fusion pore expansion and contraction during catecholamine ...mar 02, 2020 · amperometry...

Fusion pore expansion and contraction during catecholamine release from endocrine cells

M. B. Jackson

Y.-T. Hsiao

C.-W. Chang

.CC-BY-ND 4.0 International licenseavailable under a(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made

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https://doi.org/10.1101/2020.03.02.972745

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ABSTRACT

Amperometry recording reveals the exocytosis of catecholamine from individual vesicles

as a sequential process, typically beginning slowly with a pre-spike 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 recapitulated the rapid phases of a spike, but

generated relations between spike shape parameters that differed from experimental results. To

explore the possibility 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 pre-spike foot and the start of the spike, increasing ~15-fold to the peak. However,

after the spike peaks, g/V unexpectedly declines and settles to a constant value that indicates the

presence of a stable post-spike pore. g/V of the post-spike pore varies greatly between events,

and has an average that is ~3.5-fold below the peak value and ~4.5-fold above the pre-spike

value. The post-spike pore persists and g/V remains flat 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 new

framework for analyzing the actions of proteins that alter spike shape. The stable post-spike pore

conforms with predictions from lipid bilayer elasticity, and offers an explanation for previous

reports of prolonged hormone retention within fusing vesicles.

STATEMENT OF SIGNIFICANCE

Amperometry recordings of catecholamine release from single vesicles reveal a complex

waveform with distinct phases. The role of the fusion pore in this waveform is poorly understood.

A model based on a static fusion pore fails to recapitulate important aspects of the waveform. A

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 post-spike configuration.



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INTRODUCTION

Amperometry recording from catecholamine-secreting endocrine cells reveals the

exocytosis of single vesicles (1). At a course-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 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 pre-spike 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 the onset of 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 detectible. 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, 6-8). However, a role for expanding fusion pores is implied by a large number of

studies reporting that many fusion proteins influence the spike waveform (9-19). 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 (20-22). 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 indicate that

fusion pore expansion is subject to biological control (23-25).

Although amperometry recording has illuminated many aspects of exocytosis in

remarkable detail, using this technique to study the progress of fusion beyond the pre-spike 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. The present 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 could fit the fast

components of a spike, but failed to recapitulate observed correlations between shape indices.

Turning to a dynamic representation of the fusion pore lead to a new transformation of

amperometry data 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 post-spike fusion pore. The

dynamic fusion pore offers a new perspective on amperometric spikes and suggests that the post-

spike pore serves as a locus for control by proteins.



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EXPERIMENTAL METHODS

This study employed standard methods of amperometry recording from chromaffin cells,

as reported previously from this laboratory (26). Adrenal glands were dissected from newborn

wild type mice, dissociated, and cultured in DMEM containing penicillin/streptomycin and

insulin-transferrin-selenium-X on poly-d-lysine coated cover slips following the procedure of

Sorensen et al (27). Amperometry recordings were made from cells 1-3 days in vitro at room

temperature (~22 °C) with a bathing solution consisting of (in mM) 150 NaCl, 4.2 KCl, 1

NaH2PO4, 0.7 MgCl2, 2 CaCl2, 10 HEPES (pH 7.4). A carbon fiber electrode was positioned to

gently touch a cell, as 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). Exocytosis was triggered by pressure application of a depolarizing solution

(bathing solution with 105 mM KCl and reduced NaCl) for 6 seconds. 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.

Data was analyzed with the computer program Origin and with in-house software written

in C++. Analysis and modeling were performed with the computer program Mathcad.

RESULTS

Spike Properties

Amperometric current reveals many spikes occurring in a 23 second recording episode,

during and after the application of the depolarization solution (Fig. 1A). Three typical events in

this long recording, marked by a small horizontal bracket above the 8 sec time point, are

displayed on an expanded time scale in Figs. 1B1, 1B2, and 1B3. 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 ~95% 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 “post-spike foot”

described by Mellander et al (28). However, that study highlighted events with roughly stepwise

ends. In the present study the post-spike 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 it is worth noting that the

biphasic nature 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.

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. 1B1, 1B2, and 1B3), 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 from 1682

events from 77 cells (digitized at 4 kHz) were used to construct distributions (Fig. 2). Their

means and standard deviations are stated in the legend of this figure. 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. 2A reflects the use of an amplitude cutoff in the

analysis in order to focus on events that are large enough to measure accurately. The rise times of

< 1 msec 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



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prevent the release of the entire content, resulting in an apparent N0 value lower than the total

number of molecules contained within a vesicle.

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 time scales for diffusion it is instructive to consider the expression = (2Dt)1/2

for

the root-mean-square displacement in one dimension in terms of time, t, and the diffusion

constant, D (6 x 10-6

cm2 s

-1 for norepinephrine (29)). For t = 0.1, 1, and 10 msec, = 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. 2B),

but the fast decay times are somewhat longer (Fig. 2C; mean 1.84 msec implies = 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 shape.

For diffusion to the electrode surface, the site of release is taken as a point source on the

surface of a reflecting planar boundary in which N0 molecules have an initial delta function

distribution. The electrode is taken as an absorbing planar boundary parallel to the cell surface at

a distance of x. 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, 30).

𝐼 = lim𝑛→∞∑ (−1)𝑖𝑁0𝑥(1−2𝑖)

2𝑡√𝜋𝐷𝑡𝑒−𝑥

2(1−2𝑖)2/4𝐷𝑡𝑛

𝑖=−𝑛 (1)

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

spike shapes with x < 1 µm (30). 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. (31). 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

𝑑𝑁

𝑑𝑡= 𝑔𝐶 = 𝑁

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. C and N decrease

with time after the pore opens, and Eq. 2 gives

𝑁 = 𝑁0𝑒−𝑡𝑔/𝑉 (3)

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

𝜏 =𝑉

𝑔 (4)



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Note that this result depends on a static fusion pore that does not change as the vesicle empties

out. This assumption is integral 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 Eq. 1

and 3.

I = αN0∫ ∑(−1)𝑖𝑥(1−2𝑖)

2𝑠√𝜋𝐷𝑠𝑒

−𝑥2(1−2𝑖)2/4𝐷𝑠

𝑒−𝑠𝑔/𝑉

𝑑𝑠

𝑛

𝑖=−𝑛

𝑡

0 (5)

α is 2xFaraday’s constant to convert molecules/s 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.

Eq. 5 can be used to simulate spikes and explore how parameters influence their shape.

Fig. 3A illustrates the impact of varying N0 within the range of observed values (Fig. 2D). Fig.

3B illustrates the impact of varying x over the range expected for gentle contact between the

electrode and cell. The parameter g was fixed at 25 msec-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 entirely 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 (30). The smaller changes in spike shape in Fig. 3B illustrate how grading

the flux through a fusion pore with Eq. 5 dampens the effect of distance.

The spikes simulated in Fig. 3 by the diffusion-fusion pore model (Eq. 5) resembled the

phase of recorded spikes after the pre-spike foot and before the post-spike foot (the “inter-feet”

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 inter-feet portion, points were taken within 50% of the peak (dashed line

in Fig. 4). Spikes were often quite brief, so these fits were performed on data acquired at 10 kHz

to provide more points. 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 start 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 recorded from 3 cells at 10 kHz

(Fig. 4, blue curve). The mean parameter values from these fits are presented in the figure legend.

Although events were fitted well there are telling trends in the parameters obtained. The

mean value for x of 1.2 µm is larger than the spacing between the electrode and cell. This may

reflect an interaction between x and other parameters during the fitting process. 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 4 of the 140 fits was less than the

value from the total event area. The mean ratio, N0-fit/N0-area, was 0.68. When N0 was constrained

to the value from the area, the fit was very poor (Fig. 4, magenta 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 while 32% are bound

to a matrix. This implies that the matrix-bound fraction is responsible for the slower component



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of decay of the post-spike foot. In fact, post-spike 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 fusion pore model was tested more critically against experiments by

examining the relations between selected indices of spike shape. The time constant for decay

(Tau decay) of simulated spikes was plotted against peak amplitude for x ranging from 0.3 to 1.2

µm (Fig. 5A). This plot shows Tau decay decreasing weakly with peak amplitude over a modest

range. By contrast, varying N0 (for x = 0.8 µm; a value that recapitulated the observed mean rise

time of 0.5 msec.) yields the opposite dependence; Tau decay increased with peak amplitude

over a much larger range (Fig. 5C). Varying N0 shows that peak amplitude increases and

gradually reaches a plateau (Fig. 5B), while Tau decay increases linearly (Fig. 5D). This linear

increase follows from Eq. 4: for a fixed initial concentration (32), the volume, V, is proportional

to N0. The preservation of this relation in Fig. 5D underscores the point that grading release

through a fusion pore diminishes the impact of diffusion.

These relations were compared to experiments by constructing plots of peak amplitude,

Tau decay (of the fast component, as in Figs. 1B1, 1B2, and 1B3), and N0 from the 1682 events

used to construct the distributions in Fig. 2. To view trends clearly, events were grouped into

bins of 20 and averaged. A plot of Tau decay of the fast component decreases with peak

amplitude (Fig. 5E). The plot based on simulated spikes shows qualitatively similar behavior

with varying x (Fig. 5A), but the range of both Tau 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 Tau decay and amplitude of

simulated spikes (Fig. 5C) versus experimental spikes (Fig. 5E). The experimental values of Tau

decay increase with increasing N0, and saturate with large N0 (Fig. 5F), while the plot from

simulations was linear over the entire range (Fig. 5D). The parameter interdependencies

predicted by the model differed qualitatively from those observed experimentally. Thus, despite

the good fits illustrated in Fig. 4, flux through a static fusion pore cannot account for spike shape.

This point was made previously (6, 7), and the present 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 shortcomings of this approach just illustrated, the possibility of a dynamic fusion pore

was considered. This approach begins with a rearrangement of Eq. 2.

𝐼(𝑡)

𝑁(𝑡)=

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). Since 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 in terms of I(t).

𝐼(𝑡)

𝐼0−∫ 𝐼(𝑠)𝑑𝑠𝑡0

=𝑔

𝑉 (7)

I0 is the total area under the entire event from start to end (∫ 𝐼(𝑠)𝑑𝑠𝑡𝑒𝑛𝑑0

; N0 was computed from

this quantity). With the numerator and denominator both expressed in terms of current, g/V can



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be calculated versus time for each amperometric event. Eq. 7 thus transforms amperometric

current to g/V.

Fig. 6 presents examples of I and g/V (from Eq. 7) for four spikes. 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 pre-spike foot, and then a downstroke following the peak

in I. The initial increase corresponds with a rapid expansion of the initial fusion pore to end the

pre-spike 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, for as

long as the post-spike foot is visible. The plots become noisy toward the end because the

numerator and denominator of Eq. 6 both become small, but g/V remains flat for as long as its

value can accurately be determined. Thus, the fusion pore remains stable, without closing or

expanding, for as long as catecholamine flux can be measured. The transform to g/V thus reveals

that the post-spike foot (28) corresponds with a stable “post-spike pore”.

The rapid decrease in g/V implies that the fusion pore contracts immediately after it

expands, and the plateau implies that the fusion pore settles into a stable structure. The three key

levels of g/V, the pre-spike foot, peak, and post-spike foot, are highlighted in each example in

Fig. 6 with dashed horizontal lines as indicated in the legend in the upper right corner. The rapid

onset 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 post-spike 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. 6A declines by ~90%, Fig. 6B by ~75% decline, Fig. 6C by ~30%,

and Fig. 6D by ~10%. Regardless of the extent of decline, a stable post-spike pore was seen in

443 g/V plots derived from 449 events recorded from 7 cells. The mean values of g/V of the pre-

spike foot, peak, and post-spike foot are plotted Fig. 7A to illustrate the changes in g/V during

the distinct phases of release. From the pre-spike 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 that represents the time scale over which a vesicle would lose its content through a static

fusion pore of that value. Thus, g/V for the pre-spike foot indicates it would take ~30 msec 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 msec 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 post-spike foot would allow loss of 63% of a vesicle’s content in ~7 msec.

N0 is proportional to V because the catecholamine concentration in a vesicle is

independent of vesicle size (32). 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. For the

pre-spike foot the plot of tau versus N0 was fairly linear over the entire range, with an intercept

near the origin (Fig. 7B). This suggests a stable fusion pore for the duration of the pre-spike foot,

and little variation between vesicles of different sizes. By contrast, for the peak (Fig. 7C) and

post-spike foot (Fig. 7D), plots of tau have linear regions for low N0, but the intercepts are above

the origin. Furthermore, these tau values reach a plateau for N0 > 1,000,000. This may indicate

that pore permeability begins to increase when vesicles are above a critical size. This will be

discussed further below.



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The transform to g/V offers an interesting perspective on the more complex amperometric

events that occur infrequently and defy conventional analysis. Most events are spike-like, as

illustrated in Figs. 1B1, 1B2, and 1B3, but occasional events with multiple peaks are generally

omitted from analysis. Two events with second smaller peaks are displayed in Fig. 8. It is very

unlikely that the two peaks in each event are due to coincident fusion of different vesicles,

because the overall frequency is too low. The g/V traces reveal increases during the second peak,

with the fusion pores making a transition to a larger size. The second example (Fig. 8B) shows a

further increase after the second peak in current, indicating further expansion. The value of g/V

becomes noisier and less reliable toward the end of the record due to the problem with quotients

of small numbers, but the current trace does show a small departure from monotonic decay

starting at about 55 msec. Thus, the fusion pore may actually be expanding further at this point

and the g/V plot is a better way to detect this.

DISCUSSION

This study used amperometry data from endocrine cells to investigate the evolution of the

fusion pore over time as catecholamine is released from single vesicles. Two different

approaches were explored. First, a static pore model was developed which 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

plateau was 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), and fitted the inter-feet

portions very well (Fig. 4). However, a more detailed analysis based on plots of indices of spike

shape lead to conclusions that challenge the static pore model. 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 Decay time and

amplitude (Fig. 5C) was opposite to that observed experimentally (Fig. 5E). Furthermore, the

Decay time should increase linearly with N0 (Eq. 4 and Fig. 5D), without the saturation seen in

the experimental data (Fig. 5F). These disparities argue against the view that flux through a static

fusion pore underlies the rapid component of spike decay, and 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 (6-8). Knocking out the matrix protein chromogranin A reduces the packaging of

catecholamine within dense-core vesicles (33, 34). The two components of decay in the present

work could be interpreted in terms of the rapid loss of a free pool of catecholamine followed by

the slow loss of a matrix-bound pool. However, the failure of the diffusion-static fusion pore

model argues against the idea of rapid loss of the free pool through a static fusion pore.

Furthermore, matrix dissociation should have a complex time course (7, 8), while the stability of

g/V during the slow component of catecholamine loss (Fig. 6) supports a role for pore flux. One

possibility is that there is a tightly bound pool of catecholamine that dissociates very slowly, but



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this would be too slow to influence the shapes of spikes over the tens of milliseconds relevant to

the present study. A critical 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 static pore model generated results at odds with experiment,

and this 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, 35).

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 (36). In the

present study, the assumption that an amperometry spike 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 (Fig. 6) this ratio underwent a transient increase suggesting that fusion pores

expand and contract in rapid succession. 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. 8). These multi-peak events obviously require more

complex mechanisms than static pore flux or matrix dissociation. The g/V plots of these events

provides a simple interpretation for these events as abrupt increases in pore size.

Diffusion probably alters 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 post-spike fusion pore is intrinsically stable, and that this structure can resist the

expanding forces arising from SNAREpin rotational entropy (37) and membrane tension (38).

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 (39), and when

changes have been observed they are slow (40). Although the flow of lipid label through fusion

pores appears to be more rapid, it is still somewhat slower than the times relevant to

amperometry recording, and the vesicles appear to maintain their volume during this flux (41,

42). 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/(6πηR

3), where σ is the membrane

tension, r is the pore radius, and η is the viscosity of the aqueous vesicle lumen (43). With η = 1

cP, r = 1 nm, and a typical value for σ of .03 dynes/cm (38), a 100 nm vesicle will decrease at a

rate of 0.16 nm/msec due to flow through a 1 nm pore. This is far too slow to have an impact

within the time scale of these experiments.

Properties of the Post-Spike 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 (44). Fig. 9 illustrates some possible

ramifications of these points. The transition from Fig. 9A to 9B will form the initial

proteinaceious pore. This pore transitions to lipid, and Fig. 9C 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 (45) or teardrop-like (46), and thus reduce its elastic energy. This

will lengthen the fusion pore (Fig. 9D) and thus reduce its permeability. This longer pore with

lower energy cannot be formed initially because in order to fuse the membranes must be close



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together (Fig. 9A). The cylinder can only lengthen after the transition that leads to an initial

lipidic pore. The transitions illustrated in Fig. 9 illustrate how the decrease in g/V immediately

after the peak (Fig. 6) realizes an earlier theoretical prediction (45, 46).

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 (26, 47), and these events may represent

the continued opening of the post-spike pore. SNARE transmembrane domain mutagenesis also

alters the fusion pore conductance during capacitance flickers as well as the amplitudes of pre-

spike feet (26, 48), suggesting a role for proteins not only in the small pre-spike pore, but also

the larger post-spike pore. The presence of protein in both small and large pores dictates a need

for structural flexibility that could be accommodated by a hybrid pore incorporating both protein

and lipid (5, 49).

The time constant for the rapid decay of the current exhibited an anomalous dependence

on N0 (Fig. 5F), which resembled that of the time constants (expressed as V/g) for both the peak

and post-spike pore (Figs. 7C and 7D). These time constants all increased with N0, saturated, and

had non-zero intercepts. The saturation may indicate that post-spike pores are larger for larger

vesicles, or that these pores exhibit less lengthening (Fig. 9). It is also possible that larger

vesicles possess a mechanism to actively expel catecholamine. The N0 dependence of V/g of pre-

spike feet was more linear (Fig. 7B), as expected from Eq. 4, and in accord with the hypothesis

of a common pore structure for vesicles of all sizes.

Revisiting Pre-spike Feet and SNARE Complex Number. The post-spike foot

had a g/V value 4.5-fold greater than the pre-spike foot (Fig. 7A). 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 (48, 50). However, the pore conductance used

in these calculations was derived from measurements of capacitance flickers that lasted hundreds

of milliseconds. Pre-spike feet, which SNARE mutagenesis experiments suggest reflect flux

through pores formed by transmembrane domains (26, 48, 51), last only a few milliseconds.

With the factor of two in diameter between the post-spike and pre-spike 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 (52) and endocrine cells (53). However, the calculation of pore

dimensions based on conductance assumed a fusion pore length of ~10 nm (two lipid bilayers).

The bowing illustrated in Fig. 9D would require a longer pore, with a proportional increase in

area. This would raise the estimate of SNARE complex number in the initial pore.

Biological Functions of the Post-Spike Pore. The post-spike pore may be small enough to

retain peptides within vesicles after the onset of fusion (20-22, 54), 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. 5F, 7C, and 7D may

indicate that larger vesicles have larger post-spike pores. This leads to the testable prediction that

small vesicles should have greater retention of large molecules.



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The post-spike pore identifies a potential locus for proteins to influence secretion. Many

proteins influence spike shape (9-19). 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. The present analysis provides this framework. Thus, rather than altering pore expansion,

the action of dynamin on amperometric spikes (15-17, 19) can be viewed as a change in the size

of the post-spike 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 (55). Proteins that alter the

post-spike pore will influence the selectivity and extent of content loss. By tracking fusion pores

over the entire course of a fusion event, g/V derived from amperometric spikes will enhance our

understanding of how proteins can control such processes.

AUTHOR CONTRIBUTIONS

MBJ developed the models, analyzed data, and wrote the paper; YTH performed

experiments, analyzed data, and edited the paper; CWC performed experiments and edited the

paper.

ACKNOWLEDGMENT

Supported by NIH grant NS044057.



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FIGURE LEGENDS

Fig. 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 3-9 seconds)

elicits many events with variable amplitudes. The bracket above at ~8 sec indicates three events

displayed on an expanded scale in B. These three selected events occurred in sequence and

illustrate variations in amplitude and kinetics. Single exponentials were fitted to the decaying

phase within 2/3 of the peak. These fits are shown as gray curves. The later phase of current is

clearly above the exponential curve fitted to the initial phase of decay. This highlights the two

components of decay, the second of which is referred to as the post-spike foot (28).

Fig. 2 Distributions of A. peak amplitudes, B. 35-90% rise times, C. decay times of the fast

component (Tau decay-fast; from fits as in Figs. 1B1-1B3), and D. number of molecules N0,

computed from the total area of the event (charge converted to 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 msec, Tau decay-fast 1.84 ±

1.50 msec, N0 600,080 ± 611,222. Plots were based on 1682 events recorded from 77 cells.

Fig. 3. Simulated spikes from the diffusion-static pore model (Eq. 5) for varying N0 with x fixed

(A) and varying x with N0 fixed (B). g/V = 25 msec-1

.

Fig. 4. Fits of the diffusion-static pore model (Eq. 5) to the fast part (inter-feet) of a spike. The

black points are amperometry data acquired at 10 kHz. The blue trace is the fit with all

parameters varied including N0. The magenta trace is the fit with N0 constrained to the value

obtained from the area of the event. Fits were conducted on 140 of 146 events from three cells.

The 6 discarded events had irregular shapes. Means ± standard deviations. x=1.20±0.51 µm; N0 =

1060015 ± 1159924; g/V = 136 ± 614 msec-1

. The mean RMS error of the 140 fits was 0.80 pA.

Fig. 5. Plots of shape indices from simulations (A-D) and experiment (E and F). A. In spikes

such as those in Fig. 3 simulated with the diffusion-static pore model, the diffusion distance x

was varied from 0.3 to 1.2 µm and the decay time was plotted versus peak amplitude. Note that

simulated spikes decayed monotonically with 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 Tau decay versus N0 with x = 0.8 µm. E. Plot

of Tau decay for the rapid component of versus peak amplitude for 1682 events recorded from

77 cells. Values were binned in groups of 50. Means ± standard errors. F. Plot of Tau decay

versus N0 determined from the spike area. Numbers and binning as in E.

Fig. 6. Amperometry spikes (current) were transformed to g/V (red) with Eq. 7. In each of the

four examples (A-D) dashed lines indicate g/V of the pre-spike foot (magenta), peak (blue), and

post-spike foot (green). The examples illustrate the characteristic initial expansion-contraction

cycle of g/V, with settling to plateaus of variable amplitude (see text).

Fig. 7. A. Bar graph of g/V (mean ± standard error) for pre-spike foot, peak, and post-foot.

Taking V/g as tau, binning in groups of 20 and averaging produced tau plots for the pre-spike

foot (B), peak (C), and post-spike foot (D) versus N0. Means ± standard errors.



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Fig. 8. Two examples of current and g/V for events with a second peak in amperometric current.

The second peak is associated with a stepwise increase in g/V.

Fig. 9. 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 pre-spike foot is

formed by proteins and does not alter membrane curvature. C. A lipidic pore forms with highly

curved membranes and close proximity between the fusing membranes. Creating this state

produces a sharp peak in pore permeability. D. Membrane elasticity theory has shown that a

fusion pore can reduce its membrane bending energy by increasing its length through a reduction

in meridional curvature (see text). This shape corresponds with the stable permeability of the

post-spike pore



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50

100

150

200

250

D

C

B

tau

post

-foot

(mse

c)

N0

A

Figure 7

tau-

peak

(mse

c)ta

u pr

e-fo

ot (m

sec)

Pre-foot Peak Post-foot0.0

0.1

0.2

0.3

0.4

0.5

0.6

g/V

(mse

c-1)

.C

C-B

Y-N


available under a(w






; https://doi.org/10.1101/2020.03.02.972745

doi: bioR

xiv preprint

https://doi.org/10.1101/2020.03.02.972745


BA

Figure 8

0 10 20 30 40 50 60 700

20

40

60

80

100

120

140

160

g/V

(mse

c-1)

0 10 20 30 40 50 60 700.00

0.04

0.08

0.12

0.16

0.20

Time (msec)0 10 20 30 40 500

10

20

30

40

50C

urre

nt (p

A)

Time (msec)

Current

600.00

0.02

0.04

0.06

0.08

0.10

g/V



https://doi.org/10.1101/2020.03.02.972745


A B C D



https://doi.org/10.1101/2020.03.02.972745


fusion pore expansion and contraction during catecholamine ...mar 02, 2020 · amperometry...

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