Correspondence to: Paul S. Blank, Laboratory of Cellular and Molecular Biophysics, National Institute of Child Health and Human Development, National Institutes of Health, Building 10, Room 10D14, 10 Center Drive MSC 1855, Bethesda, MD 20892-1855. Fax:(301) 594-0813 E-mail:psblank{at}helix.nih.gov.
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Abstract |
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Although the relationship between exocytosis and calcium is fundamental both to synaptic and nonneuronal secretory function, analysis is problematic because of the temporal and spatial properties of calcium, and the fact that vesicle transport, priming, retrieval, and recycling are coupled. By analyzing the kinetics of sea urchin egg secretory vesicle exocytosis in vitro, the final steps of exocytosis are resolved. These steps are modeled as a three-state system: activated, committed, and fused, where interstate transitions are given by the probabilities that an active fusion complex commits () and that a committed fusion complex results in fusion, p. The number of committed complexes per vesicle docking site is Poisson distributed with mean
. Experimentally, p and
increase with increasing calcium, whereas
and the
ratio remain constant, reducing the kinetic description to only one calcium-dependent, controlling variable,
. On average, the calcium dependence of the maximum rate (Rmax) and the time to reach Rmax (Tpeak) are described by the calcium dependence of
. Thus, the nonlinear relationship between the free calcium concentration and the rate of exocytosis can be explained solely by the calcium dependence of the distribution of fusion complexes at vesicle docking sites.
Key Words: cytoplasmic vesicles, membrane fusion, sea urchins, secretion, neurosecretion
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INTRODUCTION |
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The exquisite physiological regulation of local calcium concentration at the active zone of a presynaptic terminal supports the long-debated hypothesis that synaptic plasticity depends heavily on the modulation of the relationship between calcium concentration and transmitter release. This fundamental relationship is observed in temporally diverse secretory systems including neurons, other secretory cells, and eggs. However, a single analytical description for the action of calcium at the synapse that includes the many sites of modulation and control has yet to be developed. Such a description would be equally valuable in synthesizing and testing the molecular basis of synaptic function, since calcium must interact with ensembles of proteins to effect release, and kinetic parameters need to be assigned to the underlying molecular events. Here, we present an analytical description for the final steps of calcium-triggered exocytosis that relies, on average, only upon the calcium dependence of fusion complexes at vesicle docking sites and may be applicable in describing calcium-regulated exocytosis over the entire temporal range observed from eggs to neurons.
To understand the modulation of calcium-regulated release, it is essential to fully understand the origin of the nonlinear relationship between calcium concentration (external, internal, and local) and calcium-triggered exocytosis (amplitude and rate of response).
Preparations that isolate selected steps in the exocytotic pathway reduce the complexity of the overall process, and are useful in developing an analytical description of the secretory process. Cortical vesicle exocytosis in the isolated planar cortex of the sea urchin egg, an example of calcium-triggered exocytosis, is an attractive system for directly studying the relationship between calcium and exocytosis. The final fusion steps of exocytosis are preserved in isolation from kinetically confounding processes, such as the temporal and spatial properties of the calcium signal, vesicle transport and priming, and membrane retrieval and recycling. The magnitude of the free calcium concentration is the single controlling variable determining which fraction of vesicles fuse (
Previously, we investigated the consequences of having multiple fusion complexes at fusion sites and proposed that the calcium-triggered exocytotic behavior observed in this preparation can be explained by the hypothesis that an increase in the free calcium concentration increases the average number of participating fusion complexes (
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MATERIALS AND METHODS |
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All materials and methods related to the study of exocytosis in the sea urchin, Strongylocentrotus purpuratus are described in ,
, and p were 0.4 ± 0.1%, 1.2 ± 0.2%, and 3.1 ± 0.5% (n = 73, mean ± SEM), respectively. To further test the goodness of fit upon minimization a small sample, resampling analysis was performed. In this procedure, 90% of the data was randomly selected without replacement and the process was repeated 10 times. These 10 datasets were then individually fit for the three parameters, and parameter values and error estimates were calculated from the mean and standard deviation of the 10 values obtained for each parameter. The estimated errors for all parameters were, both from each separate trial and calculated from the 10 trials, smaller than that obtained in the original dataset and strongly argues for a global minimum in the fitting. The results described were obtained from fitting 73 different fusion curves (n = 3, 19, 25, 20, and 6 for pCa 4.12, 4.46, 4.62, 4.84, and 4.98; and n = 10, 11, and 3 for pCa 4.46, 4.62, and 4.84, for single and double challenge experiments, respectively), a subset of the 111 egg preparations studied previously (
and the
ratio was evaluated using a one-factor analysis of variance (ANOVA) on both the data and a log transformation of the data. Differences between the parameters describing single and double challenge kinetics were evaluated using a two-sample t test done at each calcium level; significance was evaluated at the P = 0.05 level. Population estimates are presented as the mean ± SEM for n experiments. Note, the error (SEM) of the population estimates for the parameters
,
, and p, represents the observed biological variability and is larger than the fitting errors associated with the determination of parameter values from a single experiment.
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RESULTS |
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A Three-parameter Kinetic Analysis of Exocytosis
We have developed a three-parameter kinetic description for calcium-triggered exocytosis by including an explicit transition between a calcium-triggered precursor and a committed state, to address the major incongruity between the observed initial time course of fusion and the initial time course predicted by our previous analysis ( is the probability per time interval that an active fusion complex becomes a committed fusion complex, and p is the probability per time interval that a committed fusion complex mediates a fusion event between a vesicle and the plasma membrane. The survival of a single vesicle having a time dependent appearance of n committed fusion complexes isS(t,n,(
,t),p)=[(1-p)t]n(
,t).
In general, n(, t) = n · L(
, t), where L(
, t) allows for the introduction of a lag phase signifying that the appearance of committed fusion complexes does not occur instantaneously. The lag phase is a characteristic feature of exocytotic kinetics. The deterministic function L(
, t) = [1 - (1 -
)t] was used because it is the simplest function that described the observed transition. If higher temporal resolution data provides evidence for multiple transitions in the lag phase, then a more detailed function describing these transitions would be necessary. Both the appearance of n committed fusion complexes and the disappearance (fusion) of a vesicle have been formulated as Bernoulli trials (
represents the average number of committed complexes per docking site. Fusion, F(t,
,
,p)=1-S(t,
,
,p). The rate of fusion, R(t,n,
,p) is:
As described previously, the extent of fusion is:
In the limit of small and p (
0.1), (1 -
)t and (1 - p)t approach exp(-
t) and exp(-pt), respectively. In this limit, an alternative expression for the Poisson-weighted sum of individual vesicle survival curves that is continuous in time is:
Now, and p represent rate constants for the specified transition. For the same transition probability (for example, 0.1) but different time intervals (millisecond and second) the characteristic time constants for the transitions
= 1/
and
P = 1/p, are 10 ms and 10 s, respectively. Using a discrete time parameter, represented by a sequence of independent trials, is analogous to approximating a one-dimensional random walk using interval transition probabilities to describe movement to the left or right. The discrete and continuous expressions for the Poisson-weighted sum of individual vesicle survival curves describe the kinetics with statistically indistinguishable parameters. Both analytical expressions eliminate the need to fit data to exponential sums, a notoriously difficult analysis requiring data of high precision over a wide range (
Kinetic Analysis of the Calcium Dependence of Exocytosis
We have used multiple calcium challenges to investigate submaximal exocytotic responses of isolated planar cortices of the sea urchin S. purpuratus at suboptimal calcium concentrations (, and
is shown in Fig 2. There is no statistical difference between the parameters describing either single or double challenge kinetics: this analysis describes both responses equally well (Fig 1). Note, in the present study,
is estimated from a fitting parameter and not calculated from the extent of fusion. Over the ranges of calcium concentrations studied, the
ratio and the parameter
were found to be independent of pCa (-log [Ca2+]free) (Fig 2). Both the
ratio and the log transformation of
, log (
), are independent of pCa with
= 0.029 ± 0.002 (mean ± SEM, n = 73 experiments; F = 0.514, df = 5, 67, P = 0.765, and F = 0.671, df = 5, 67, P = 0.647, ANOVA). The invariance of
with [Ca2+]free (
= 0.113 ± 0.013 [mean ± SEM], n = 73 experiments; F = 1.722, df = 5, 67, P = 0.141, ANOVA; Fig 2 C) is consistent with either calcium-independent conversion of activated to committed complexes or calcium-dependent conversion saturating at
5 µM calcium. In particular, as neither the ANOVA nor the within subset, two-sample t tests were significant, the hypothesis that no significant trend was detected in either
or the
ratio for both single and double challenges is supported. The correlation between p and
is consistent with a rate constant proportional to
. Since p represents a bounded quantity in the discrete expression, the invariance of
with [Ca2+]free (Fig 2 D) suggests that this is a limiting relationship of the form
=
, a characteristic constant. This was tested by fitting all pairs of p and
with p = 1 - exp(-
), which approaches
and 1 for small and large values of the exponent, respectively. The value of
was identical to that obtained by ANOVA of
with [Ca2+]free. For 0 <
< 0.2, >98% of vesicles have zero or one activated complex, suggesting that at low [Ca2+]free, p has a limiting value whose distribution is presently unknown. Substituting
= 0.113 and p = 0.029
ignores the distribution of
and
, but reduces the analysis to one parameter that should, on average, describe the kinetics of fusion. This was tested using a reduced kinetic analysis with only one controlling variable (pCa) derived using the relationship between the extent of fusion and
and the empirical relationship (log-normal cumulative distribution with midpoint M = 18.2 µM and width W = 0.23), which describes the extent of fusion as a function of [Ca2+]free (
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The maximum rate and the time to reach the maximum rate were calculated as a function of pCa and compared with measured values (Fig 3). Note this is not a fit to the average data, but rather it is the predicted behavior following reduction to one controlling variable, the calcium concentration. The maximum rate is a quadratic function of , (Rmax
a; a = 1.93 ± 0.25); this is exactly the dependence predicted when p is proportional to
. The relationship between the maximum rate and
suggests that
represents the local concentration of fusion complexes. Furthermore, these predicted characteristic relationships strongly support the hypothesis that understanding the properties of the local and stochastic concentration of fusion complexes is important for a full kinetic description of calcium-triggered exocytosis. The nonlinear relationship between the maximum rate of exocytosis and the free calcium concentration can be described by the calcium dependence of
and two characteristic constants of the system,
and
.
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Extension of the Analysis to the Millisecond Time Scale
Variations in the model parameters can capture kinetic features observed in both "egglike" and "neuronal-like" calcium-triggered systems (Fig 4). Calcium concentrations eliciting
5 will trigger fusion of >99% of all vesicles present. Changing the time constants from the second to millisecond time scale and decreasing
results in limited depletion of the available vesicle pool with fusion occurring on a millisecond time scale. Both the extent of vesicle release and the maximum rate of release can be approximated by a [Ca2+]4 power-law dependence (Fig 5A and Fig B). Calcium-dependent variations in the lag (time to first fusion event) and time to peak rate (Fig 5 C) are similar to those observed in neurons (
), coupled with variations in the kinetic time constants and distribution of calcium thresholds is therefore sufficient to explain the wide range in rates and extents of fusion observed in other calcium-triggered exocytotic systems.
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DISCUSSION |
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What factors contribute to the observed nonlinear relationship between exocytosis and calcium concentration? We present an analytical description for the final steps of calcium-triggered exocytosis that relies, on average, only upon the calcium dependence of Poisson-distributed fusion complexes at vesicle docking sites. The calcium dependence of distributed fusion complexes is sufficient to explain the nonlinear relationship observed in sea urchin cortical vesicle exocytosis. This analysis may be applicable in describing experimental features of calcium-triggered exocytosis that are observed in diverse systems covering a wide temporal range.
Kinetic Properties of Exocytosis in Eggs Are Similar to Those of Other Calcium-triggered Systems
How do the rates of exocytosis in neurons and other secretory cells compare with those observed in the egg? An 80-µm-diam S. purpuratus egg has a density of 0.9 vesicles/µm2 based on
1.8 x 104 vesicles/egg (
4.5 x 103 vesicles, which is in agreement with measured values (
200% fusion/s (
104 vesicles/s) when challenged with saturating calcium concentrations (>1 mM) that activate all fusion complexes. As a function of [Ca2+]free, the maximum rates calculated from the analysis of the resolved fusion kinetics correspond to
202,700 vesicles/s. In the urchin cortex, such rates are primarily a consequence of the large number of releasable vesicles rather than the underlying kinetic rate constant (less than
10 s-1 maximum based on the time to peak rate occurring in 0.10.2 s at saturating [Ca2+]free). The releasable pool in other preparations is estimated to be
101,000 vesicles which, at the highest rates, are released on a
110-ms time scale (for review see
104 vesicles at a maximum rate of
2,000 vesicles/s (
100 ms, in melanotrophs and neutrophils
10 ms (
1 ms (
0.1 ms (
) and the coupling between the fusion probability and the number of committed complexes (fusion efficacy [
]) must be sites of modulation if an underlying conserved mechanism, captured in this analysis, is responsible for the final fusion pathway in such temporally diverse systems.
Are Poisson-distributed Fusion Complexes with Distributed Calcium Thresholds a Conserved Feature of Calcium-triggered Exocytosis?
One major feature of sea urchin cortical vesicle exocytosis is submaximal secretion at suboptimal stimulation, also observed in a wide variety of permeabilized preparations (for reviews see Max) is approximately seven to nine (
The calcium dependence of this readily releasable pool was determined in calyces of Held where 20% of 700 quanta (vesicles) are released, on average, by a single presynaptic action potential under physiological conditions (20% suggests that when stimulation is low, synaptic transmission operates with
< 0.2; vesicles have only one activated complex. We predict that manipulations decreasing the available calcium decrease
further and results in a kinetic response that normalizes to a common time course in which the number of participating quanta varies with [Ca2+]free. Do synaptic vesicles utilize multiple fusion complexes with distributed calcium thresholds under conditions of higher calcium concentrations then those observed during a single action potential?
A single presynaptic action potential is capable of depleting the readily releasable pool in calyces of Held, provided the external calcium concentration is high enough (10 µM released
100% of the releasable pool while the release rate continued to increase with free calcium concentrations greater than the minimum concentrations required to release
100% of the releasable pool (
increases, corresponding to the appearance of vesicles with two or more activated complexes, additional terms in the kinetics begin to appear and may manifest as poorer fits with a single exponential. The failure to rigorously describe synaptic release kinetics with one scalable process is predicted to increase with increasing concentrations of calcium and may provide evidence for the existence of reserve capacity on synaptic vesicles.
Does Max Vary in Different Calcium-triggered Systems?
The size of an exocytotic vesicle may limit the maximum average number of complexes Max present at vesicle docking sites. For example,
Max on synaptic vesicles may be fractional such that the proportion of vesicles with two or more complexes is small. One consequence of
Max = 0.50.1 is that only 8% to <1% of the vesicles present will have two or more complexes, and that 6190% of the vesicles present will be incapable of fusion at any calcium concentration. The pool of inactive vesicles may represent inefficiency in the process of creating the readily releasable/recycling pool and may not be detected using techniques that rely solely on vesicle release. Such a large pool of inactive vesicles is consistent with the observations that, even under strong stimulus conditions, only
10% of the total synaptic vesicle population in a terminal participates in neurotransmitter release and recycling (
Max because of the hypothesis that the overall population of complexes is described by an underlying distribution of thresholds defined by the derivative of the calcium activity curve (
and p representing the described previously rate constants, and Thresh(pCa) describing the normalized calcium activity curve, an alternative formulation for the fusion process is:
Although this expression is not appropriate for the urchin, where reserve capacity is well established (
Issues in Identifying the Molecular Basis of Calcium-triggered Exocytosis
Understanding the interactions of calcium with ensembles of proteins is a key step in identifying the molecular basis of calcium-triggered exocytosis. The conserved multigene families of SNARE proteins, VAMP, SNAP-25, and syntaxin, have homologues present in the cortical membranes of sea urchin eggs (
Conclusion
The nonlinear relationship between [Ca2+]free and the rate of exocytosis is a characteristic feature of calcium-triggered secretory systems. The final steps of calcium-triggered vesicle exocytosis are described by an analysis using three parameters: (1) the interval probability that an active fusion complex becomes committed (); (2) the average number of committed complexes (
); and (3) the interval probability that a committed fusion complex results in fusion (p). This analysis is based on the hypothesis that exocytotic vesicle docking sites have multiple fusion complexes (reserve capacity), and that increasing the free calcium concentration increases the average number of participating fusion complexes. In the sea urchin planar cortex, the average kinetic behavior of submaximal exocytosis at suboptimal free calcium concentrations, including maximum (peak) rate and time to reach maximum rate, is described by the calcium dependence of the participating fusion complexes. The reserve capacity may be limited in other systems when the rapid release of only a small number of vesicles is required. In contrast, the egg requires that essentially every cortical vesicle fuse after fertilization and utilizes reserve capacity to ensure that this level of calcium-triggered exocytosis occurs.
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Acknowledgements |
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We thank Drs. Jens R. Coorssen and Nevin A. Lambert for stimulating discussions and critically reading our manuscript.
S.S. Vogel has received support from the National Institutes of Health grant No. NS41055.
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