How “Full” is “Full Fusion” during Exocytosis from Dense Core Vesicles? Effect of SDS on “Quantal” Release and Final Fusion Pore Size

In this work, release was elicited from PC12 using sufﬁciently small concentrations of sodium dodecyl sulfate (SDS) to perturb normal release mechanism in an attempt to reveal concealed information while keeping physiologically compatible conditions. Amperometry was used to monitor and quantify the released ﬂuxes and kinetics in individual vesicular events. This showed that stimulating release with SDS 350 μ M leads to a doubling of the quantity of catecholamine cations released per event and much larger release ﬂuxes as compared to controls (release elicited with K + 105 mM under same conditions) or SDS 250 μ M. These quantitative measurements conﬁrm our previous theoretical model and reports based on ex situ cytometric experiments on isolated PC12 vesicles, which established that release is far from being total under normal exocytotic conditions. Secondly, this establishes that the maximal size of fusion pores at the end of the “full fusion” phase is limited by some contraption unrelated to the membrane. Indeed, the present results are entirely consistent with the fact that SDS 350 μ M allows the fusion pore to expand to a double size (ca. 28 nm radius) compared to controls and SDS 250 μ M (ca. 14 nm radius).

The considerable importance of the mechanism of vesicular exocytosis in biology and medicine [1][2][3][4][5][6] has stimulated an increasing number of reports. This high importance is evidenced, for example, by the award of two recent Nobel prizes in physiology and medicine bearing on these issues, the latest one being awarded in 2013 to James E. Rothman, Randy W. Schekman, and Thomas C. Südhof. [3][4][5][6] In neurons and endocrine cells neurotransmitters are stored and transported inside vesicles to be finally delivered at specific release sites of the outer cell membrane. 7 Vesicles and cells membranes connect there through activation of SNAREs complexes following intracellular gated calcium ions influxes to form a nanometric fusion pore through which neurotransmitters can diffuse away. [7][8][9] Most of the biochemical cellular processes regulating the formation and the intracellular traffic of these vesicles -as well as the corresponding biomolecular machineries involved -are now well established and documented. However, albeit this recognition, and after more than 20 years of important intensive and thoughtful works the crucial ultimate stages of the process which govern vesicular exocytotic events, viz., the very delivery of neurotransmitters in the extracellular space, are not fully understood beyond those relative to the transient initial fusion pore through which only a modest amount of neurotransmitters may be released 10-12 whose dimensions (ca. 1.2 nm radius) and fast dynamics (Kiss and Run) have been characterized by patch-clamp, [13][14][15][16][17][18] and very recently through amperometry. 19 In endocrine cells, the main releasing stage involves a fast expansion of the initial fusion pore, generally thought to lead to a full incorporation of the former vesicle membrane into the cell one, 20 through a process usually termed "full fusion" in biological textbooks and by many authors. This phase involves a rapid significant increase of the surface area of the matrix surface exposed to the solution compared to that allowed by the initial fusion pore. This leads to a sharp increase of the released flux of neurotransmitter that may be readily detected by amperometry using an "artificial synapse" configuration (see Figure 1A). [21][22][23][24][25][26][27][28] When this expansion terminates and the fusion pore stabilizes at its maximum opening radius R pore (see below), this flux decreases following an exponential clearing of the vesicle initial * Electrochemical Society Member. z E-mail: christian.amatore@ens.fr; zqtian@xmu.edu.cn content. [26][27][28] When monitored by amperometry at carbon fiber microelectrodes, i.e., through the 2e-oxidation of catecholamines, 23 this gives rise to the classical "spike" pattern shown in Figure 1A whose time-integration provides the detected charge Q, viz., the overall released quantity per vesicle through application of the Faraday law. Note that the release through the initial fusion pore gives rise to a small pre-spike feature (PSF or "foot") that is observable in ca. 30% of the events (see Figure 1B). 22,[27][28][29][30][31][32] Up to very recently, it was assumed that amperometric spikes featured the complete unloading of the neurotransmitter amount present in the vesicle before fusion, viz., that Q = Q tot = 2eN tot where e is the absolute charge of an electron and N tot is the total number of catecholamines molecules. However, Ewing and coll recently established that this hypothesis was invalid and that Q = 2eN rel , where N rel , the number of released molecules, is only ca. 40 to 60% of N tot . 33 Several effects may be invoked to rationalize such observation. A first one, put forward by Ewing and colleagues [31][32][33] consists in considering that the fusion pore closes before complete release could occur. However, even if several cases in which this certainly occurs have been reported by the same group, this cannot be general. Indeed, this contradicts the general observation of exponential current decay after the spike maximum up to the point where the currents reach the baseline. Indeed, such exponential behavior implies that the surface area, A pore , of the interface between the vesicle matrix and the extracellular fluid is constant. 26,27 In this respect, it must be mentioned that our own previous quantitative analyses of current spikes from chromaffin cells evidenced that the expansion of the fusion pore during the "full fusion" stage generally stops after a few millisecond when the fusion pore radius has reached ca. 10% of the vesicle radius. [26][27][28] Note that such final pore radius is much larger than that of the initial fusion pore (ca. 10 times, i.e., producing a ca. 100 times increase in A pore ), a fact that perfectly justifies the observation of sharp current rises as soon as the initial fusion pore architecture is ruptured. Conversely, this shows that "full fusion" is very far from being complete as could be inferred from TIRFF 20 but ends up when only ca. 1% of the vesicle matrix surface area is exposed to the extracellular medium. In other terms, vesicles matrixes remain constrained by the vesicles membranes when release occurs, i.e., they cannot swell as they do when their membranes are fully removed. 33,34 This implies that the partition coefficient of the neurotransmitter cations inside of the matrixes (vs. the extracellular fluid) remains sufficiently large to ensure a certain kinetic stability to the whole matrix structure. 35 In our view, this is most certainly the main reason justifying that N rel is smaller than N tot . Evidently, any additional effect such as a closure of the fusion pore would eventually aggravate the discrepancy between N rel and N tot . In a previous report, 35 we introduced a theoretical concept that justifies this point based on a model inferred from de Gennes' theory of polyelectrolytes condensation by monocations 36,37 and found that its thermodynamic and kinetic consequences were fully consistent with the present experimental observations. In particular, this model predicts that when the vesicles have significantly unloaded their fast-releasing content, the decay branch of spikes may display a second exponential behavior with a larger time constant than that characterizing the main release mode. Within this model, this second and slow-releasing mode corresponds to slow kinetic exchanges between rather compacted matrix domains and less condensed ones through which diffusion occurs fast enough to sustain the fast-releasing mode currents. Interestingly, Ewing and colleagues have recently shown that this is the case for PC12 cells since about 60-70% of the events display decay branches involving two-exponential modes. 31 Therefore, the most recent quantitative data about vesicular exocytosis point out that the former "full fusion" stage does not proceed usually to a complete incorporation of the vesicle membrane into the cell cytoplasmic membrane even if this may happen as evidenced by a few reports based on internal reflectance microscopy observations (TIRF). 20 However, owing to the high surface tension of the membrane due to the strong curvatures around the vesicle matrix and especially along the nanometric-sized fusion pores, one expects that a pure membrane-driven system 38,39 should evolve irreversibly to a complete "full fusion" in order to relax all curvatures. 40,41 Hence, it is clear that the fusion pore expansion dynamics is not only regulated by bilipidic membranes dynamics but is constrained by some external biological feature 10 whenever its radius reaches a given threshold value. This is fully consistent with previous quantitative reports from this group that established that the relative energy of fusion pores drastically increases when this threshold radius (ca. 15 nm in chromaffin cells) is approached. 28 Considering the necessary involvement of the sub-membrane actin-cytoskeleton during the initial stages leading to exocytosis, as well as the high density of such structures at releasing sites, it is reasonable to expect that fusion pores consist of membrane tubes 42,43 connecting the vesicle and cells membranes and passing across a dynamic actin-fiber network. [44][45][46][47][48] Therefore, the mesh-size of the actin-fiber sub-membrane network is expected to regulate the fusion pore expansion through imposing an additional high edge-tension energetic component compensating the membrane surface tension. This hypothesis is again fully consistent with a recent report from Ewing's group that showed that tampering with the actin sub-membrane cytoskeleton polymerization/depolymerization rates mediated the fusion pore size up to eventually enforcing its closure. 32 In this work, we wish to contribute to this search by examining the quantitative and kinetic changes induced in PC12 exocytotic events when these are elicited following their brief stimulations by very dilute sodium dodecyl sulfate (SDS) solutions. Based on previous studies, SDS concentrations lower than 400 μM cannot affect cells membranes structure 49,50 but may be transferred across them and weaken actin assembling in sub-membrane cytoskeletons. 49 It is shown hereafter that eliciting release with SDS 350 μM led to physiologically realistic vesicular exocytotic events, i.e., comparable to those elicited by classical methods such as brief stimulations by K + 105 mM, except that the released quantities resulted almost doubled.
Sodium dodecyl sulfate (SDS) was obtained from Sinopharm Chemical Reagent Co., Ltd. (catalog number: 30166428) and used as received.
Working electrodes were constructed from carbon fiber (10 μm diameter, Thornel P-55S or 5 μm diameter, Hexcel -IM7). A single carbon fiber of 3 cm long was isolated. Half of the single carbon fiber length was glued onto the end of a 0.25 mm diameter 8 cm long silver wire by silver adhesive 503 (12686-15, Electron Microscopy Sciences). The carbon fiber mounted on the silver wire was then inserted into a glass capillary (o.d. 1.2 mm i.d. 0.69 mm, BF120-69-10, Sutter Instrument). The outside silver wire was fixed tightly to the capillary end with a Teflon tape. The capillary was then pulled with a microelectrode puller (Model P2000, Sutter Instrument Co., USA) and the carbon fiber protruding from the tip was insulated by a thin layer of poly(oxyphenylene) according to previously reported electropolymerization method. 67 The insulated carbon fiber was beveled on a diamond particle whetstone microgrinder (Model EG-400, a HEPES buffer. Single spikes parameters were extracted from amperometric traces using the commercial program pClamp and statistically analyzed with Origin to determine their median values; first (25%) and third (75%) quartiles are indicated between parentheses. b Data for K + stimulations encompass the whole set of controls used for SDS 250 μM (n = 333, Figure 5) and SDS 350 μM (n = 152, Figure 6). c For SDS 350 μM, only 16% of the spikes displayed a singleexponential decay branch i decay fit (t) ∝ exp(−t/τ) (time constants and v rise values shown in the table); the 84% remaining ones corresponded to two-exponentials decays modes, i.e., i decay fit (t) ∝ exp(−t/τ)+ γ exp × exp(−t/τ slow ), with τ / ms = 1.1 (0.9; 1.6), τ slow / ms = 5.4 (3.9; 7.3) (see Figure 7) and γ exp = 0.12 ± 0.02. Narishige, Tokyo, Japan) at an angle of 45 • for 3 min to expose a fresh and regular surface. Only carbon fiber electrodes with noise smaller than 3 pA rms were used. Micropipettes with openings of ca. 5 μm were prepared by pulling glass capillaries of the same type and were used as such.
For stimulated exocytosis detection, cells were washed and bathed in HEPES saline buffer (containing 125 mM NaCl, 5.5 mM KCl, 0.8 mM MgCl 2 , 1.8 mM CaCl 2 , 20 mM HEPES, 24 mM Glucose and 36.5 mM Sucrose at pH 7.3), unless stated otherwise. The high K + stimulating solution contains 105 mM KCl, 25.5 mM NaCl, 0.8 mM MgCl 2 , 1.8 mM CaCl 2 , 20 mM HEPES, 24 mM Glucose and 36.5 mM Sucrose at pH 7.3. The SDS stimulating solutions consisted of SDS dissolved at the required concentration in the same HEPES saline buffer used in the Petri dish. A glass micropipette containing the stimulating solution was positioned 20 μm from the investigated single cell. Repetitive stimulations involved 5 s injections (80 psi) at 45 s intervals through the micropipette coupled to a microinjector (FemtoJet, Eppendort). All experiments were performed at room temperature. All control data were collected in the same day as the experiment using the same cell batch.
Electrodes were held at + 680 mV vs. Ag/AgCl electrode (locally constructed by polarizing a 0.5-mm-diameter silver wire at a current density of 0.1 mA·cm −2 in 0.1 M HCl for 6 h) immersed directly in the HEPES saline buffer, using a commercially available patchclamp amplifier (Axopatch 200B, Axon Instruments). The output was digitized at 10 kHz and filtered at 1 kHz using an internal low-pass Bessel filter. Data were displayed in real time using the Clampex 10.2 software (from pClamp, MDS Analytical Technologies) and stored to the computer with no subsequent filtering.
The mean baseline current of each amperometric trace were manually set as the current origin for the whole trace. Exocytotic spikes were identified by "Threshold search". Only single spikes with peak current values larger than 9 pA (S/N > 3) were visually scrutinized. When a spike current did not returned to the mean baseline before a second spike started, the two spikes were discarded. The characteristics (Q, i max , t peak , t 1/2 , v max and τ, see Table I and Figure 1A for definitions) of the remaining spikes were determined using the Clampfit 10.2 software (from pClamp, MDS Analytical Technolo-gies) and analyzed statistically with Origin. The frequencies of events exhibiting pre-spike features were determined by visual inspection.

Delineation of the range of SDS concentrations apt to eliciting
exocytosis.-At first glance, using a detergent such as SDS to affect delicate functions in living cells may seem fully inappropriate since it is well known that when used at moderate concentrations (mM or above) detergents cause membranes lysis followed by cells death.
However, exposure of cells to brief injections of small enough SDS concentrations (i.e., 250 and 350 μM as is used in this work) has been reported to cause only reversible effects into cytoplasmic membranes. 49,50 This amounts to only increase the life-time of the nanopores 49 which spontaneously and constantly form and close due to thermal disorders in bilipidic membranes. 38 On the one hand, transient stabilization of spontaneously forming nanopores 38 in cell membranes is expected to allow direct calcium ions intake from the extracellular medium 49 without the need of relying on cells exposure to high concentrations pulses of potassium ions. On the other hand, this should also allow the formation of wider exocytotic fusion pores by relaxing at a molecular level the important local curvature strains created into lipid nanotubes or toroid junctions connecting cell and vesicle membranes. 42,43 Conversely, at the low concentrations used in this work SDS has been shown to have no effect on the SNAREs machineries that lead to initial fusion pores formation. 51,52 Hence, eliciting exocytosis by SDS at these low concentrations should not tamper at all with the formation of calcium-induced SNAREs complexes that initiates the critical process leading to the opening of the initial exocytotic fusion pores. Finally, it is important to note that exposing a cell to a brief pulse of low SDS concentrations cannot at all modify its vesicles internal structure nor their catecholamine content since this should require at least several minutes.
Of high interest for our purpose here, is also the fact that small SDS amounts that may penetrate within the cell through SDS-stabilized membrane nanopores have been reported to induce reversible disorganization of the actin-assembling proteins. 53 Hence, submitting cells to brief SDS pulses at concentrations less than 400 μM appears perfectly safe regarding the important physiological mechanisms involved in exocytosis while providing a significant tampering with the actin membrane cytoskeleton stability or dynamics. This was therefore investigated in this work in order to test the recent views recalled in the Introduction about exocytotic mechanisms.
To explore and test the range of validity of these hypotheses, PC12 cells have been stimulated by brief exposures to different SDS concentration covering the 200 μM -2 mM range and their ensuing exocytotic behavior investigated by amperometry. This serve to delineate the SDS concentration range leading to near-physiological responses, as compared to control ones elicited classically, e.g., with 105 mM K + (Figure 2A) that will be used as controls hereafter. A first observation is that even in the absence of potassium ion stimulation (see more below) release occurred immediately after a brief SDS pulse was applied to the cells ( Figures 2B-2D). However, clearly different responses were evoked depending on the SDS concentration.
In agreement with expectations based on previous reports, 49,50 too high SDS concentrations (e.g., 1.5 mM in Figure 2B) led to intense broad signals after the first stimulation and the cells rapidly became inert after a few stimulations suggesting profound damages and possibly cell death. Only the first stimulation produced a discrete series of overlapping amperometric spikes superimposed onto the broad signals ( Figure 2B). The global charge of the broad current signals corresponded to an amount of catecholamine cations exceeding by far the expected content of a few hundreds of vesicles. Presumably, at this concentration, the cell membrane structure is so drastically affected so that significant SDS quantities may diffuse inside the cell to reach vesicles and lyse them allowing a considerable quantity of catecholamine cations to be released and freely diffuse toward the electrode. 49,50 This would lead to broad diffusion-controlled current traces while some intact vesicles may still provide sharp spikes. However, this does not evidence that such spikes featured normal exocytotic processes. Indeed, cells membranes lesions provoked by this high SDS range may have been sufficient for vesicles to leak out from the cell as a whole and collapse directly on the electrode surface. 54,55 Evidently, such situation is of no interest for our purpose here but may serve as a marker for signalling disrupting effects induced on PC12 cells by SDS at too large concentrations. Much smaller SDS concentrations elicited amperometric traces ( Figures 2C and 2D) similar to those obtained with 105 mM K + in terms of the spike number and frequency. SDS 350 μM ( Figure 2C) led to long terms effects that resulted in the near suppression of release when a second pulse was applied though the first stimulation led to a behavior similar to that induced by K + elicitation. Conversely, SDS 250 μM ( Figure 2D) elicited responses qualitatively similar to those of K + 105 mM even after several stimulations of a same cell. The responses observed during successive stimulations up to the 7 th one resulted quantitatively undistinguishable from those evoked by the first one (data not shown) as evidenced qualitatively in Figure 2D showing that no significant long-term effects occurred. In agreement with previous reports, [49][50][51][52][53] this survey of SDS on exocytosis confirmed that 250-350 μM corresponded to an adequate concentration range for our purpose in this study. Yet, to ensure the absence of any non-obvious long-term effects, only the spikes delivered during the first 10 s range after the first stimulation were treated quantitatively. Also, for keeping a certain homogeneity, spikes that did not exhibit a clear return to the baseline were discarded (though these may be perfectly compatible with our recent model considering that vesicles matrixes have a grainy structure). 35

SDS elicits exocytosis through calcium-mediated processes.-
Under normal conditions, calcium intake through calcium-ion channels near release sites enforces SNAREs complexes to assemble, leading first to vesicles docking and then to the formation of initial fusion pores between the cell and vesicle membranes. 9 In K + elicited release, the sudden increase in potassium ions extracellular concentration affects the electrical potential of the membrane, allowing ultimately Ca 2+ triggering of release. 56,57 Such mediated calcium-ion entry should result impossible when SDS alone is used to elicit vesicular release. On the other hand, SDS is reported to stabilize the transient nanopores that constantly form in cellular membranes 38 or contribute to the formation of trans-membrane channels. 49,50 Hence, Ca 2+ intake is expected to occur spontaneously after brief SDS stimulation, thus initiating exocytosis by triggering the physiological Ca 2+ -induced cascade recalled above. 9 Therefore, to validate the physiological relevance of the results presented and discussed hereafter it was essential to firstly assess if this is effectively the case when exocytosis is elicited by SDS. For this purpose, we investigated if SDS 250 or 350 μM could, or not, induce exocytosis in the total absence of calcium ions in the extracellular solution.
To test this crucial issue, the calcium (and magnesium) ions contents in the HEPES buffer were progressively reduced up to a complete suppression of even traces of these ions by adding a strong chelating agent (ethylene glycol tetraacetic acid, EGTA) into the buffer. Figure 3 establishes that when no Ca 2+ or Mg 2+ were purposely added in the preparation of the HEPES buffer ( Figure 3B), the amount of exocytotic spikes stimulated by SDS 350 μM was drastically reduced compared to those observed with normal HEPES buffers (compare Fig. 2C and Fig. 3A). Furthermore, few release events occurred more than 30 s after the end of the stimulation. In Figure 3C, 100 μM EGTA (ethylene glycol tetraacetic acid) was added to the buffer used in Figure 3B to remove divalent cations traces with the result that absolutely no exocytotic spikes could be detected. This series of experiments confirmed that the exocytotic events elicited by SDS involved an intracellular Ca 2+ -mediated mechanism. Furthermore, it also demonstrated that the amperometric spikes detected after SDS 250 or 350 μM stimulation cannot be ascribed to vesicles collapsing on the electrode surface after their leaking away from the cell through structural defects generated by SDS in the cell membrane. Indeed, would the contrary be true, the amperometric traces would be almost independent of the presence or not of calcium ions in the extracellular buffer. 54,55 SDS shortens the half-lives of initial fusion pores.-An important characteristic of vesicular exocytosis is that it proceeds through formation of initial fusion pores by SNAREs-mediated mechanisms. As recalled in the Introduction, in ca. 30% of the events elicited by usual methods, the initial fusion pores have a sufficiently long life-times to give rise to small current plateaus or ramps of variable duration (termed pre-spike feature, PSF, or "foot") preceding the fast increasing branch of the main amperometric spikes ( Figure 1B). 22  PSFs were also observed when exocytosis was simulated with SDS 250 or 350 μM. In both cases, the proportion of spikes with PSFs resulted ca. 40% of that in K + controls indicating that a fraction of the initial fusion pores had smaller life-times than those of controls and could not last sufficiently long to be observed. Nonetheless, in K + or SDS 250 μM elicited events, PSFs with plateau shapes corresponded to an average current intensity of 3.6 pA. This value was similar to the average one (3.9 pA) of single PSFs monitored when exocytosis was elicited by SDS 350 μM indicating that the three methods of stimulation led to the creation of initial fusion pores of similar radii, viz., involved similar SNAREs complexes machineries and SNAREsinduced outcomes. Interestingly, for SDS 350 μM about half of the clearly observable PSFs exhibited two successive components before the exponential rising branches of the corresponding spikes were displayed (compare Figures 4A and 4B for ramp and plateau shaped dual PSFs). For plateau-shaped PSF the average current intensity of the second PSF plateau had an average current intensity of 7.3 pA relative to the baseline. Such unusual double-PSF features were not noted for K + -controls or SDS 250 μM in this work but have already been evidenced previously for K + -controls after quantitative reconstructions of fusion pore opening time-function. 28 Characteristics of exocytotic amperometric spikes elicited by SDS 250 and 350 μM.-The qualitative identity of exocytotic responses observed in Figures 2A and 2D between the responses evoked by K + 105 mM and SDS 250 μM was further confirmed by that of the quantitative comparison of the released spikes characteristics whose analyses are shown on Figure 5 and whose median, first and third quartile values are reported in Table I. Interestingly, while the released charges are almost identical, the peak current values of the spikes, i max , were ca. 16% higher and the rising rates, v, were ca. 42% larger when release was elicited with SDS. This suggested that SDS 250 μM acted on fusion pore widths, leading to their faster expansion toward wider final radii.
Though statistically significant, these increases in i max and v were moderate. Hence, to examine if they evidenced a clear drift in the spikes characteristics, it was decided to also treat quantitatively the spikes elicited by SDS 350 μM. Since amperometric traces such as that in Figure 2C evidenced that, at this concentration, SDS had some long-time effects these treatments were restricted to the spikes monitored during 10 s after the first stimulations. It was also checked that for this restricted population no systematic drift of the spike characteristics occurred. This was also true for the (untreated) spikes monitored between 10 and 20 s after the first stimulation. Hence, one may reasonably consider that the spikes samples that were analyzed quantitatively did not involve any significant contribution of longterm effects, though such effects become apparent at longer times (see Figure 2C). The data in Figure 6 and summarized in Table I confirmed the trends observed for SDS 250 μM. Indeed, i max and v increased by 250% and 210%, respectively, compared to the K + controls. Importantly, although the median charge released following SDS 250 μM was similar to that of K + control, stimulations by SDS 350 μM led to a doubling of the median released quantities.
Note that some of the amperometric data were recorded with carbon fiber electrodes of different diameters (10 μm in Figure 5; 5 μm in Figures 6 and 7). However, it has been established previously that this does not affect at all the time characteristics and intensities of individual spikes including their mean PSFs shapes and probabilities of observation. 58 Only the number of spikes in a given amperometric trace decreased with the electrode size because more events are collected with a larger electrode that explores a larger surface area of the cell. 58 We favored the 5 μm electrodes when investigating spikes elicited by SDS 350 μM (Figures 6 and 7) so as to allow a better precision on the measurements of the longer time constants of the two-exponential decays since this increases artificially the mean time interval between two spikes.

Discussion
The series of investigations reported above establish that brief pulses of extremely low SDS concentrations ([SDS] ≤ 350 μM) elicit vesicular exocytosis from PC12 cells (Figs. 1, 2) under conditions that appear physiologically valid. When monitored by amperometry at carbon fiber microelectrodes the ensuing exocytotic events display all the main qualitative features characterizing those provoked by classical elicitors such as potassium ions. Importantly, the presence of calcium ions in the extracellular medium was shown to be an absolute requirement for stimulating release (Figure 3). This evidently establishes that the amperometric spikes observed cannot be ascribed to vesicles externalized from the cell through SDS-induced lesions in the cell membranes and collapsing directly onto the electrode carbon surface, 54,55 but proceed through classical calcium-mediated processes. In strong support of this statement is also the observation of PSF features that are identical in shape and intensity ( Figures 1B and  4) to those induced by K + 105 mM that characterize the SNAREs mediated formation of initial fusion pores. 9 This result perfectly conforms with previous published data showing that SDS at concentrations less than 400 μM do not affect SNAREs. 51,52 Hence the SNAREs machineries may be put into effect following calcium ions intake inside the cell through nanopores that constantly forming transiently in cell membranes and are certainly stabilized by the presence of SDS. 38 The biological mechanism of Ca 2+ intake thus differs from that induced by K + but the ensuing biological pathways are not expected to be significantly different. Therefore, all the independent tests performed and discussed above strongly support that SDS-elicited exocytotic events have a valid physiological relevance provided that SDS is used at concentrations of 350 μM or below.
In other words, the resulting amperometric spikes may be treated quantitatively to examine if this uncommon elicitor allows unravelling aspects relative to extent of "full fusion" that are not experimentally accessible when using classical elicitors and that we wish to discuss hereafter. A first aspect is brought by the decrease by ca. half of the probability of observing PSF features (i.e., from ca. 30% for spikes elicited by K + to ca. 12% for SDS) and to the fact that at the largest SDS concentration used here (350 μM) a significant fraction of the PSFs exhibit double-plateaus or double-ramps shapes. A second one concerns the spike rising branches whose rates are drastically increased with the result that the peak currents result larger and eventually double for SDS 350 μM (see v rise and i max values in Table I). Finally, the released charges also increased vs. K + controls. This increase is moderate but detectable for SDS 250 μM but leads   Table I. to a doubling of the released quantities for SDS 350 μM. This is of extreme importance since according to Ewing et al. such doubling is expected to represent a near complete emptying of the vesicles. 54,55 Interestingly, this changes correlates with the fact that while most of the spikes decay branches could be closely modeled by single-exponential fits, viz., i decay fit (t) ∝ exp(−t/τ), see Figure 1A, with similar time constants to those elicited by K + (Table I and Figure 5C) when SDS 250 μM was used, most (84%) of those elicited by SDS 350 μM displayed two-exponential decays modes with the smaller time constant value τ being ca. half of those reported in Table I for K + and SDS 250 μM, and the largest one τ slow nearly three times larger (Figure 7).
We wish to establish in the following that all these quantitative changes are closely connected together and stem from the fact that SDS increases the expansion rates of fusion pores and, for SDS 350 μM, leads to a near doubling of their final radius at the end of the fast expansion phase. Our goal in doing so is not so much related to what happens when vesicular exocytosis is elicited by SDS since anyway this is not an effector with proper physiological characteristics. Instead, we wish to use this conclusion to establish that the "full fusion" classical view is largely incorrect. Indeed, this evidently shows that under normal conditions the fusion pores reach sizes that are much smaller than those of their parent vesicles, and that the Figure 6. Statistical analyses of single amperometric spikes elicited in HEPES buffer from PC12 cells by SDS 350 μM (red bins, n = 100; see text for the specific sampling used) or K + 105 mM (black bins, n = 152). Spikes were monitored with 5 μm diameter carbon fiber electrodes held at +680 mV vs Ag/AgCl and placed in close contact with single PC12 cells apical poles (artificial synapse configuration). See Figure 1A for the definition of the spikes characteristics: (A) released charges, Q; (B) current maxima, i max ; (C) time constants, τ, for the 16% of the spikes exhibiting decay branches that could be modeled by single exponential fits (see Figure 7 for the distributions of the two time constants of the 84% remaining spikes); (D) half-widths, t 1/2 ; (E) rising rates v rise . Median, first and third quartile values of each distribution are reported in Table I. released quantities are only a fraction of those initially contained inside vesicles.
For this purpose, we need first to establish or recall a series of quantitative relationships in order to allow a proper quantitative treatment of the different parameters reported in Table I. exponential decay modes of current spikes.-In a previous report, 35 we established that dense core matrixes cannot swell significantly during release unless fusion pores may expand to approach sizes that are comparable to those of the parent vesicles as advocated by the classical "full fusion" concept. This occurs because small fusion pores is tantamount to the fact that the matrixes remain essentially constrained by the vesicles membranes at the end of catecholamine cations release. Hence, the corresponding Laplace pressure counteracts the swelling pressure developing inside of the matrixes when released catecholamine cations are replaced by hydrated monovalent ions. Consequently, would the matrixes be isotropic, release would necessarily stop before complete release may occur in order to ensure some stability to the whole system. However, we established in the same report that to comply with the established physical laws of polyelectrolytes condensation 36,37 (viz., chromogranins A and B in the present case) by monovalent cations (catecholamines) and smaller amounts of divalent ones (calcium), the matrixes must adopt a composite grainy structure in which highly compacted chromogranins nanodomains are immersed into a much less compacted bulk (the "two-pool" model sketched in Figure 8). This view is fully coherent Figure 8. Schematic depiction of a local nanoscopic domain of the grainy structure of dense core matrixes in endocrine cells vesicles according to the two-pool model. 35 The black solid curves represent the chromogranin polyelectrolyte backbone being more or less folded by its condensation by catecholamine and calcium cations (see text).

Connection between released quantities and single-or double-
with the outcome of molecular dynamic simulations. 59,60 Such twopools structure allows the catecholamine cations stored in the less compacted areas to diffuse at significant rates and be released at a fast rate. Conversely, those stored in the tightly packed domains may be released only after they may migrate into the fast-releasing pool, 35 i.e., only after this latter one is almost emptied.
Within this framework, release maybe modeled by the global equation shown in Eq. 1, where q slow and q fast represent the time-dependent quantities of catecholamine cations stored in the slow-releasing (i.e., in the tightly compacted chromogranin domains) and fast-releasing (i.e., in the more or less continuous domain) compartments of the matrix while q out is the quantity that has been released, i.e., detected by the electrode and whose time variations give rise to the spike current in Eq. 2 that follows from Faraday's law.
i(t) = n F(dq out /dt) [ 2 ] k slow and k fast are kinetic parameters equivalent to rate constants that feature the exchange between the two compartments; note that assuming that the matrix is at equilibrium before release, one has k slow /k fast = q t=0 fast /q t=0 slow while the total quantity initially stored in the matrix is q t=0 total = q t=0 fast + q t=0 slow . k diff ρ = ρD ves (π/R ves ) 2 is the reciprocal of the time constant τ shown in Table I and Figures 5-7. 26-28 D ves is the mean apparent diffusion coefficient across this tortuous domain whose outer radius is identical to that, R ves , of the vesicle. Provided the value of the fusion pore radius, R pore , is small, viz., such as R pore /R ves < 0.4, 26-28 a condition that largely encompasses all the situations considered in this work, ρ is very closely approximated by ρ = R pore /(π 2 R ves ), 26 35 was an entirely theoretical contribution this did not change at all any of its conclusions.
The formulation in Eqs. (1,2) allows formulating analytical expressions of the decay branches of amperometric spikes under two circumstances that are of importance here as well as for rationalizing other experimental observations reported by Ewing et al. 31,32 Indeed, the observation of amperometric spikes with exponential decay branches is tantamount to saying that R pore has achieved a constant value after the spikes maxima, 26,27 so that k diff ρ is constant. This is achieved at different specific times depending on the rate of the fusion pore expansion. So, for sake of simplicity, let us first consider that the kinetics of opening is infinitely fast compared to release.
A first case of interest is observed when the exchange between the slow and fast compartments is too slow vs the releasing rate from the fast one. Then, only the catecholamines contained initially in the less condensed domains can be released during a spike, the release from the second compartment, if it occurs, giving rise to a negligible current that cannot be observable due to the noise level. Integration of the system in Eqs. 1, 2 then affords: that characterizes a single-exponential decay mode with a time constant τ = 1/k diff ρ , and a total charge released equal to Q = n Fq t=0 fast < n Fq t=0 total . Conversely, when the exchange rate k slow is not so small vs. k diff ρ , the fast depletion of the less condensed domain enforces a continuous transfer from the highly packed one into it. As discussed elsewhere 35 this leads to a variety of situations depending on the value of the ratios k slow /k diff ρ and k slow /k fast . Though, only one of these possibilities is of interest here since it leads to the observation of a slow second exponential mode (τ slow = 1/k slow ) following the fast first one (τ = 1/k diff ρ ), as also observed by Ewing et al.: 31,32 [5] so that Q = n Fq t=0 total , showing that the total initial vesicle content is released.
Interestingly, these two situations seem to correspond exactly to what was observed in the present work. For the spikes elicited by K + or SDS 250 μM and 16% of the events for SDS 350 μM singleexponential decays corresponding to Q ≈ 100 fC (Table I), while for the majority (84%) of those prompted by SDS 350 μM doubleexponential decays were observed correlating with a doubling of the released quantities (Q ≈ 200 fC, Table I).
Identifying the time constants in Eqs. 3 or 4 with the experimental ones reported in Table I for the spikes with single (or first) exponential decays evidences that for controls, 1/k diff ρ = τ = 1.9 (controls), 2.2 (SDS 250 μM) or 1.1 ms (SDS 350 μM). k diff ρ = ρD ves (π/R ves ) 2 , where D ves (π/R ves ) 2 is an intrinsic property of the matrix that is not expected to depend on the elicitor. Therefore, ρ = R pore /(π 2 R ves ), necessarily depends on the concentration of SDS, a fact that is fully coherent with the reported effect of SDS dilute concentration in stabilizing bilipidic membranes pores. 49,50 It is then inferred that for SDS 250 μM the fusion pore achieves a final radius similar to that reached for K + -controls while this value is more than doubled for SDS 350 μM, though in all circumstances the maximum fusion pore size remains smaller than that of the vesicle.
Since the diffusion rate, D ves /R 2 ves , within PC12 matrixes is not known, it is impossible to precisely deduce R pore values from those of τ. However, a crude estimate of D ves /R 2 ves for PC12 cells can be obtained by comparing the current plateaus value of single PSF events recorded here (3.6 to 3.9 pA) to those (ca. 0.6 pA) recorded for chromaffin cells for which D ves /R 2 ves = 415 s −1 has been established. 28 This suggests that the diffusion rate is ca. 6.2 times faster in PC12 matrixes than in those of chromaffin cells, viz., (D ves /R 2 ves ) PC12 ≈ 2.6 × 10 3 s -1 . Using this estimated value and a mean radius of 80 nm for PC12 vesicles radius yields R pore values of ca. 28 nm and 14 nm respectively for SDS 350 μM and K + controls. Interestingly, the R pore value thus evaluated for controls is similar to that (ca. 12-15 nm) determined for chromaffin cells when exocytosis is also elicited classically. 27,28 This brings both support to this estimate and suggests that under normal circumstances the expansion of the fusion pore is limited by a similar superstructure in both cells.
The formulation in Eq. 3 establishes that the spikes displaying a single exponential decay mode (K + , SDS 250 μM, and 16% of the events elicited by SDS 350 μM) release only the fraction q t=0 fast of their initial content, viz., that Q = n Fq t=0 fast . From Table I, this implies that ca. 3 × 10 5 molecules are released per vesicle after K + , SDS 250 μM stimulations and 16% of the events elicited by SDS 350 μM. Conversely, for the majority (84%) of the events elicited by SDS 350 μM, i.e., those that display a two-exponential decay mode, one has Q = n Fq t=0 total from Eq. 4. Hence, ca. 6 × 10 5 molecules are released per vesicle, showing that under control conditions or SDS 250 μM stimulation the vesicles empty only ca. half of their initial contents. This indicates that catecholamine cations are approximately equipartitioned in the two matrix domains before release. Each number is larger than those reported by Ewing and his group for the PC12 cell lines they investigated, 33 but it is established that the vesicular content of PC12 depend on the PC12 cell subculture investigated. 61 More significantly, their ratio, viz., q t=0 fast /q t=0 total ∼ 0.5, corresponds perfectly to that, i.e., 0.4 ≤ q t=0 fast /q t=0 total ≤ 0.6, evaluated by Ewing et al. based on a thoroughly different series of measurements. 33 To conclude this section, we wish to stress an important caveat. Indeed, one may be tempted to use the values extrapolated at zero time of the exponential regressions of the decay branches to directly evaluate q t=0 fast or q t=0 total based on Eq. 3 or Eq. 4 respectively. However, this would be fundamentally correct only if fusion pores were to open infinitely fast compared to the time constants of the exponential decay branches.
When this is not the case, as it occurs for most experimental spikes that display a clear rising branch, the opening rate of the fusion pore introduces a time delay, t lag , in the exponential behavior(s) of the spike decay. This evidently does not affect the values of the time constants τ and τ slow but only the values of the pre-exponential factors. Note that the situation is formally similar to that encountered when considering the Cottrellian decay branch of a voltammetric peak that is proportional to (t − t lag ) −1/2 , where t lag increases with the sluggishness of the voltammetric peak, instead of being proportional to t −1/2 as for a strict Cottrellian response (i.e., that which would be observed for the same system in chronoamperometry). This is clearly visible upon considering the series of spikes in Figure 9B that were simulated considering the series of different opening kinetics, R(t)/R pore , shown in Figure 9A. Figure 9B evidences that the slower the fusion pore opening rate the larger is the value of t lag , so that the exponential decay branches result increasingly shifted along the time axis. In the general two-exponential case, these decay branches are thus given by: (note that the single-exponential case corresponds to = 0, and τ = 1/k diff ρ and τ slow = 1/k slow ). Eq. 6 establishes that the amplitudes of the exponential regression laws do not provide any direct experimental access to the values of q t=0 fast and (i.e., to q t=0 slow /q t=0 fast would Eq. 5 be strictly valid) but this requires that t lag is known. In particular, the ratio of the pre-exponential terms in Eq. 6 is: [7] rather than γ = /(1 − ) as predicted by Eq. 4. This explains why the γ exp value (0.12) reported in Table I is smaller than that (γ = 0.25) that would be deduced from Eq. 5 for τ = 1.1 ms, τ slow = 5.4 ms (Table I) and q t=0 slow ≈ q t=0 fast as determined above. In fact, all data become coherent upon considering a mean time lag value in the range of 1 ms. Such t lag value seems qualitatively coherent with the spikes mean half-width (t 1/2 = 2.1 ms, Table I) Figure 9B considering the sharp average spikes shapes elicited by SDS as illustrated in Figure 10.
i max values and expansion rates of fusion pores.-The above section and Figure 9B have evidenced that spike peak current values are not directly correlating with the maximum fusion pore size since they result from a convolution between its rate of opening and that of diffusional release, as well as of the possible contribution of the second-exponential kinetics that characterizes the transfer of catecholamine cations from the slow pool into the fast one (see Eq. 1). Furthermore, without a proper quantitative analysis it is impossible to know if i max corresponds to the overall release of the quantity q t=0 fast or of q t=0 total = q t=0 slow +q t=0 fast , or of any intermediate value except when a single exponential decay branch is observed. Indeed, then it necessarily features the release of q t=0 fast since the transfer from the slow domains into the fast one is frozen during release. This is precisely what occurs when comparing the values in Table I for controls and SDS 250 μM. Hence, the increase by ca. 15% of i max when release is elicited by SDS 250 μM compared to K + indicates that the fusion pore opens faster in Figure 10. Comparison between two representative spikes during release elicited by K + 105 mM (controls) or SDS 350 μM. Note that the second one is much sharper near its maximum but displays of longer lasting tail due to the progressive release of the slow pool through transfer in the fast one, see Eq. 1 and Figure 8. the former case, a result that is in full coherence with the increase by ca. 42% in v rise that leads to sharper spikes than for controls (as is illustrated in Figure 9). Conversely, when release is elicited by SDS 350 μM, i max is ca. 2.5 times larger than for controls because v rise is even greater (ca. twice that for controls) leading to much sharper spikes in the time range containing their maxima as evidenced in Figure 10. Indeed, owing to the relative values of τ slow (ca. 5.4 ms, Table I) and τ (ca. 1.1 ms, Table I) the transfer of catecholamine cations between the slow pool into the fast one is small at the level of the spike maximum. Conversely, this transfer becomes substantial while the current decays significantly after the spike maximum thus producing a comparatively smoother tail due to the second exponential slow component ( Figure 10).
Therefore i max values should be handled with care. However, in the above it was established that for SDS 350 μM the fusion pore achieves a maximum radius ca. twice that reached for controls and SDS 250 μM. This increase in size also corresponds to a faster expansion rate, thus evidencing that SDS 350 μM plays two separate roles, while SDS 250 μM acts only on the expansion rate. Let us focus here on the expansion rates.
SDS at the micromolar concentrations used here has been reported to allow stabilizing transient pores that spontaneously and continuously open and close into bilipidic membranes. 38,49,50 That was indeed the rationalization that was retained above to explain how SDS may elicit Ca 2+ -triggered release. In fact, based on a model proposed by de Gennes and Taupin, 38 the energy of a pore of radius r forming into a free bilipidic membrane is determined by two terms. One relates to the surface membrane tension that is decreased by W surf = −σπr 2 where σ is the surface tension coefficient and πr 2 is the pore surface area. W surf favors a pore radius increase. A second component, W edge = +ω(2πr ), where ω is the line tension coefficient, opposes this trend. This is due to the energy of the bilipids that line up its rim (viz., of perimeter 2πr ) and are exposed in an increasing number to the extracellular medium when a pore expands. This shows that, the total energetic cost of a pore opening of radius r is: W pore (r ) = W surf + W edge = −σπr 2 + 2ωπr [8] This evidences that small pores that constantly and spontaneously form in cell membranes tend to close immediately because their line tension energy (∝ r ) increases faster than their surface tension H863 (∝ r 2 ) may stabilize them, i.e., dW pore (r )/dr > 0. Conversely, larger ones whose radius exceeds the critical radius value r critical = ω/σ tend to become wider since dW pore (r )/dr is negative for r > r critical . Therefore if a small area of the cell membrane receive a local excess of energy, mk B T, under the form of m thermal quanta (k B is the Boltzmann constant, and T the absolute temperature) a pore of radius r therm,m ≈ mk B T/(2πω) r critical will open provided that m is such as m πω 2 /(σ k B T). This evidences that any decrease of ω, e.g., favored by the detergent properties of SDS, provokes the formation of larger transient pores. These necessarily last longer than smaller ones due to the slower viscous dissipation of their excess of energy, [39][40][41] thus allowing larger calcium ions influx inside the cytoplasm.
However, this is valid for spontaneous pores formation but cannot account for our observations 27,28 and those of Ewing et al. 31,32 that evidence that exocytotic fusion pores rapidly expand to achieve a maximum radius value that is much smaller than that of vesicles. Exocytotic fusion pores significantly differ from those that spontaneously form in cell membranes due to thermal fluctuations. 38 First of all, the action of the SNAREs machineries 10 provokes their initial opening at a dimension much larger than r critical (ca. 1.2 nm based on patch-clamp measurements). 17 Hence, unless other extra-membrane components act on them and force them to close as observed in classical Kiss-and-Run situations, 14,62 fusion pores should enlarge rapidly leading to a total mechanical transfer of the vesicle membrane into that of the cell, [39][40][41] viz., a "full fusion" as was reported in a few TIRFF measurements. 20 The fast expansion stage exists since this is what causes the fast rising currents observed in amperometric spikes (Figures 1 and 10) and its occurrence is also observable in patch-clamp measurements. 17,62 However, our previous results 27,28 as well as those disclosed here and those of Ewing et al. 31,32 establish that this expansion stops while fusion pores radii are still much smaller than those of their vesicles. This clearly evidence that their expansion shifts at some stage from a pure membrane-controlled dynamics, whose energy is governed by Eq. 8, to a stage in which a non-lipidic external constraint limits the fusion pore enlargement. While such external constraint is not identified it is impossible to formulate a precise alternate to Eq. 8 when it applies. However, an electrostatic or a van der Waals-type force such as F struct (r ) = ϑ/(R struct − r ) p seems a reasonable option (ϑ is the force constant, p an integer with p = 2 for an electrostatic repulsion, or p < 6 for van der Waals-type forces, and R struct the inner radius of the external component that applies the constraint). Such a force adds a positive energy term to Eq. 8. Since we are looking for the final position of the pore edge, viz., that at which dW pore (r )/dr = 0, it is sufficient to consider the elementary work due to this force, viz., such as dW struct (r )/dr = 2πϑr/(R struct − r ) p since this force applies all over the fusion pore edge and plays the role of an edge energy. Neglecting the intrinsic edge energy of the pore (viz., the 2ωπr term in Eq. 8 which is negligible vs. the surface tension term for r r critical ), shows that the fusion pore reaches a maximal radius given by: [9] at which its surface tension energy is compensated by its edge one due to the constraints that impedes its opening. Though entirely symbolic, Eq. 9 has the merit to show that the maximal radius of the fusion pore increases when R struct is increased and ϑ/σ decreased. In other words, if the prevailing experimental conditions result in an increase of R struct and/or in a decrease of ϑ/σ vis-à-vis the control conditions, the final R pore value is increased. However, as soon as p is large enough, the effect of ϑ/σ is presumably much weaker than that of R struct showing that R pore ≈ R struct . This is an interesting conclusion in view of the variations in R pore values observed in the presence of SDS. Indeed, for SDS 350 μM, R pore was found to be twice larger than in controls or SDS 250 μM. Within the above framework, this evidences that the dimension (R struct ) of the intracellular structure that blocks the fusion pore growth is significantly affected by SDS 350 μM but almost not by SDS 250 μM. Owing to the reported effect of SDS on actin fibers, one good candidate for the structure that ultimately opposes the fusion pore exponential expansion seems to be the actin cytoskeleton sub-membrane Figure 11. Schematic depiction of the geometries and scales of fusion pores after they have reached their maximum sizes for the three exocytosis elicitors considered in this study (drawings are in correct scales only for R pore /R ves and for the relative R pore values between A and B but approximate for other dimensions), for an estimated thickness of a few nm of the actin sub-membrane cytoskeleton. mesh, 44,63-65 as sketched in Figure 11. Indeed, vesicular exocytosis in chromaffin cells, hence presumably also in PC12 cells, is accompanied by local transient cyclic disturbance of the actin network. [63][64][65] Furthermore, SDS at a sufficient concentration has been reported to destabilize the actin polymer through a weakening of the proteinprotein interactions involved in actin filaments remodeling. 49 Link between R pore , k diff ρ , total released charge and display of single vs. two-exponential decay branches.-The present results suggest that the doubling in R pore , viz., in k diff ρ , induced by SDS 350 μM correlates with the increase of the total released charge (from ca. half the vesicle content in controls to full release) and to a near systematic observation of spikes displaying two-exponential decay branches (vs a single-exponential mode in controls). This may seem puzzling since SDS, being a negatively charged organosulfate with a 12-carbon alkyl tail is not expected to interfere with the anionic matrix structure. In fact, a similar observation was made by some of us upon briefly incubating chromaffin cells with Lyso-phosphatidylcholine (LPC) or Arachidonic Acid (AA). 66 Thus, it was observed that LPC increased the releasing rate (ca. 80% increase in i max ) while AA decreased it (ca. 55% decrease in i max ) compared to controls, while t 1/2 values decreased by ca. 30% for LPC and increased by ca. 80% for AA. This was perfectly consistent with topological consequences of the positive (LPC) or negative (AA) membrane curvature induced by these exogenous lipids based on their cone angles and the ensuing opposite effects on the corresponding fusion pore sizes (R LPC pore > R controls pore > R AA pore ). 66 However, these observations went by pair with a decrease of the mean released charge for AA (to ca. 40% of controls) and an increase for LPC (by ca. 60% vs. controls), a fact that is fully coherent with our present observations with SDS but for which we could not offer any rationale because, as SDS, LPC and AA are not supposed to interfere with the matrix structure.
However, the two-pool model allows providing some rationalizations. Indeed, it is evident from the mechanism in Eq. 1 that the slow pool cannot refill significantly the fast pool while q fast is still substantial because the expected relative thermodynamic stability of catecholamines cations in each pool (i.e., k slow /k fast ≤ 1) imposes that the equilibrium can be shifted toward the fast pool only when q fast /q slow becomes small enough for k fast q fast < k slow q slow . However, if this happens too late, i.e., when the spike current has already almost reached the baseline, this exchange will not be observable in amperometry. Hence, the total released charge detectable will reflect only that, q t=0 fast , contained initially in the fast pool while the second contribution, viz., q t=0 slow , has to remain undetectable even if the fusion pore does not close before this occurs. Therefore, in order to observe experimentally the slow → fast exchange, hence a dual-exponential decay branch as predicted by Eq. 6 and a total release, viz., Q = 2Fq t=0 total = 2F(q t=0 fast + q t=0 slow ), this must happen while the spike current is still significant vs. the baseline one. In other words, q fast has to drop rapidly enough toward its quasi steady state concentration, q stst fast ≈ q slow k slow /(k fast + k diff ρ ). Since k slow and k fast are intrinsic properties of a vesicle matrix, this can occur and lead to a significant release current only if k diff ρ is large enough, viz. R pore large enough so that q stst fast ≈ q slow (k slow /k diff ρ ). Then, since i(t)/n F = dq out /dt ≈ −dq slow /dt ≈ k slow q slow , one may observe the slow exponential component in Eq. 6. Said differently, the observation of a total release and of a spike with a double-exponential decay branch requires a large k diff ρ value (viz. a small time constant τ), i.e., a large R pore one. This is precisely, what has been observed here or with LPC in our previous work (while the converse was observed for AA). 66 Furthermore, the recent data reported by Ewing et al., also confirm implicitly this prediction. Indeed, though this was not correlated with the released charge, they reported most of the events exhibiting a double-exponential decay mode (ca. 70% of the total) were observed for spikes with the smallest τ values. 31,32 One may then envision that all spikes are borne to display a twoexponential releasing mode and all events to lead to a complete unloading of the initial vesicle content unless the fusion pore closes before this may proceed up to the end. However, when the maximum fusion pore radius R pore is not large enough, the emptying of the slow pool provides a negligible contribution that cannot be detected amperometrically due to the signal-to-noise level, or may be mistaken for a local drift of the baseline (as often observed). 35

Conclusions
Although sodium dodecyl sulfate (SDS) has no physiological relevance to exocytosis and may lead even to cell death when used at too large concentration and during too long duration by thoroughly disorganizing their membranes and many other internal biological structures, we established that brief SDS pulses of low sub-millimolar concentrations offered an useful "chemical tool" for unravelling key features of the mechanism of vesicular exocytosis that remain hidden upon using classical elicitors and have therefore eluded most previous studies.
Amperometric spikes characteristics established that eliciting exocytotic events from PC12 cells with SDS at concentrations of 350 μM or below required, as for K + -controls, calcium ions influxes through the cell outer membrane, and led to the formation of initial fusion pores of same sizes as for controls. In agreement with previous reports, this confirmed that in this range of concentrations SDS did not alter the biological machineries involving calcium-dependent SNAREs assembling, etc., which are critical in leading to the formation of initial fusion pores. Therefore, the initial stages leading to the formation of fusion pores were undoubtedly similar to those occurring under control conditions. This ensured the biological compatibility of the "SDS-perturbation" approach used in this work.
In agreement with the expected increase in fluidity of the membranes near the pores mouths due to SDS, the fusion pores expansion rates increased drastically (being 1.4 and 2.1 times larger for SDS 250 and 350 μM respectively) vs. K + -controls. This was fully coherent with the decreased life-times of the initial fusion pores evidenced by a reduction to ca. half their probability vs. K + -controls of being observable through pre-spike current features (PSF). However, the so-called "full fusion" phase during which initial fusion pores expand rapidly leading to massive release of neurotransmitter was observed to significantly depend on the concentration (250 or 350 μM) of SDS stimulating pulses. This concerned (i) the drastic increase of the amount of catecholamines released during the "full-fusion" phase, (ii) and that of the current spike maxima, i max , as well as (iii) that of the probability (ca. 84% for SDS 350 μM) of observing spikes exhibiting two-exponential decay branches. For 250 μM SDS spikes charges increased by only a few percent but were doubled for SDS 350 μM, while i max values increased by ca. 15% or 250%, respectively.
Whatever is(are) the exact mechanism(s) of SDS action(s), this series of results establishes that vesicles release at most half of the initial loading during control exocytotic events, a result that parallels that reported by Ewing et al. based on a thoroughly different methodological approach (cytometry vs normal exocytosis). 33 Furthermore, all these spectacular variations were shown to be fully coherent with the predictions of the recent two-pool model developed in our group 35 with a near doubling of the final fusion pore radius for SDS 350 μM (R pore ∼ 28 nm) compared to K + -controls (R pore ∼ 14 nm). Consequently, these data fully disprove the classical representation of the "full fusion" stage by establishing that fusion pores radii remain much smaller than the vesicles ones when they reach their maximal expansion. This is definitely in contradiction with what should occur if the fusion pores expansion phase was driven and regulated only by the energetics and dynamics of bilipidic membranes submitted to a surface tension. [38][39][40][41] This is most certainly the case at the onset and beginning of the expansion phase, thus giving rise to a fast exponential enlargement. [39][40][41] However, the present data evidence that this fast growing phase is ultimately stopped when the outer tubular edge of the fusion pore collides onto a non-lipidic intracellular structure.
Fluorescence microscopy has established that vesicular exocytosis in chromaffin cells, 63 hence presumably also in PC12 cells owing to the close relationship between the two cells types, involves a local reversible formation of a hole through the actin membrane cytoskeleton in order to allow the cell and vesicle membranes to be brought into close contact by the SNAREs machineries, thus leading to their fusion and the opening of the initial fusion pore. 10 It seems therefore reasonable to identify the structural constraint imposing the final R pore values to the actin network. Owing to the known action of SDS in decreasing the protein-protein interactions that leads to actin filaments polymerization, 49 such view appears entirely coherent with the observation of an increase of R pore values in the presence of SDS 350 μM. Furthermore, it is also coherent with recent results reported by Ewing et al. 32 Finally, based on our previous two-pool model, 35 the whole set of observations reported in this investigation strongly suggests that, unless the fusion pore is forced to close, 31,32 all exocytotic vesicles are borne to release their whole initial neurotransmitter cargo. However, this has to occur through two different kinetic regimes featuring a successive unloading of the fast and slow domains of the vesicle matrix. However, whenever R pore cannot reach a sufficient size, i.e., the fast domain cannot be unloaded sufficiently rapidly for the slow pool contribution to be observable before the amperometric current has reached too small values to be detected. Under these conditions, only the fast pool release is observable by amperometry, giving rise to amperometric spikes displaying single-exponential decay branches and corresponding to the release of only ca. half the content of neurotransmitter initially present in the vesicle.