Fusion Pore Expansion and Contraction during Catecholamine Release from Endocrine Cells

Abstract

Amperometry recording reveals the exocytosis of catecholamine from individual vesicles as a sequential process, typically beginning slowly with a prespike foot, accelerating sharply to initiate a spike, reaching a peak, and then decaying. This complex sequence reflects the interplay between diffusion, flux through a fusion pore, and possibly dissociation from a vesicle’s dense core. In an effort to evaluate the impacts of these factors, a model was developed that combines diffusion with flux through a static pore. This model accurately recapitulated the rapid phase of a spike but generated relations between spike shape parameters that differed from the relations observed experimentally. To explore the possible role of fusion pore dynamics, a transformation of amperometry current was introduced that yields fusion pore permeability divided by vesicle volume (g/V). Applying this transform to individual fusion events yielded a highly characteristic time course. g/V initially tracks the current, increasing ∼15-fold from the prespike foot to the spike peak. After the peak, g/V unexpectedly declines and settles into a plateau that indicates the presence of a stable postspike pore. g/V of the postspike pore varies greatly between events and has an average that is ∼3.5-fold below the peak value and ∼4.5-fold above the prespike value. The postspike pore persists and is stable for tens of milliseconds, as long as catecholamine flux can be detected. Applying the g/V transform to rare events with two peaks revealed a stepwise increase in g/V during the second peak. The g/V transform offers an interpretation of amperometric current in terms of fusion pore dynamics and provides a, to our knowledge, new frameworkfor analyzing the actions of proteins that alter spike shape. The stable postspike pore follows from predictions of lipid bilayer elasticity and offers an explanation for previous reports of prolonged hormone retention within fusing vesicles.

Significance

Amperometry recording of catecholamine release from single vesicles reveals a complex waveform with distinct phases. The role of the fusion pore in shaping this waveform is poorly understood. A model based on a static fusion pore fails to recapitulate important aspects of the waveform. A, to our knowledge, new transform of amperometric current introduced here renders fusion pore permeability in real time. This transform reveals rich dynamic behavior of the fusion pore as catecholamine leaves a vesicle. This analysis shows that fusion pore permeability rapidly increases and then decreases before settling into a stable postspike configuration.

Introduction

Amperometry recording from catecholamine-secreting endocrine cells reveals the exocytosis of single vesicles (1). At a coarse-grained level, a single vesicle appears to release its catecholamine content in an instantaneous burst. Closer inspection reveals a succession of stages that are thought to reflect a number of different factors, including flux through a fusion pore, diffusion from the cell surface to the electrode surface, and dissociation of catecholamine from the protein matrix of an endocrine vesicle’s dense core. The earliest phase of release that is visible in an amperometry recording is the prespike foot (2,3), which has been studied to gain insight into the nature of the initial fusion pore (4,5). This initial stage is followed by a spike as the fusion pore expands. Once this expansion has started, it becomes very difficult to tease apart the various contributions, and the role of the fusion pore becomes difficult to define. The rise of the spike is so rapid that it appears to be diffusion limited, and the influence of the fusion pore may not be detectable. The decay of the spike is too slow to be diffusion limited, and dissociation of catecholamine from the proteins of the vesicle matrix has been invoked to account for this feature (3,6, 7, 8). However, a role for expanding fusion pores is implied by the large number of studies reporting that many proteins influence the spike waveform (9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20). Most of these proteins reside in the cytoplasm, out of reach of the matrix within a vesicle. To alter the shape of a spike these proteins must interact with a vesicle from the outside, presumably with membrane at or near the fusion pore. These results thus support the idea that the fusion pore has a significant role in shaping an amperometric spike.

Fusion pores can also limit the release of peptide hormones tagged with fluorescent proteins (21, 22, 23, 24). The prolonged retention of these large molecules within a vesicle after the onset of fusion suggests that fusion pores remain narrow for seconds. Furthermore, the selective release of small molecules alone or small molecules together with large molecules indicates that fusion pore expansion is subject to biological control (25, 26, 27).

Although amperometry recording has illuminated many aspects of exocytosis in remarkable detail, using this technique to study the progress of fusion beyond the prespike foot has proven challenging. Changes in spike shape have often been interpreted qualitatively in terms of alterations in expanding fusion pores, but the quantitative relationship between fusion pores and amperometric spikes is not well understood. This study explores this relationship. A model incorporating diffusion and flux through a static pore was developed and its predictions tested against experiment. A static fusion pore model fitted the fast components of a spike but failed to recapitulate observed correlations between shape indices. Turning to a dynamic representation of the fusion pore led to a new transformation of amperometric current that yields fusion pore permeability divided by vesicle volume. This approach suggests that an initial rapid component of spike decay represents a change in the fusion pore. A slow component of spike decay represents flux through a stable postspike fusion pore. The dynamic fusion pore offers a, to our knowledge, new perspective on amperometric spikes and suggests that the postspike pore serves as a locus for control by proteins.

Materials and Methods

This study employed standard methods of amperometry recording from chromaffin cells, as reported previously from this laboratory (28). Adrenal glands were dissected from newborn wild-type mice, dissociated, and cultured in Dulbecco’s modified Eagle’s medium containing penicillin and streptomycin and insulin-transferrin-selenium-X. Cells were plated on poly-d-lysine-coated coverslips, following the procedure of Sørensen et al. (29). Amperometry recordings were made from cells 1–3 days in vitro at room temperature (∼22°C) with a bathing solution consisting of 150 mM NaCl, 4.2 mM KCl, 1 mM NaH₂PO₄, 0.7 mM MgCl₂, 2 mM CaCl₂, and 10 mM HEPES (pH 7.4). A carbon fiber electrode was positioned to gently touch a cell because this has been shown to minimize the time for diffusion from the release site to the electrode surface (6). Signals were amplified with a VA-10 amplifier (ALA Scientific Instruments, East Farmingdale, NY). Exocytosis was triggered by pressure application of a depolarizing solution (bathing solution with 105 mM KCl and reduced NaCl) for 6 s. Pressure of 15 PSI was applied with a Picospritzer (Parker Hannifen, Hollis, NH) through a glass micropipette with a tip diameter of ∼2 μm positioned ∼20 μm from the cell. Records were acquired with an Intel-based computer running PCLAMP software. Amperometric current was low-pass filtered at 2.5 kHz and digitized at either 4 or 10 kHz. An amplitude cutoff of 20 pA was applied, and smaller events were not analyzed except when noted. Entire events were analyzed for spike properties, starting with departure of current 1 pA above baseline and ending with return to within 1 pA of baseline.

Data were analyzed with the computer program Origin and with in-house software written in C++. Analysis and modeling were performed with the computer program Mathcad. All measurements are presented as mean ± standard deviation or ± standard error as noted. Model fitting was performed either with the Mathcad Minerr function or with the exponential fitting feature of Origin.

Results

Spike properties

Amperometric current reveals many spikes occurring in a 23 s recording episode during and after the application of the depolarization solution (Fig. 1 A). Three typical events in this long recording, marked by a small horizontal bracket above the 8 s time tick, are displayed on an expanded timescale in Fig. 1, B1–B3. In each trace, an exponential was fitted to the top 2/3 of the decay, revealing a slower component. This biphasic decay was evident in ∼90% of the events. The slow component had a relatively small and variable amplitude, but it was generally clear. This slow component is comparable to the “postspike foot” described by Mellander et al. (30). However, that study highlighted events with roughly stepwise endings. In this study, the postspike feet generally decayed exponentially to baseline. The decay of the slow component will be explored further below, and the modeling efforts will attempt to illuminate each phase of decay separately. At this point, we note that the biphasic decay is qualitatively what one would expect for rapid release of a free fraction of catecholamine, followed by the slow release of a fraction bound to the vesicle matrix. From this perspective, the rapid phase of decay should be limited by flux through a pore.

Figure 1.

Amperometry recordings of single-vesicle release events in chromaffin cells. (A) One long trace of current versus time illustrates that depolarization (thick horizontal bar from 3 to 9 s) elicits many events with variable amplitudes. The bracket above at ∼8 s encompasses the three events displayed on an expanded scale in (B). These three selected events occurred in sequence and illustrate variations in size and shape. Single exponentials were fitted to the decaying phase within 2/3 of the peak (gray curves). The later phase of current is clearly above the exponential curve fitted to the rapid initial phase of decay. This highlights the two components of decay, the second of which is referred to as a postspike foot (30).

For each event, we determined the peak amplitude, 35–90% rise time, time constant of the rapid component of decay (from fits such as in Fig. 1, B1–B3), and the number of molecules released, N₀ (the integral of the amperometric current over an entire event gave the total charge, which was converted to molecule number by assuming two electrons per catecholamine molecule and multiplying by Faraday’s constant). Measurements of 1682 events from 77 cells and eight cultures (digitized at 4 kHz) were used to construct distributions (Fig. 2; see figure legend for means and standard deviations). The distributions in Fig. 2 illustrate the variations in all of the quantities, making the point that spike shape is quite variable. The absence of events below 20 pA in Fig. 2 A reflects the use of an amplitude cutoff in the analysis to focus on events that are large enough to measure accurately. The rise times of <1 ms are consistent with the close contact between the electrode and cell, which minimizes the diffusion time (6). It should be noted that kiss and run caused by fusion pore closure would prevent the release of the entire content, resulting in an apparent N₀-value lower than the total number of molecules contained within a vesicle.

Figure 2.

Distributions of (A) peak amplitudes; (B) 35–90% rise times; (C) decay times of the fast component (τ decay-fast; from fits as in Fig. 1, B1–B3); and (D) number of molecules N₀, computed from the total area of the event (charge converted to number of molecules with Faraday’s constant, assuming two electrons per molecule of catecholamine). Means ± standard deviations are peak amplitude = 59.9 ± 50.7 pA, 35–90% rise time = 0.50 ± 0.19 ms, τ decay-fast = 1.84 ± 1.50 ms, and N₀ = 600,080 ± 611,222. Plots were based on 1682 events recorded from 77 cells and eight cultures.

Static fusion pore and diffusion

Previous efforts to understand spike shape include the use of an exponentially modified Gaussian (6), as well as a model incorporating matrix dissociation and fusion pore expansion (8). Here, we first explore a model that combines diffusion and flux through a static fusion pore. To appreciate the timescales for diffusion, it is instructive to consider the expression x = (2Dt)^1/2 for the root mean-square displacement in one dimension in terms of time, t, and the diffusion constant, D (6 × 10⁻⁶ cm² s⁻¹ for norepinephrine (31)). For t = 0.1, 1, and 10 ms, x = 0.35, 1.1, and 3.5 μm, respectively. Gently touching the electrode to the cell surface should produce an approximately flat contact with a separation of a few tenths of a micrometer. The rise times for amperometric spikes fall within the range of times for diffusion over such distances (Fig. 2 B), but the fast decay times are somewhat longer (Fig. 2 C; mean 1.84 ms implies x = 2.8 μm). Thus, even the fast component of decay is too slow to be diffusion limited. The following analysis uses a more quantitative treatment of diffusion to model spike shapes.

For diffusion to the electrode surface, the site of release is taken as a point source on the surface of a reflecting planar boundary, and the electrode is taken as an absorbing planar boundary parallel to the cell surface at a distance of x (Fig. 3 A). N₀ molecules have an initial δ-function distribution. Ignoring edge effects, the solution of the diffusion equation for these conditions gives the rate of absorption by the electrode, which is the amperometric current versus time (2,32).

$$I=\underset{n\to \infty }{\lim }\sum _{i=-n}^n{\left(-1\right)}^i\frac{N_{0}x\left(1-2i\right)}{2t\sqrt{\pi Dt}}{e}^{-x^2{\left(1-2i\right)}^2/4Dt}$$ (1)

Figure 3.

(A) Sketch of the diffusion geometry for an electrode gently touching and flattening the cell surface. Simulated spikes from the diffusion-static pore model (Eq. 5) are shown. (B) N₀ was varied with x = 0.8 μm (A). (C) x was varied with N₀ = 600,000. For all simulations, g/V = 25 ms⁻¹. (D) Fits of the diffusion-static pore model (Eq. 5) to the fast part (interfeet) of a spike are shown. The black points are amperometry data acquired at 10 kHz. The black curve is the fit with all parameters varied, including N₀. The gray curve is the fit with N₀ constrained to the value obtained from the area of the event. The horizontal dashed line indicates the fits were to the top half of the spike. This excluded the prespike and postspike feet, which are governed by different processes. Fits were conducted on 140 of 146 events from three cells. Means ± standard deviations: x = 1.20 ± 0.51 μm, N₀ = 1,060,015 ± 1,159,924, g/V = 136 ± 614 ms⁻¹. The RMS error of the 140 fits was 0.80 pA.

This series converges rapidly; increasing n above 5 produces no discernable changes. This expression can produce a range of shapes by varying x, but it cannot account for the range of experimentally observed spike shapes with x < 1 μm (32). This supports the view that release is not instantaneous and that other processes slow the loss of catecholamine from a vesicle.

To incorporate fusion pore flux, we start with a point introduced by Almers et al. (33). If flux through a fusion pore is rate limiting, gradients inside the vesicle are small. Because the electrode is an absorbing surface, the external concentration remains low. The flux through the fusion pore is then proportional to the concentration within the vesicle. The rate of loss of molecules from the vesicle is

$$-\frac{dN}{dt}=gC=N\frac{g}{V}$$ (2)

N is the number of molecules in a vesicle as a function of time, V is the vesicle volume, and C is the concentration in the vesicle (the conversion of units is irrelevant at this point but will be addressed as needed). g represents the coefficient of proportionality between vesicle concentration and flux and can be viewed as the fusion pore permeability. N decreases with time after the pore opens, and if the vesicle retains its volume, C tracks the decline in N. Eq. 2 leads to

$$N=N_0{e}^{-tg/V}$$ (3)

Thus, pore-limited flux predicts an exponential decay with a time constant

$$\tau =\frac{V}{g}$$ (4)

Note that this result depends on a static fusion pore that does not change as the vesicle empties out. This assumption is essential to the analysis of this section and will be relaxed in the ensuing section.

The effects of diffusion and pore flux can be combined by taking the convolution of Eqs. 1 and 3.

$$I=2F{N}_0\underset{0}{\overset{t}{\int }}\sum _{i=-n}^n\frac{{\left(-1\right)}^{i}x\left(1-2i\right)}{2s\sqrt{\pi Ds}}{e}^{-x^2{\left(1-2i\right)}^2/4Ds}{e}^{-sg/V}ds$$ (5)

F is Faraday’s constant, and its incorporation converts molecules/second to current. This expression bears some resemblance to the exponentially modified Gaussian function used previously (7), but Eq. 5 treats diffusion explicitly and incorporates a dependence on x, the distance to the electrode surface (Fig. 3 A).

Eq. 5 can be used to simulate spikes and explore how parameters influence their shape. Fig. 3 B illustrates the impact of varying N₀ within the range of values shown in Fig. 2 D. Fig. 3 C illustrates the impact of varying x over the range expected for visual contact between the electrode and cell. g/V was fixed at 25 ms⁻¹, a value that generates realistic spikes within the ranges used for N₀ and x. Increasing x broadens spikes by slowing both the rise and decay. Increasing N₀ also broadens spikes but the effect is mostly on the decay. Thus, for a static pore, the decay primarily reflects the emptying of the vesicle, even when diffusion is taken into account. Eq. 1, which ignores the impact of the fusion pore, produces dramatic changes in spike shape when x is varied (32). The smaller changes in spike shape in Fig. 3 C illustrate how grading the flux through a fusion pore with Eq. 5 dampens the effect of distance.

The spikes simulated in Fig. 3, B and C resembled the phase of recorded spikes between the prespike and postspike feet (the “interfeet” portion). Furthermore, Eq. 5 fitted the rapid components of individual spikes very well. The sum-of-squares error between Eq. 5 and recorded currents was minimized with the Minerr function of Mathcad. To isolate the interfeet portion, points were taken within 50% of the peak (dashed line in Fig. 3 D). Spikes were often quite brief, so these fits were performed on data acquired at 10 kHz to provide more points over what was often a short time interval. Eq. 5 has three parameters to vary for the fit, x, N₀, and the ratio g/V. The onset time was also varied as a fourth parameter because this value is not readily extracted from the data. The onset time was generally within a millisecond of the inflection between the foot and spike upstroke. Eq. 5 produced good fits in 140 of 146 events from three cells (Fig. 3 D, black curve); the figure legend presents mean parameter values from these fits.

Although Eq. 5 fitted individual events well, there are telling trends in the parameters obtained. The mean value for x of 1.2 μm is larger than the apparent distance between the electrode and cell of a few tenths of a micrometer. This may reflect an interaction between x and other parameters during the fitting process. This could also reflect an inaccuracy in our value for the diffusion coefficient. x is sensitive to this parameter, and lower values of x can be obtained by reducing D. As a final possibility, we note the role of fusion pore dynamics to be examined in the next section. The rising phase of the spike may reflect the speed with which a fusion pore expands. There was a systematic discrepancy between the value N₀ yielded by the fit and the value determined independently from the total area of an event. N₀ from all but four of the 140 fits was less than the value from the total event area. The mean ratio, N_0-fit/N_0-area, was 0.68 ± 0.015 (standard error), which is significantly below one. When N₀ was constrained to the value from the area, the fit was very poor (Fig. 3 D, gray curve). This represents a meaningful difference between the model and data. A particularly appealing explanation for this result is that 68% of the molecules in a vesicle are free and readily released, whereas the remaining 32% are bound to a matrix. This implies that the matrix-bound fraction is responsible for the slower component of decay of the postspike foot. In fact, postspike feet accounted for 34% of the spike area on average. Thus, the number of free molecules determined by fitting Eq. 5 is in good agreement with the number contained within the fast component of the spike.

The diffusion-static pore model was tested more critically against experiments by examining the relations between various indices of spike shape. The time constant for decay (τ decay) of simulated spikes was plotted against peak amplitude for x ranging from 0.3 to 1.2 μm (Fig. 4 A). This plot shows τ decay decreasing weakly with peak amplitude, reaching an asymptote of ∼1.5 ms at higher amplitudes at which x is small. With small x, diffusion times are very short, and flux through the fusion pore is rate limiting. By contrast, when N₀ was varied and x was fixed (x = 0.8 μm to recapitulate the observed mean rise time of 0.5 ms), the relation between τ decay and peak amplitude was reversed. τ decay increased with peak amplitude over a much larger range (Fig. 4 C).

Figure 4.

Plots of spike shape indices from simulations with the diffusion-static pore model using Eq. 5 (as in Fig. 3) (A–D) and experiment (E and F). (A) The diffusion distance x was varied from 0.3 to 1.2 μm, and the decay time was plotted versus peak amplitude. Simulated spikes decayed monotonically, and the decays were well described by a single exponential. (B) Peak amplitude was plotted versus N₀ with x = 0.8 μm. (C) For the spikes simulated with N₀ varied in the range used for (B), decay time was plotted against N₀. (D) Plot of τ decay vs. N₀ with x = 0.8 μm is given. (E) Plot of τ decay for the rapid component (illustrated in Fig. 1, B1–B3) versus peak amplitude for 1682 events recorded from 77 cells and eight cultures is shown. Values were binned in groups of 50. Means are ± standard errors. (F) Plot of τ decay vs. N₀ determined from the spike area is shown. Numbers and binning are the same as in (E).

Turning to the relation between peak amplitude and N₀ (Fig. 4 B), we see that at low N₀, the peak amplitude increases but gradually reaches a plateau. This behavior is not straightforward. The scaling between area and N₀ (34) leads to an initial concentration within a vesicle that does not depend on a vesicle’s size. Thus, the initial driving force for pore flux does not depend on N₀, and if the pores are the same, the initial current through the pore will also not depend on N₀. However, the peak in recorded current is not the initial flux through the pore. The peak of a spike occurs after the pore opens. As N(t) declines because of the loss of catecholamine through the fusion pore, the driving force and flux decline. The peak amplitude varies depending on how much N(t) declines before the current reaches its peak, and this time depends on diffusion. With low N₀, a small vesicle will be depleted more rapidly, thus reducing the peak. With high N₀, the same flux produces less depletion of a large vesicle, and the peak of the spike is higher. The flattening in Fig. 4 B reflects the diminished impact of depletion on the content of larger vesicles during the brief time it takes for the current to peak. τ decay increases linearly (Fig. 4 D), as expected from Eq. 4. Again, for a fixed initial concentration (34), the volume, V, is proportional to N₀. The preservation of this relation in Fig. 4 D underscores the point that grading release through a fusion pore alters the impact of diffusion.

These relations were compared with experiments by constructing plots of peak amplitude, τ decay (of the fast component, as in Fig. 1, B1–B3), and N₀ from the 1682 events used to construct the distributions in Fig. 2. To view trends clearly, events were grouped into bins of 50 and averaged. A plot of τ decay of the fast component decreases with peak amplitude (Fig. 4 E). The plot based on simulated spikes shows qualitatively similar behavior with varying x (Fig. 4 A), but the ranges of both τ decay and peak amplitude are much wider in the experimental plot than the theoretical plot. To account for these wide ranges, variations in N₀ must be considered, but this results in the opposite relation between τ decay and peak amplitude between simulated spikes (Fig. 4 C) and experimental spikes (Fig. 4 E). The experimental values of τ decay increase with increasing N₀ and saturate with large N₀ (Fig. 4 F), whereas the plot from simulations was linear over the entire range (Fig. 4 D). The parameter interdependencies predicted by the static fusion pore model differed qualitatively from those observed experimentally. Thus, despite the good fits illustrated in Fig. 3 D, flux through a static fusion pore cannot account for spike shape. This point was made previously (6,7), and this analysis extends this point to a focus on the fast component of spike decay, with a model that treats diffusion explicitly.

Dynamic fusion pores

The preceding analysis of spike shape was based on the assumption of a static fusion pore. Given the failings of the model based on this assumption just illustrated, the possibility of a dynamic fusion pore was considered. This approach begins with a rearrangement of Eq. 2.

$$\frac{I\left(t\right)}{N\left(t\right)}=\frac{g}{V}$$ (6)

The time dependences of I and N are now emphasized (again, the difference in units of I and N is irrelevant at this point). Because N(t), the number of remaining molecules, is N₀ minus the number lost and the number lost can be obtained as the integral of I(t) from 0 to t, we can express the left-hand side of the above expression in terms of I(t).

$$\frac{I\left(t\right)}{Q_0-{\int }_0^{t}I\left(s\right)ds}=\frac{g}{V}$$ (7)

Q₀ is the total area under the entire event from start to end (${\int }_v^{t_{end}}I\left(s\right)ds$; N₀ was computed from this quantity). With the numerator and denominator both expressed in terms of current, g/V can be calculated versus time for each amperometric event. Eq. 7 thus transforms amperometric current to g/V.

Fig. 5 presents four examples of I along with g/V computed from Eq. 7. These plots exhibit highly characteristic patterns. One important feature is that g/V undergoes two major transitions, first with an upstroke at the end of the prespike foot, and then with a downstroke after the peak in I. The initial increase corresponds with a rapid expansion of the initial fusion pore to end the prespike foot and start the spike. The rapid decrease after the peak comes as a surprise. Not only does g/V decline precipitously, it settles into a stable plateau that lasts tens of milliseconds. The plots become noisy toward the end because the numerator and denominator of Eq. 7 both become small; I(t) and $Q_0-{\int }_0^{t}I\left(s\right)ds$ both go to zero as the current returns to baseline. But g/V remains flat for as long as its value can be determined. Thus, in these examples, the fusion pore remains stable, without closing or expanding. This stable state persists for as long as catecholamine flux can be measured. The transform to g/V thus reveals that the postspike foot (30) corresponds with a stable “postspike pore.”

Figure 5.

Amperometry spikes (current, black) were transformed to g/V (red) using Eq. 7. In each of the four examples (A–D), dashed lines indicate g/V of the prespike foot (magenta), peak (blue), and postspike foot (green). The examples illustrate the characteristic initial rise and fall of g/V as the pore undergoes an expansion-contraction cycle and then settles to a plateau. The level of the plateau varies from event to event (see text). To see this figure in color, go online.

The rapid decrease in g/V after the peak implies that the fusion pore contracts immediately after it expands. The plateau implies that this contraction ends with the fusion pore settling into a stable structure. The three key levels of g/V, the prespike foot, peak, and postspike foot, are highlighted in each example in Fig. 5 with colored dashed horizontal lines, as indicated in the legend in the upper right corner. The rapid upstroke of the spike is likely to reflect both diffusion and pore expansion. The transform to g/V does not take diffusion into account, so the actual value of g/V at the peak could be larger than the apparent peak in the plots. By contrast, diffusion should play essentially no role in the final plateau of the postspike pore.

The plots of g/V show a large amount of variation in the magnitude of the decline from the peak to the plateau. Fig. 5 A shows a decline by ∼90%, Fig. 5 B an ∼75% decline, Fig. 5 C an ∼30% decline, and Fig. 5 D an ∼10% decline. Regardless of the extent of decline, a stable postspike pore was seen in 443 g/V plots derived from 449 events recorded from seven cells. The mean values of g/V of the prespike foot, peak, and postspike foot are plotted in Fig. 6 A to illustrate the changes in g/V during the distinct phases of release. From the prespike foot to the peak, g/V increases ∼15-fold on average and then declines ∼3.5-fold to the plateau. g/V is essentially a time-dependent rate constant. At any particular time, it represents the time over which a vesicle would lose its content through a static fusion pore of that value. Thus, g/V for the prespike foot indicates it would take ∼30 ms for loss of 63% of a vesicle’s content. By contrast, the much larger pore at the peak of the plot would only need ∼2 ms for a vesicle to lose the same fraction of content. The peak lasts about this long, so during the peak, a vesicle can lose roughly half its content. The intermediate-sized pore of the postspike foot would allow loss of 63% of a vesicle’s content in ∼7 ms.

Figure 6.

(A) Bar graph of g/V (mean ± standard error) for prespike feet, peak, and postspike feet from experimentally recorded spikes used for the distributions in Fig. 2. Taking V/g as τ, binning in groups of 20, and averaging produced plots versus N₀ for the prespike feet (B), peak (C), and postspike feet (D) versus N₀. Means are ± standard errors.

As noted above, N₀ is proportional to V because the catecholamine concentration in a vesicle is independent of vesicle size (34). Thus, we can focus on g by examining how g/V varies with N₀. To relate this analysis to Eq. 4, the reciprocal of g/V was taken to give a time constant (τ). For the prespike foot, the plot versus N₀ was fairly linear over the entire range, with an intercept near the origin (Fig. 6 B). This suggests that the initial fusion pore of the prespike foot has a permeability that does not vary with vesicle size. By contrast, for the peak (Fig. 6 C) and postspike foot (Fig. 6 D), the plots have linear regions for low N₀, but the intercepts are above the origin. Furthermore, these plots plateau for N₀ above ∼1,000,000. This may indicate that pore permeability increases for vesicles above a critical size. This will be discussed further below.

Nested events

The transform to g/V offers an interesting perspective on more complex amperometric events that occur infrequently and defy conventional analysis. Most events are spike-like, as illustrated in Fig. 1, B1–B3, but occasional events appear with multiple peaks. Such events are generally omitted from analysis. These “nested” events, as illustrated in Fig. 7, B and C, are unlikely to result from coincidental fusion of two different vesicles. This can be demonstrated by analyzing the frequency of fusion events. The interval between peaks of spikes was determined and their distribution plotted in Fig. 7 A1. This distribution was well fitted by a single exponential (Fig. 7 A1; time constant 496 ms), suggesting that vesicles fuse randomly over the course of a recording interval. The interspike intervals used for Fig. 7 A1 were analyzed with the software described in the Materials and Methods, which initiates the searches for new events starting from the end of a preceding event once the current has returned to baseline. Because in nested events, the current does not return to baseline before the second peak, the return-to-baseline criterion excludes nested events. To examine intervals within nested events, we selected events with a second peak appearing before the current returns to baseline. These intervals were not included in Fig. 7 A1. For these pairs, the first peak was >10 pA, and the second was smaller than the first. The distribution of these intervals was also exponential but with a time constant of only 25 ms (Fig. 7 A2). Thus, nested events are distinct in their kinetics of appearance. It is possible that they are caused by the fusion of two vesicles, but they would have to have some shared triggering mechanism. The absence of a rapid contraction during the second phase favors the view that nested events reflect expansion of a single fusion pore.

Figure 7.

Interspike intervals and nested peaks. (A1) The distribution of 2925 interspike intervals, based on the time between peaks, is shown, with the search for the next peak beginning when the first peak returned to 1 pA of the baseline current (see Materials and Methods). An exponential fit yielded a mean of 496 ± 20.6 ms (reduced χ² = 29.3). (A2) The distribution of 331 nested intervals in which the second peak was smaller than the first and the event had not returned to baseline is shown. An exponential fit yielded a mean of 25.4 ± 5.6 ms (reduced χ² = 43.7). (B and C) Two examples of current and g/V for events with a second peak are shown. The second peak is associated with a stepwise increase in g/V. To see this figure in color, go online.

Applying the g/V transform of Eq. 7 to two events reveals that g/V increases during the second peak (Fig. 7, B and C). This indicates that the fusion pores are making a transition to a larger size. Fig. 7 C shows a further increase after the second peak in current, indicating further expansion of the fusion pore. The g/V trace becomes noisier toward the end of the record because of the problem with quotients of small numbers noted above. However, the current trace does show a small departure from monotonic decay starting at ∼55 ms. Thus, the fusion pore may actually be expanding further at this point, and the g/V plot is a good way to detect this.

Discussion

This study used amperometry data from endocrine cells to investigate the processes that control the time course of catecholamine release from single vesicles. Two different approaches were taken. First, a static pore model was developed that failed to account for important experimental observations. The assumption of a static fusion pore was then relaxed to explore the consequences of dynamic changes in permeability. This yielded a highly characteristic fusion pore permeability time course, beginning with a rapid expansion-contraction cycle and then settling into a state that is stable for tens of milliseconds. The assumption of a static pore is restrictive and generates testable predictions. The assumption of a dynamic fusion pore is more robust and suggests interesting new possibilities. It is significant that the stable plateaus in permeability (Fig. 5) were generated by a dynamic model, which makes no assumptions about stability.

The failure of static fusion pores

The model of a static fusion pore incorporated diffusion, as represented by Eq. 5. This model simulated realistic spikes (Fig. 3, B and C) and fitted the interfeet portions very well (Fig. 3 D). However, a more detailed analysis based on plots of indices of spike shape led to sharp contradictions with experiment. The vesicles of endocrine cells vary in size, and N₀ is probably the most important source of variation when events are recorded with an electrode gently touching a cell (6). The predicted relation between τ decay and amplitude (Fig. 4 C) was opposite to that observed experimentally (Fig. 4 E). Furthermore, the decay time should increase linearly with N₀ (Eq. 4; Fig. 4 D), without the saturation seen in the experimental data (Fig. 4 F). Fusion pore conductance has been shown to vary dynamically on a slower timescale (35,36). The failure of the static model in this work suggests that over the brief time of an amperometric spike, the fusion pore is changing rapidly. A static fusion pore cannot explain the rapid component of spike decay, and this motivated the consideration of dynamic changes in pore permeability.

Matrix dissociation

Previous studies suggested that catecholamine dissociation from the vesicular matrix provides a better account of amperometric spike shape than flux through a static fusion pore (6, 7, 8). Knocking out the matrix protein chromogranin A reduces the packaging of catecholamine within dense-core vesicles (37,38). The two components of spike decay in this work could be interpreted in terms of the rapid loss of free catecholamine followed by the slow loss of matrix-bound catecholamine. However, the failure of the static fusion pore model argues against the view that the rapid phase of the spike reflects loss of the free pool through a static fusion pore. Furthermore, matrix dissociation should have a complex time course (7,8), whereas the stability of g/V during the slow component of catecholamine loss (Fig. 5) suggests a simple exponential decay. One possibility is that there is a tightly bound pool of catecholamine that dissociates very slowly, but this would be too slow to influence the shapes of spikes over the tens of milliseconds relevant to our study. A more detailed analysis of the slow component of decay in terms of quantitative models of matrix dissociation may provide a rigorous test for the role played by the vesicle matrix in catecholamine release kinetics.

Fusion pore dynamics

The failures of the static pore model prompted the consideration of a fusion pore that changes dynamically as release progresses. Some previous studies assumed that fusion pores expand at a constant rate (8,39). Patch-amperometry recording indicates that the conductance of a fusion pore sometimes increases transiently before a rapid contraction that terminates a kiss-and-run event (40). In our study, the assumption that amperometry current tracks the dynamics of the fusion pore served as the basis for a mathematical transformation of current into the ratio g/V (Eq. 7). During most fusion events, this ratio underwent a transient increase, suggesting that fusion pores expand and contract in rapid succession (Fig. 5). The contraction terminates with a stable plateau. Furthermore, in the occasional amperometry event with a second peak in current, we find a roughly stepwise increase in g/V (Fig. 7). These nested multipeak events obviously require more complex mechanisms than static pore flux or matrix dissociation. The g/V plots of these events provide a simple interpretation for these events as abrupt increases in pore size.

Diffusion probably influences the shape of the rapid rising phase of the g/V plots, but the most likely explanation for the plateau in g/V is the formation of a stable fusion pore. This indicates that the postspike pore is intrinsically stable and that this structure can resist the expanding forces arising from SNAREpin rotational entropy (41) and membrane tension (42). The possibility that g and V both vary in parallel to keep the ratio constant cannot be formally ruled out. However, vesicle area changes very little during capacitance flickers (43), and when changes have been observed, they are slow (44). Although the flow of lipid label through fusion pores can be more rapid, it is still somewhat slower than the times relevant to amperometric spikes, and the vesicles appear to maintain their volume during this flux (45,46). Membrane tension and hydrostatic pressure could drive a burst of content loss as the force balance changes abruptly during pore formation or expansion. This would drive a reduction in vesicle radius, R, at a rate given by the expression dR/dt = −σr³/(6πηR³), where σ is the membrane tension, r is the pore radius, and η is the viscosity of the aqueous vesicle lumen (47). With η = 1 cP, r = 1 nm, and a typical value for σ of 0.03 dyn/cm (42), a 100 nm vesicle will decrease its radius at a rate of 0.16 nm/ms because of flow through a 1 nm pore. This is far too slow to have an impact within the timescale of amperometric spikes.

Properties of the postspike pore

Changes in the shapes of lipidic fusion pores have been predicted previously based on the theory of lipid bilayer elasticity. The earliest lipidic pore represents a state reached by the lowest energy trajectory during pore formation, but this is not the same as the global minimum in the energy landscape (48). Fig. 8 illustrates some possible ramifications of these points. The transition from Fig. 8 A to Fig. 8 B forms an initial proteinaceous pore. This pore transitions to lipid, and Fig. 8 C represents the shape most easily reached from the proteinaceous pore. This shape does not represent a global energy minimum, and subsequent changes in shape can lower the energy. A fusion pore can decrease its meridional curvature by becoming bowed (49) or teardrop-like (50) and thus reduce its elastic bending energy. This will lengthen the fusion pore (Fig. 8 D) and thus reduce its permeability. This longer pore with lower bending energy cannot be formed initially because the membranes must be close together to fuse. The cylinder can only lengthen after the transition that leads to an initial lipidic pore. The transitions illustrated in Fig. 8 illustrate how the decrease in g/V immediately after the peak (Fig. 5) realizes a theoretical prediction (49,50).

Figure 8.

Pore states illustrating changes in elastic membrane bending energies. (A). A vesicle contacts the plasma membrane to initiate fusion. (B) The initial pore of the prespike foot is formed by proteins and does not bend the membranes. (C) A lipidic pore forms with highly curved membranes and close proximity between the fusing membranes. Creating this state produces a sharp rise in pore permeability at the energetic cost of sharply curving lipid membranes. (D) Membrane elasticity theory has shown that a lipid bilayer fusion pore can reduce its membrane bending energy by increasing its length and reducing the meridional curvature (see text). This will reduce pore permeability producing a stable shape that may correspond to the postspike pore.

The amperometry data cannot be used to estimate how long the g/V plateau lasts because once the catecholamine has left the vesicle, there is no signal to report the status of the pore. Single-vesicle capacitance measurements from chromaffin cells indicate that capacitance flickers have durations of hundreds of milliseconds to seconds (28,51), and these events may represent the postspike pore. SNARE transmembrane domain mutagenesis alters the fusion pore conductance during capacitance flickers as well as the amplitudes of prespike feet (28,52), suggesting a role for proteins not only in the small prespike pore but also the larger postspike pore. The presence of protein in both small and large pores dictates a need for structural flexibility that could be met by a hybrid pore incorporating both protein and lipid (5,53).

The time constant for the rapid decay of the current exhibited an anomalous dependence on N₀ (Fig. 4 F), similar to the N₀ dependence of the time constants (expressed as V/g) of both the peak and postspike pore (Figs. 6 C and 7 D). These time constants all increased with N₀, saturated, and had nonzero intercepts. The saturation may indicate that postspike pores are larger for larger vesicles or that these pores exhibit less lengthening (Fig. 8 D). It is also possible that larger vesicles possess a mechanism to actively expel catecholamine. The N₀ dependence of V/g of prespike feet was more linear (Fig. 6 B), as expected from Eq. 4, and supports the hypothesis of a common initial pore structure for vesicles of all sizes.

Revisiting prespike feet and numbers of SNAREs

The postspike foot had a g/V-value 4.5-fold greater than the prespike foot (Fig. 6 A). Assuming pore permeability scales with area suggests the diameters of the two pores differ by a factor of roughly two. This suggests a significant revision of prior estimates of the number of SNARE protein transmembrane domains that form the initial fusion pore. These studies used the conductance of the fusion pore and the dimensions of an α-helix to estimate that 5–10 transmembrane domains can form a barrel with the appropriate dimensions (52,54). However, the pore conductance used in these calculations was derived from measurements of capacitance flickers that lasted hundreds of milliseconds. Prespike feet, which SNARE mutagenesis experiments suggest reflect flux through pores formed by transmembrane domains (28,52,55), last only a few milliseconds. With the factor of two in diameter between the postspike and prespike pores derived from the respective g/V-values, we can halve the previous transmembrane domain estimate of 5–10 to obtain 2.5–5 SNARE complexes in an initial fusion pore. This brings the number closer to the values estimated for synapses (56) and endocrine cells (57). However, the calculation of pore dimensions based on conductance assumed a fusion pore length of ∼10 nm (spanning two lipid bilayers). The bowing illustrated in Fig. 8 D would require a longer pore, with a proportional increase in area. Taking this into account would raise the estimate of SNARE complex number in the initial pore.

Biological functions of the postspike pore

The postspike pore may be small enough to retain peptides within vesicles after the onset of fusion (21, 22, 23, 24), thus representing an amperometric counterpart to the cavicapture configuration invoked to explain large molecule retention. As noted above, the saturation in the plots displayed in Figs. 4 F and 6, C and D may indicate that larger vesicles have larger postspike pores. This leads to the testable prediction that small vesicles should have greater retention of large molecules.

The postspike pore identifies a potential locus for proteins to influence secretion. Many proteins influence spike shape (9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20). These results have generally been interpreted as an effect on fusion pore expansion, but these studies lacked a framework for relating spike shape to fusion pores. This analysis provides this framework. Thus, rather than altering pore expansion, the action of dynamin on amperometric spikes (15, 16, 17,19) can be viewed as a change in the size of the postspike pore or in the speed of the constriction during its formation. This could be related to the collar-forming activity of dynamin around lipidic pores (58). Proteins that alter the postspike pore will influence the selectivity and extent of content loss. By extending the time over which fusion pores can be tracked, g/V derived from amperometric spikes will enhance our understanding of how proteins can control such processes.

Author Contributions

M.B.J. developed the models, analyzed data, and wrote the article. Y.-T.H. and C.-W.C. both performed experiments, analyzed data, and edited the article.

Editor: Brian Salzberg.