𝟎𝟐𝟓 𝐧𝐦^$𝟏 after using 𝜸 = 𝟎. 𝟏 pN/nm.

This shows that the exact solution has a small curvature ~. 𝟎𝟐𝟓𝐧𝐦^-𝟏 at the ND edge. For example, the membrane angle 𝜶 is only ~𝟑^𝟎 a distance 𝟐 𝐧𝐦 inwards from the ND edge, corresponding to the width of the flat outer annulus of the TP. This is consistent with our numerical calculations of the membrane shape, which generated angles ~𝟑° − 𝟐𝟎° and curvatures ~𝟎. 𝟎𝟐 − 𝟎. 𝟏 𝐧𝐦-^𝟏 within 2 nm of the ND edge. In conclusion, the exact solution of the membrane shape shows a small downward displacement of the membrane in the flat annulus region assumed by the TP model, showing that the TP model provides a reasonable approximation to the actual shape of the fusion pore in this region.

"The protein scaffold around the nanodisc can be formed by various configurations of the apolipoprotein E variant containing the N-terminal 22 kDa fragment (ApoE422K) [38]. In all cases, it is thought that two rows of stacked α-helical segments form a belt at the boundary of the nanodisc. The α-helical segments interact laterally and are connected by short linkers [38]. The torque contribution could arise either from the twisting rigidity of the α-helices or from the interactions between the proteins and the lipid molecules.

As the reviewer says, we assumed constant torque. We found a potential quadratic in the twisting angle could not reproduce the energetics of large pores of radii ~ 3 – 6 nm when ~15 SNARE complexes are present at the fusion pore without Synaptotagmin-1 [3].

In fact, we did consider the effect of the torque for pores of smaller radii. The proteins are twisted only when the radius or the height of the pore are large enough so that the rim of the toroidal pore where it joins with the flat membranes reaches the boundary of the nanodisc. Such radii or heights are larger than the equilibrium values predicted by the model, so it costs energy to access them. Thus, such states do not contribute much to the statistical average at the equilibrium values of radius and height."

A proposal about a specific mechanism of a constant (independent of deformation) torque generation should enable quantitative estimation of this factor. Otherwise, this energy contribution appears too speculative to be published.

We have discarded the constant torque assumption. We developed a simple mechanical model of ND scaffold rotation. The model predicts a torque linear in the scaffold rotation angle for small deflections, and non-linear for large deflections. Since our solutions of the fusion pore shape equations predict small deflections at the ND edge (~𝟏𝟎°), the linear torque response is appropriate. We predict deflection angles somewhat smaller than the ~ 45° deflections reported in Martini simulations of SNARE-mediated ND-planar membrane fusion (Sharma and Lindau, 2019). We expect our deflection angles to be smaller, since the NDs in our experiments are larger than the NDs used in these Martini simulations.

Our model treats the scaffold as an elastic rod with rectangular cross-section, a simple representation of the two parallel α helices. The elastic bending energy of the rod is

F = \int_{}^{} dL (\frac{K_{soft}}{2} C_{soft}^{2} + \frac{K_{hard}}{2} C_{hard}^{2})

where 𝑲_{𝐬𝐨𝐟𝐭} and 𝑲_{𝐡𝐚𝐫𝐝} are the bending moduli of the rod in the material directions across its narrow and wide faces, respectively, 𝑪_{𝐬𝐨𝐟𝐭} and 𝑪_{𝐡𝐚𝐫𝐝} are the respective material curvatures, and 𝑳 measures the arclength around the scaffold. (The rod is inherently more difficult to bend across its wider face, i.e. is less soft in this direction.) The material curvatures represent the curvature of the scaffold projected onto the basis vectors of the material cross section. Now we treat the scaffold as if it were a homogeneous material with a Young’s modulus 𝑬 and a rectangular cross-section of width 𝒘 and height 𝒉, and we use a classical result from elasticity theory that 𝑲_{𝐬𝐨𝐟𝐭} = 𝑬𝒘^𝟑𝒉/𝟏𝟐, 𝑲_{𝐡𝐚𝐫𝐝} = 𝑬𝒘𝒉^𝟑/𝟏𝟐 (Landau and Lifshitz, Theory of Elasticity, 1959). Thus 𝑲_{𝐬𝐨𝐟𝐭} = 𝟐 𝑲_𝜶 and 𝑲_{𝐡𝐚𝐫𝐝} = 𝟖 𝑲_𝜶, where 𝒌_𝜶 = 𝒌𝑻 𝑳_𝐩 is the bending modulus of a single α helix of persistence length 𝑳_𝑷 ≈ 𝟏𝟎𝟎 𝐧𝐦. Thus 𝒌_{𝐬𝐨𝐟𝐭} ≈ 𝟐𝟎𝟎 𝒌𝑻 𝐧𝐦 and 𝒌_{𝐡𝐚𝐫𝐝} ≈ 𝟖𝟎𝟎 𝒌𝑻 𝐧𝐦.

Suppose the cross section of the scaffold is rotated such that the long axis of the cross section makes an angle 𝜽 with the vertical direction, while maintaining the shape of the scaffold as a ring of radius 𝑹_𝑵𝑫. Then the material curvatures are

C_{soft} = \frac{cos θ}{R_{ND}} C_{hard} = \frac{sin θ}{R_{ND}}

This gives an elastic bending energy

F = 2 π R_{ND} (\frac{k_{soft}}{2} \frac{{cos}^{2} θ}{R_{ND}^{2}} + \frac{K_{hard}}{2} \frac{{sin}^{2} θ}{R_{ND}^{2}})

The torque per unit length to twist the scaffold through an angle 𝜽 is thus

τ = \frac{1}{2 π R_{ND}} \frac{\partial F}{\partial θ} = \frac{K_{hard} - K_{soft}}{{2 R}_{ND}^{2}} s i n 2 θ \approx \frac{K_{hard} - K_{soft}}{R_{ND}^{2}} θ

Using the parameter values above, the model predicts that a torque per unit length ~2 pN twists the boundary scaffold of the ND an amount ~𝟑𝟎^𝟎. We incorporated these effects in our calculation of the fusion pore shape by imposing a torque equilibrium condition at the ND edge, so that membrane torque is resisted by the ND scaffold. Numerical solutions of the membrane shape equation with this boundary condition predicted deflections ~𝟏𝟎° at the ND edge, and curvatures ~0.05 nm^-1.

Summary of new model calculations and changes to text in the revised manuscript

Exact numerical solutions of the nanodisc-cell membrane fusion pore shape and energetics with and without Syt-SNARE complexes

In response to comments from the reviewers and editor, we abandoned the toroidal pore assumption and instead we solved the exact membrane shape equation for the ND-cell membrane fusion pore in the framework of the Helfrich model that accounts for membrane tension and bending energy. The model includes a torque equilibrium between the outer edge of the ND membrane and the ND scaffold, using a simple mathematical model of the elastic bending energy of the ND scaffold to predict the energy of scaffold rotation. This torque equilibrium is implemented as a boundary condition in our solutions of the shape equation. From numerical solutions, we determined the free energy of the pore versus pore radius and inferred the ND membrane tension by comparing these predictions to our previous experimental measurements of fusion pore conductances. We then added a contribution to the free energy representing the effect of SNARE complexes, dependent on the number of SNAREs present. (This parallels the procedure we used in our earlier toroidal pore-based calculation.)

We then repeated this procedure in the presence of Syt-SNARE complexes at the fusion site. These complexes imposed a constraint on the possible fusion pore shapes, since a Syt-SNARE complex must bind the membrane at a certain angle at both the C-terminal end of the SNARE complex, where SNARE TMDs insert into the bilayer, and the N-terminal end, where the Syt C2B domain Ca²⁺-binding loops tightly bind acidic phospholipids. In the presence of the Syt-SNARE complexes, smaller fusion pores had higher free energies. Thus, in the presence of Ca²⁺ when the Syt Ca²⁺-binding loops bind the membrane, pores of larger radius are energetically favored due to this geometric lever-like constraint. We find the predicted free energy versus pore radius profile is consistent with our experiments, both in the presence and absence of Ca²⁺. The model quantitatively reproduces the experimentally observed increase in conductance in the presence of Ca²⁺ with high accuracy.

Summary of changes to the manuscript related to the new mathematical modeling results

1. The changes to our model and our new results are detailed in the section “Mathematical modelling suggests that Syt1 and SNARE proteins cooperatively dilate fusion pores in a mechanical lever action.” Figure 6, referenced in that section, was updated with our new results. Figure 6B shows examples of our numerical solutions of the membrane shape equation with and without the constraint imposed by the Syt-SNARE complex. Figures 6C and 6D show quantitative data from the updated model. Figure 6E was updated to be consistent with our model of the ND scaffold that accounts for its finite twisting rigidity.

2. The SI subsections: “Mathematical model of the fusion pore with SNAREs and Synaptotagmin-1,” “Membrane free energy,” “Short-ranged steric hydration free energy”, “Free energy of SNAREs”, “Total free energy as a function of pore size, minimum membrane separation, total number of SNAREs”, and “Pushing forces from the membranes are insufficient to disrupt the SNARE-Syt primary-interface interaction” were updated to be consistent with our new model. New SI subsections were added entitled “Geometric constraints imposed by the Syt-SNARE complex,” “Mathematical Model of the ApoE scaffold,” and “Numerical method of solving the membrane shape equation.” Figure S8 was updated to include our fit of the membrane tension to previously obtained experimental data and to include predictions of the new model.

Experimental part

The reviewers were disappointed to learn that the authors chose not to do an additional experiment, in particular, of determining the binding kinetics of nanodiscs to the cell membranes. The reviewers believe this experiment would yield an important piece of data showing what constitutes the rate-limiting step in the fusion pore assay the authors have developed. Moreover, the technical difficulties stated in the rebuttal, mainly high fluorescence backgrounds, may be bypassed using techniques such as FRET.

However, the senior author professed difficult situations in his lab midst the current pandemic situation. Therefore, at least regarding Comment 1, the authors need to state these potential issues in their experimental assay-including low rates of fusion pore opening, low cooperativity and unawareness of the rate-limiting step-and discuss the limitations and reservations in interpreting their data sets. It may then be possible to proceed as the authors have suggested (on page 7 of the rebuttal).

We thank the reviewers and the editor for accommodating pandemic-related issues, which are still ongoing. We now explicitly state throughout the manuscript the potential issues raised by the reviewers and the editor. Specifically:

a. We now explain the low rates of fusion pore opening in the first paragraph of the Results section (p. 4).

b. We have added two paragraphs to Discussion (pp.13-14) explaining the low cooperativity, the lack of knowledge about pre-fusion stages, and the need to be careful about interpretation of our results.

We have then implemented the revision plan suggested on p. 7 of the rebuttal. Namely:

c. To clarify what is meant by the rate of fusion pore opening (pores/min), we have edited the first paragraph in Results (p. 4), and the first paragraph in section "Syt1 promotes fusion pore expansion" (p. 5). We also moved SI Figure S8 to an earlier position (it is now SI Figure S2) and made changes accordingly to the text. This figure shows examples of current recordings, explains how pore currents are selected, how the fusion rate increases with nanodisc concentration in the pipette, and an alternative calculation of the fusion rate.

d. We have added a new panel (F) to Figure S6, showing how the fusion rate (pores/min) increases with calcium concentration. This panel is now referenced in section

"Calcium-dependence of pore dilation by Syt1 C2AB" on p. 7.

We made additional changes in response to issue #3 ("Some parts of the presentation need clarification"), as we had outlined in the revision plan:

e. We added some clarifications about pore lifetimes in the first paragraph of Results (p. 4) and referred to Karatekin, FEBS Lett, 2018 for a discussion of the relevance of nanodisc-based single pore assays to exocytotic fusion pores.

f. We edited the sections regarding curvature generation by Syt1, such that the relevant literature is cited, but not overemphasized.

In response to a minor comment, we moved the paragraph about the effects of the R398QR399Q mutation to Discussion.

[Editors’ note: what follows is the authors’ response to the second round of review.]

Essential Revisions:

We request no additional experiments. We are only asking for some revisions that are mostly aimed at improving the clarity the manuscript as well as some extra computations regarding the model's assumptions. These additional computations should be relatively straight-forward for the authors. For these required revisions, see the detailed reports from Reviewer #1 and Reviewer #3. In particular, we'd like to emphasize on the following:

1. About the BCs used for the computations (see e.g. Eq. (8) of the SI Appendix): the authors should study (or provide a solid argumentation on why this might not be necessary) the shape and energies when the tCell membrane does not relax to a perfectly flat state but to a catenoidal shape.

We performed additional calculations relaxing our assumptions about how the fusion pore membrane connects up to the tCell membrane. We found that relaxing these assumptions makes very little difference to the shape of the fusion pore. We added a figure to the appendix demonstrating this, see below.

2. The final section of Results presents some modeling work with C2A. There are no relevant experiments and the results are not discussed in the Discussion section. It is not clear how this section fits into this paper, so unless the authors can adapt it to provide a logical explanation in the context of this paper, this section should probably be removed.

We have removed this section from the paper.

Reviewer 1:

[…]

That being said, I have some specific comments about the model, and about some of the assumptions made there:

1. Perhaps to me the most important one is the BCs shown in Eq. (8) of the SI Appendix. There the authors assume that the membrane (on the tCell side) is flat (phi(L)=0) at a certain distance (R_inf=30nm) from the pore axis. A couple of thoughts.

– R_inf is chosen somehow arbitrarily.

– Why does the membrane need to relax to a flat state far away from the pore and not a catenoidal geometry (which also has zero bending energy)? This latter condition could be implemented by assuming phi(L)≠0. To me, intuitively (so maths might proof me wrong of course), such a geometry could make that zipping does not lead to pore expansion but maybe to a change in the catenoidal angle? I think that the authors should discuss if this makes sense or not.

We thank the reviewers for these constructive comments. Our choice of R_inf was actually not completely arbitrary, although no systematic analysis was performed to choose an optimal value. The only requirement we insisted on is that R_inf is sufficiently large that the boundary conditions imposed at the location (r=R_inf) where the pore joins the tCell membrane have little to no effect on the pore shape. This is expected to be true provided R_inf > 𝑙_cap where $l_{cap} = \sqrt{k / 2 γ}$ is the capillary length. Thus, we expect that provided R_inf is significantly greater than 20 nm, our model should reasonably describe the true pore shape. This observation is now mentioned in the appendix, in the section “Numerical method of solving the membrane shape equation”.

To verify this, we performed additional calculations of the fusion pore shape assuming a larger value of R_inf (50 nm). The fusion pore shapes were nearly identical to those with the original R_inf value in the region where their domains overlap. In particular, in the vicinity of the fusion pore, the two shapes were visually indistinguishable.

Our assumption that the membrane is flat where it meets the tCell membrane is motivated by the assumption that the large tCell membrane is itself flat (far enough away from the site of the fusion pore). To verify that this boundary condition did not influence the model results, we performed additional calculations, relaxing the assumption that the tCell membrane is asymptotically flat far away from the pore and instead implementing freely hinged boundary conditions where the pore meets the tCell membrane. These boundary conditions allow the membrane to choose the angle it makes at the point where it joins the tCell, equivalent to imposing zero torque at this location. This boundary condition produced very little change in the pore shape, as expected since the torque at this location was very small even with the previous zero slope boundary condition. Again, in the vicinity of the fusion pore the pore shape was indistinguishable from the shape obtained with zero slope boundary condition. This insensitivity to the boundary conditions used is now stated in the main text in the subsection “Mathematical modelling suggests that Syt1 and SNARE proteins cooperatively dilate fusion pores in a mechanical lever action” and in the appendix in the section “Numerical method of solving the membrane shape equation”.

We added a supplementary figure (Figure S8E) showing solutions of the fusion pore shape for each of these boundary conditions, so readers can easily and instantly compare them visually.

2. I've noticed some inconsistencies in the "Mathematical Model of the ApoE scaffold" in the SI Appendix. In particular:

– some references are missing in the appendix.

Thank you, this has been fixed.

– Eq. (14) in the app. please use U_scaffold and not F.

Thank you, this has been fixed.

– pg. 11 appendix: with the definition given in Eq. (14) of k=(K_hard-K_soft)/(2 R_NLP²), and using the values in the text just above that, I get k=2.1 kBT/nm and not 4.2 kBT/nm as the authors wrote. Please verify. And then the evaluation of the twist angle for a 2 pN torque, in my hands, appears to be phi=7.5 degrees and not 30 degrees. If this is correct, how does it alter the results of the model?

We thank the reviewer very much for alerting us to these arithmetic errors. We corrected these errors. Note that these errors were present only in the text of the SI appendix, and were not used in the calculations of the model, and therefore have no impact on our results.

3. What's the relative importance of the hydration energy to the overall free energy of the pore? I'm asking because the pore is assumed toroidal for Eq. (16) in the SI appendix, but the shape is not toroidal anymore. Could the authors elaborate on that?

The hydration energy only affects the energetics of the pore at very small pore radii, less than ~0.5 nm, due to the very rapid drop off of the hydration forces (exp (−𝑟/(0.1 nm))). Thus, this term has little effect on our results; it primarily serves to account for the repulsive self-interaction of the pore at very small radii. Unfortunately, this effect cannot be accounted for analytically without a closed form expression describing the shape of the fusion pore, and an assumption about the shape is therefore required at this step.

4. Figure 1B: Is it fair to compare IF signal of PIP2 in permeabilized cells to the signal in non-permeabilized cells?

Our goal was to compare the amount of exogenous, short-chain PI(4,5)P₂ incorporated into the outer leaflet of the plasma membrane with the amount of endogenous PI(4,5)P₂ found in the inner leaflet. To access the endogenous PI(4,5)P₂ in the inner leaflet, permeabilization was required. These results are meant to show that the amount of exogenous PI(4,5)P₂ incorporated into the outer leaflet is not completely off the mark which might put into question the relevance of the PI(4,5)P₂ dependence we find. This type of comparison is the best we could do, and we believe it is adequate for the question we asked.

5. Figure 2A: Did the authors considered a multiple comparison test when inferring the statistical significance, or just performed one-to-one Student's t-test between the different conditions? If the answer is the latter, then caution should be taken in interpreting the observed differences (see e.g. PMID: 31596231)

We do not think a multiple comparison test is appropriate for the data presented in Figure 2A, because the results summarize two different biological questions with associated control experiments.

In order to determine which statistical test is most appropriate, McDonald

(http://www.biostathandbook.com/) recommends starting with a biological question, then formulating the question in the form of a biological null-hypothesis and an alternative hypothesis. The statistical null-hypothesis and the alternative hypothesis (which are about the data only) are formulated next, as they must follow from the biological hypotheses.

The first biological question we asked was whether the presence of Syt1 affected the rate of SNAREmediated membrane fusion. The biological null-hypothesis is that Syt1 does not affect the rate of SNARE-mediated membrane fusion. The statistical null hypothesis is that the mean fusion rate in the presence of Syt1 is the same as the rate in its absence. The other three conditions tested in the presence of Syt1 were control experiments. We know from the literature that Syt1 binds calcium and acidic lipids, and these interactions are needed for its function. Thus, if either of these co-factors are omitted, no effect of Syt1 is expected. Treatment with TeNT has in fact nothing to do with Syt1; TeNT cleaves the vSNARE Syb2/VAMP2 and is expected to reduce the fusion rate if fusion is indeed SNARE-dependent.

The second biological question we asked was whether the soluble C2AB domain of Syt1 alone behaves similarly to the full-length protein, given that Syt1 increased the rate of membrane fusion. The biological null-hypothesis is that C2AB does no increase the fusion rate. The statistical null hypothesis can be formulated as "the mean fusion rate in the presence of C2AB is not higher than in its absence". If the statistical null-hypothesis is rejected, then we would conclude that C2AB behaved similarly to Syt1. Alternatively, we could formulate the statistical null hypothesis as "the fusion rate in the presence of Syt1 or C2AB are the same" (which is likely not to be rejected given the scatter in the data, leading to the conclusion that the C2AB domain behaves like Syt1). The other three conditions tested in the presence of C2AB were controls as above.

We could of course ask: "does Syt1 or its soluble domain promote SNARE-mediated membrane fusion under any condition shown in Figure 2A?", which would require an adjustment for multiple comparisons, but this question would be too general. The biological null-hypothesis would then be: "Syt1 or its C2AB domain do not affect membrane fusion under any conditions tested", and the statistical null-hypothesis would be: "the mean fusion rate is the same under any condition tested".

Multiple comparison tests were developed because if one performs pair-wise comparisons over multiple conditions, the probability of falsely rejecting the null-hypothesis increases with the number of conditions. Multiple comparison tests add a penalty to avoid this type of error. However, if one includes in the multiple comparisons conditions that are not directly related to the biological hypothesis, then the probability of finding an actual effect decreases, because there is an unnecessary penalty paid for the comparisons that should not be included in the first place.

Of course, the biological question and the null-hypothesis can be formulated after performing the experiments in such a way that only some conditions appear relevant and are included in multiple comparisons. In our case, the TeNT experiments should clearly be excluded from multiple comparisons (because they do not directly test the role of Syt1 in fusion), but one might argue that Syt1 might affect fusion without its co-factors and that the conditions omitting calcium or PI(4,5)P₂ should be considered nominal variables that should be included in a multiple comparison test.

A one-way ANOVA between the first four conditions in Figure 2A resulted in a p-value of 0.0064, suggesting the group means are different. A comparison between the control (SNARE-alone) and Syt1+calcium+PI(4,5)P₂ adjusted for multiple comparisons using Tukey’s Honestly Significant Difference Procedure yielded a p-value of 0.0128. Thus, the mean fusion rate in the presence of Syt1 and its cofactors is higher than the SNARE-alone case (at the %5 level of significance). (The conditions omitting either co-factor are not significantly different than the control.) Repeating this procedure with C2AB, we find a p-value of 0.1231 for one-way ANOVA and 0.1661 when comparing the control to the condition with C2AB+calcium+PI(4,5)P₂ (using the Tukey procedure as above). That is, at face value, the multiple comparison test would change the earlier conclusion that the fusion rate with C2AB in the presence of calcium and PI(4,5)P₂ is significantly larger than the rate observed with the control group.

However, this raises an issue regarding the use of multiple comparisons, and more broadly of null hypothesis significance testing. The same SNARE-alone (i.e. "no C2AB") control group and the "C2AB" (with calcium and PIP₂) group are re-plotted in Figure 3B and Figure 5B for comparison with other conditions. These different figures address different biological questions. Because the number of groups are different in each case, the p-value for comparing the control group against the C2AB group changes depending on how we present the data, which is somewhat arbitrary.

Due to its shortcomings, alternatives to null-hypothesis significance testing are being developed. We explored the use of the estimation graphic introduced by Ho et al.¹ to visualize the effect size together with an indicator of precision (the 95% confidence interval, CI), derived from bootstrapping. Compared to parametric methods, this approach is more robust for data sets with non-normal distributions. Author response image 1 shows the mean difference between control (SNAREs alone) and Syt1 in the presence of calcium and PI(4,5)P₂ (Syt1CaPIP2) is 0.535 pores/min, with 95.0%CI=[0.258, 1.35], whereas the mean difference between control and C2AB in the presence of calcium and PI(4,5)P₂ (C2ABCaPIP2) is 0.294 pores/min, with 95.0%CI = [0.0685, 0.785]. That is, this approach supports the conclusion that the fusion rate with C2AB in the presence of calcium and PI(4,5)P₂ is larger than the rate observed with the control group.

Author response image 1. — The raw data is plotted on the upper axes. On the lower axes, mean differences are plotted as bootstrap sampling distributions. Each mean difference is depicted as a dot. Each 95% confidence interval is indicated by the ends of the vertical error bars. 5000 bootstrap samples were taken; the confidence interval is bias-corrected and accelerated. (see ref. 1).

Our fusion rate data in Figure 2A and other figures should indeed be interpreted with caution, not so much because adjustments for multiple comparisons were omitted in null-hypothesis testing, but because the assay is not optimal for reliably estimating fusion rates, which are not a focus of our study. We require the fusion rate to be low by design in order to detect single events. As the rate increases, the number of events counted does not increase as rapidly, because events that may be overlapping (which increase in frequency with increasing fusion rate) are not counted in the analysis – an issue not captured by the statistical analyses above.

In summary, our interpretation of these results is that in the presence of calcium and PI(4,5)P₂, Syt1 increases the fusion rate. Fusion is still dependent on SNAREs, as TeNT inhibits fusion. The soluble C2AB domain of Syt1 seems to recapitulate the effects of Syt1 on fusion rates, but we are less confident about whether C2AB really causes an increase in the fusion rate in the presence of its co-factors.

We note that our main conclusions are based on single-pore conductance measurements which are more robust and not affected by our fusion rate estimates.

We have left the pair-wise comparisons as they are, but we added two notes of caution in the text:

last paragraph on p. 5:

“Note that our fusion rate estimates throughout should be interpreted with caution, because they are inherently noisy and they systematically underestimate fusion rates when the rates are high. Both effects are due to the fact that in the assay only a few fusion pores can be analyzed per patch (see SI Methods and ref. (2)).”

last paragraph on p. 6:

“Similar to the results with full-length Syt1, there was little change in the fusion rate compared to the SNARE-alone case if either calcium or exogenous PI(4,5)P₂ was omitted (Figure 2A). When both calcium (100 μM) and PI(4,5)P₂ were present, the fusion rate was higher, but we are not as confident about this increase as in the case of Syt1. The mean conductance was significantly above the SNARE-only value in the presence of calcium and PI(4,5)P₂, but not when either was omitted (Figure 2B).”

Reviewer #3:

This study by Wu et al. presents interesting new results obtained with a very sophisticated experimental system and incorporating very sophisticated modeling into their interpretations. The principal results advance the idea that synaptotagmin promotes fusion pore expansion through its interactions with membranes. The idea of a role for synaptotagmin in pore expansion has been around for quite some time but the present results extend what we know about this process. In particular, Syt1 binding to the lipid bilayer to exert force and change fusion pore shape is novel and interesting. All in all, it is a strong paper but a number of concerns require attention.

1. When the authors state ~4 copies of syt1 and VAMP2 per disc face (page 4 and 5), this is an average and the actual number will have a wide range due to inherent fluctuations when numbers are small. This variation in copy number must be incorporated into the discussion.

We agree. We have added the following sentence to Discussion:

"Another, possibly related, limitation is that due to the small numbers of proteins that can be incorporated into nanodiscs, large fluctuations are expected in the actual copy numbers from disc-to-disc. Such fluctuations likely contribute to the variability observed in our single-pore measurements, e.g., of mean conductance values. "

2. How do the authors arrive at 10 nm maximum diameter (top of P 5)? There must be a limit in a 25 nm NLP but the actual value is hard to specify, and the 10 nm value seems like a guess.

This is an estimate based on geometrical constraints and measurements of maximum conductance values by Wu et al.³. Shi et al.⁴ previously used similar arguments for smaller, MSP-based nanodiscs. A more direct estimate was provided by Bello et al.⁵ who monitored the efflux of encapsulated fluorescent dextrans of different sizes during fusion between v-SNARE reconstituted NLPs and t-SNARE liposomes. They concluded that NLP-liposome fusion pores can reach >9 nm in size. We have added this reference to the relevant passage (top of p. 5).

3. The authors use the Boltzmann distribution to go from the observed pore size distribution to the size dependence of pore energy. This is an impressive leap of insight and creativity. But the Boltzmann distribution applies to systems at equilibrium and the observed conductance time course is probably very far from equilibrium. The underlying process appears to be irreversible. Each pore opening episode looks like a trajectory through a complex energy landscape. Some acknowledgement of these shortcomings must be made.

We agree. We have added ref. Wu et al.3 where a similar approach was used (and the assumptions discussed). We also added the following passage on p. 6:

“Invoking the Boltzmann distribution amounts to assuming the membrane-protein system is approximately in equilibrium, i.e. the conductance measurements are approximately passive and only weakly perturb the fusion pore. We cannot exclude substantial non-equilibrium effects, as application of a potential difference may in itself promote pore formation and affect the structure and dynamics of the pores that result, as seen in lipid bilayer electroporation studies (84), although the potential difference used in our studies is much lower (<20 mV). Generally, the profiles we report should be interpreted as effective free energies.”

4. On P 9 the authors discuss changes in pore radius, height, and shape. Doesn't that complicate the relation between diameter and conductance?

Changes in the shape of the pore do in general change the relation between diameter and conductance. We used a general formula to determine the conductance of the fusion pores predicted by our model, see equation (20) of the SI appendix. This formula makes no assumptions about the pore shape other than it being axially symmetric.

5. The last sentence of the Mathematical modeling section on P 10 states that increasing pore height increases membrane bending energy. Ref 109 shows that increasing height reduces bending energy.

The membrane energy does not depend monotonically on the height of the pore: there is a height that minimizes the energy of the pore, which we assume is selected in the absence of forces associated with the Syt-SNARE complex. Whether a change in the pore height increases or decreases the energy of the pore thus depends on the initial state of the pore. Our statement refers specifically to the situation when the initial condition is the pore that minimizes the bending energy as a function of height; from this state, increasing (or decreasing) the height of the pore will by definition increase the bending energy. In Ref 109 increasing the height of the pore decreases the energy because the initial state of the pore is a compressed state. (In fact it could not be the case that increasing the height of the pore decreases the membrane energy quite generally, since were this true the height of fusion pores would increase without bound.)

6. The final section of Results presents some modeling work with C2A. There are no relevant experiments and the results are not discussed in the Discussion section. I do not see how this section fits into this paper.

We agree with the reviewer that this section is disconnected from the remainder of the paper. We have removed this section from the paper.

References

1. Ho J, Tumkaya T, Aryal S, Choi H, Claridge-Chang A. Moving beyond P values: data analysis with estimation graphics. Nature Methods16, 565-566 (2019).

2. Karatekin E. Toward a unified picture of the exocytotic fusion pore. FEBS Lett592, 3563-3585 (2018).

3. Wu Z, et al. Dilation of fusion pores by crowding of SNARE proteins. elife6, e22964 (2017).

4. Shi L, et al. SNARE Proteins: One to Fuse and Three to Keep the Nascent Fusion Pore Open. Science335, 1355-1359 (2012).

5. Bello OD, Auclair SM, Rothman JE, Krishnakumar SS. Using ApoE Nanolipoprotein Particles To Analyze SNARE-Induced Fusion Pores. Langmuir32, 3015-3023 (2016).

6. Wang S, Li Y, Ma C. Synaptotagmin-1 C2B domain interacts simultaneously with SNAREs and membranes to promote membrane fusion. elife5, (2016).

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PERMALINK

The neuronal calcium sensor Synaptotagmin-1 and SNARE proteins cooperate to dilate fusion pores

Zhenyong Wu

Nadiv Dharan

Zachary A McDargh

Sathish Thiyagarajan

Ben O'Shaughnessy

Erdem Karatekin

Roles

Abstract

Introduction

Results

Co-reconstitution of Synaptotagmin-1 and v-SNAREs into nanolipoprotein particles

Syt1 promotes fusion pore expansion

Figure 1. Detection of single fusion pore currents mediated by Syt1 or its C2AB domain.

Figure 2. Syt1 promotes fusion and expands fusion pores in a calcium and PI(4,5)P2 dependent manner, and soluble Syt1 C2AB largely recapitulates these effects.

Pore dilation by Synaptotagmin-1 C2AB requires binding to calcium, PI(4,5)P2, and likely SNAREs

Figure 3. Pore expansion by Syt1 C2AB requires calcium, PI(4,5)P2, and putative SNARE binding sites to be intact.

Calcium-dependence of pore dilation by Syt1 C2AB

Figure 4. Calcium-dependence of pore properties.

Calcium-dependent membrane-insertion of Syt1 C2AB is necessary for pore dilation

Figure 5. Calcium-induced membrane insertion of Syt1 C2AB hydrophobic loops are critical for both pore nucleation and expansion.

Mathematical modeling suggests that Syt1 and SNARE proteins cooperatively dilate fusion pores in a mechanical lever action

Figure 6. Mathematical model of the fusion pore in the presence of Syt1 and SNAREs suggests a mechanical calcium-triggered pore dilation mechanism.

Discussion

Materials and methods

Recombinant protein expression and purification

Reconstitution of synaptotagmin-1 and VAMP2 into nanodiscs

Stable flipped SNARE cell lines

Single fusion pore conductance assay

Statistical analysis

Acknowledgements

Appendix 1

Recombinant protein expression and purification

Co-reconstitution of Synaptotagmin-1 and VAMP2 into nanolipoprotein particles (NLPs)

Stable flipped SNARE cell lines

PI(4,5)P2 incorporation and immunostaining

Whole-cell conductance of flipped t-SNARE cells

Single fusion pore conductance assay

Detection of fusion pore currents

Estimation of fusion rate

Estimation of fusion pore parameters

Estimation of fusion pore expansion rates

No evidence for ATP-dependent channel activity in flipped t-SNARE cells

Cell membrane potential changes do not significantly distort cell-attached fusion pore recordings

Statistical analysis

Mathematical model of the fusion pore with snares and synaptotagmin-1

Membrane free energy

Numerical method of solving the membrane shape equation

Mathematical Model of the ApoE scaffold

Geometric constraints imposed by the Syt-SNARE complex

Short-ranged steric hydration free energy

Free energy of SNAREs

Total free energy as a function of pore size, minimum membrane separation, and total number of SNAREs

Model-predicted pore conductance

Pushing forces from the membranes are insufficient to disrupt the SNARE-Syt primary-interface interaction

Appendix 1—table 1. Parameters used in the mathematical model with coarse-grained membranes, SNAREs and Synaptotagmin-1 C2B domains.

Appendix 1—figure 1. Co-reconstitution of Synaptotagmin-1 and VAMP2 into nanolipoprotein particles (vsNLPs).

Appendix 1—figure 2. Fusion rates.

Appendix 1—figure 3. Additional properties of single fusion pores in the presence of full-length Syt1 or soluble C2AB.

Appendix 1—figure 4. Syt1 C2AB dilates fusion pores in a calcium and PI(4,5)P2 dependent manner.

Appendix 1—figure 5. Additional fusion pore properties for Syt1 C2AB domains carrying mutations in D309, K326-327 and R398-399.

Appendix 1—figure 6. Additional fusion pore properties as a function of free calcium concentration, [Ca2+]free.

Appendix 1—figure 7. Additional fusion pore properties for Syt1 C2AB membrane penetration mutants.

Appendix 1—figure 8. Results of the mathematical model of the fusion in the presence of SNAREs and Syt1 C2AB domains.

Appendix 1—figure 9. Lack of ATP-regulated channel activity in flipped t-SNARE cells.

Appendix 1—figure 10. Average pore conductance as a function of time, after aligning pores to the moment of opening (blue) or closure (red).

Appendix 1—figure 11. Whole-cell conductance of flipped t-SNARE HeLa cells.

Funding Statement

Contributor Information

Funding Information

Additional information

Competing interests

Author contributions

Additional files

Data availability

References

Decision letter

Roles

Author response

Figure 2. Syt1 promotes fusion and expands fusion pores in a calcium and PI(4,5)P₂ dependent manner, and soluble Syt1 C2AB largely recapitulates these effects.

Pore dilation by Synaptotagmin-1 C2AB requires binding to calcium, PI(4,5)P₂, and likely SNAREs

Figure 3. Pore expansion by Syt1 C2AB requires calcium, PI(4,5)P₂, and putative SNARE binding sites to be intact.

PI(4,5)P₂ incorporation and immunostaining

Appendix 1—figure 4. Syt1 C2AB dilates fusion pores in a calcium and PI(4,5)P₂ dependent manner.

Appendix 1—figure 6. Additional fusion pore properties as a function of free calcium concentration, [Ca²⁺]_free.