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Single-Pixel Optical Fluctuation Analysis of
Calcium Channel Function in Active Zones of
Motor Nerve Terminals
Article in The Journal of Neuroscience : The Official Journal of the Society for Neuroscience · August 2011
DOI: 10.1523/JNEUROSCI.1394-11.2011 · Source: PubMed
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J Neurosci. Author manuscript; available in PMC 2012 August 06.
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Published in final edited form as:
J Neurosci. 2011 August 3; 31(31): 11268–11281. doi:10.1523/JNEUROSCI.1394-11.2011.
Single-Pixel Optical Fluctuation Analysis of Calcium Channel
Function in Active Zones of Motor Nerve Terminals
Fujun Luo1,2, Markus Dittrich3, Joel R. Stiles1,3,4, and Stephen D. Meriney1,2
1Department of Neuroscience, Center for Neuroscience, University of Pittsburgh, Pittsburgh,
Pennsylvania 15260
2Center
for the Neural Basis of Cognition, Pittsburgh, Pennsylvania 15213
3National
Resource for Biomedical Supercomputing, Pittsburgh Supercomputing Center,
Pittsburgh, Pennsylvania 15213
4Department
of Biological Sciences, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213
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Abstract
We used high-resolution fluorescence imaging and single-pixel optical fluctuation analysis to
estimate the opening probability of individual voltage-gated calcium (Ca2+) channels during an
action potential and the number of such Ca2+ channels within active zones of frog neuromuscular
junctions. Analysis revealed ~36 Ca2+ channels within each active zone, similar to the number of
docked synaptic vesicles but far less than the total number of transmembrane particles reported
based on freeze-fracture analysis (~200–250). The probability that each channel opened during an
action potential was only ~0.2. These results suggest why each active zone averages only one
quantal release event during every other action potential, despite a substantial number of docked
vesicles. With sparse Ca2+ channels and low opening probability, triggering of fusion for each
vesicle is primarily controlled by Ca2+ influx through individual Ca2+ channels. In contrast, the
entire synapse is highly reliable because it contains hundreds of active zones.
Introduction
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Nerve terminal active zones contain highly organized components that underlie synaptic
vesicle docking and fusion (Zhai and Bellen, 2004). Such organization is readily apparent in
adult frog neuromuscular junctions (NMJs), in which electron microscopy has revealed
hundreds of linear active zones, each arrayed with 200–250 intramembraneous particles and
25–40 closely associated synaptic vesicles (Heuser et al., 1979; Pawson et al., 1998; Harlow
et al., 2001; Rizzoli and Betz, 2005). Previous investigators have hypothesized that these
intramembraneous particles include the presynaptic Ca2+ channels that trigger vesicle fusion
(Pumplin et al., 1981; Robitaille et al., 1990; Cohen et al., 1991). Because other channels
and release machinery proteins are also present in the active zone (Robitaille et al., 1993),
only some of the active zone particles observed in freeze-fracture replicas are expected to
represent voltage-gated Ca2+ channels. Although the NMJ is known as a reliable synapse in
which a single presynaptic action potential (AP) can trigger release of several hundred
quanta (eliciting an action potential in the muscle) (Wood and Slater, 2001), each individual
Copyright©2011 the authors
Correspondence should be addressed to Dr. Stephen D. Meriney, Department of Neuroscience, A210 Langley Hall, University of
Pittsburgh, Pittsburgh, PA 15260. meriney@pitt.edu. .
Author contributions: F.L., M.D., J.R.S., and S.D.M. designed research; F.L., M.D., and S.D.M. performed research; F.L., M.D., and
J.R.S. analyzed data; F.L., M.D., J.R.S., and S.D.M. wrote the paper.
Luo et al.
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active zone operates as a low probability release site, averaging only one vesicle released
following every other action potential (Katz, 1969; Katz and Miledi, 1979; Poage and
Meriney, 2002).
Despite >60 years of study, many important questions persist regarding Ca2+-dependent
transmitter release. For example, it is not known how many voltage-gated Ca2+ channels are
positioned in an active zone or what is the in situ probability (p) that they will open during
an action potential [which is distinct from the channel open probability (Po) traditionally
measured during long depolarizing steps]. Answers to both of these questions will provide
important constraints on models of Ca2+-triggered vesicle fusion, including the
stoichiometric and spatial relationships between Ca2+ channels and docked vesicles. To
address these questions, we developed single-pixel optical fluctuation analysis (SPOFA) and
applied it to action potential-evoked Ca2+ indicator fluorescence measurements in frog
motor nerve terminals.
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Variance analysis of Ca2+ fluorescence signals has been applied previously to small
neuronal compartments and used to reveal stochastic openings of Ca2+ channels in
presynaptic boutons and postsynaptic spines (Frenguelli and Malinow 1996; Sabatini and
Svoboda, 2000) (but see Brenowitz and Regehr, 2007). In addition, we have previously
described stochastic Ca2+ signals arising from frog NMJ active zones (Wachman et al.,
2004). We now extend this approach to automated acquisition and analysis of signal
variance at the level of single pixels overlying portions of active zones. In doing so, we
characterize the spatial resolution of data acquisition, the methods used for selection of
active zone pixels, and the possible contribution of single-channel current variability to the
measured variability. We demonstrate optical resolution at subactive zone dimensions, show
that our results are primarily independent of pixel selection criteria, and also consider the
effect of additional sources of variation on our results via Monte Carlo (MCell) simulations.
Based on our findings, we conclude that relatively few Ca2+ channels line each active zone
of frog NMJs and that each action potential normally opens only a small fraction of such
channels. These results lead us to hypothesize that action potential-evoked vesicle fusion at
this synapse is likely triggered by the Ca2+ ion flux through one or very few Ca2+ channels.
Materials and Methods
Dye loading and staining of cutaneous pectoris nerve–muscle preparations
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Adult frogs (Rana pipiens) were decapitated and pithed after anesthesia in 0.1% tricaine
methane sulfonate. Cutaneous pectoris muscles were dissected bilaterally and bathed in
normal frog Ringer’s solution (NFR) (in mM: 116 NaCl, 2 KCl, 1.8 CaCl2, 1 MgCl2, and 5
HEPES, pH 7.4). The nerve was cut near its entrance into the muscle, and the cut end was
drawn into a Vaseline well containing 30 mM Calcium Green-1 (3000 molecular weight
dextran conjugate; Invitrogen) dissolved in distilled water. After 7–8 h of dye loading at
room temperature, the preparation was rinsed in NFR and stored at 4°C for 2–3 h. For
stimulation and imaging, preparations were pinned over an elevated Sylgard (Dow Corning)
platform in a 35 mm dish mounted on the microscope stage. The nerve was drawn into a
suction electrode, and stimulation threshold was determined by observation of muscle
twitch. Postsynaptic acetylcholine receptors then were blocked and labeled using 2 μg/ml
Alexa Fluor 594-conjugated α-bungarotoxin (α-BTX) for 10 min. α-BTX staining was used
to locate and focus the postsynaptic receptor bands, which are directly opposed to the
presynaptic active zones, and to evaluate possible z-axis drift over the course of data
collection. Superficial nerve terminals were chosen for study, and most lay in a single focal
plane as judged by α-BTX staining. Except as noted, all Ca2+ imaging was performed in
NFR containing 10 μM curare to prevent nerve-evoked muscle contractions not completely
blocked by α-BTX.
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Calcium imaging and nerve stimulation protocol
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Images were collected at 0.5 Hz using a 1 ms laser illumination time. An acousto-optic
tunable filter (ChromoDynamics) was used to select wavelengths and gate the laser with
submillisecond time resolution (krypton–argon laser; Innova 70 Spectrum; Coherent). The
laser was fiber coupled to the epi-illumination port of an upright fluorescence microscope
(Olympus BX61WI) equipped with a long-working-distance water-immersion objective
(100×, 1.0 NA; Lumplan/FL IR; Olympus). Calcium Green-1 was excited at 488 nm, and
emitted light was collected through a 530 ± 20 nm filter. Alexa Fluor 594–α-BTX was
excited at 567 nm, and emitted light was collected using a 620 ± 30 nm filter. Images were
recorded on one of two cooled, back-thinned CCD cameras (LN1300B by Roper Scientific;
or Ixon DV887 by Andor), which provided the high sensitivity and low noise necessary for
imaging acquisition during 1 ms illumination times. Pixel size was 200 nm (LN1300B) or
160 nm (Ixon DV887). Analysis of data from either camera gave similar results. In
comparing theoretical Rayleigh’s and FWHM criteria (based on the optics within our
microscope and the excitation wavelength of the fluorescent dye), our axial resolution can
be no better than between 864 and 976 nm. The lateral resolution of the microscope was
experimentally determined by measuring the point-spread function (PSF) imaged using 20
nm fluorescent beads (after Gaussian fit, width at half-maximum amplitude of 450 nm) (Fig.
1C). Furthermore, a plot of the cross-correlation analysis of action potential-evoked
fluorescent signals in the nerve terminal detected by adjacent pixels revealed a width at halfmaximum amplitude of 410 nm (Fig. 1 D). These data indicate that, as a result of our brief 1
ms acquisition window, signals sampled by a given pixel derive mainly from channels
underlying this pixel. This distribution is best fit by a Lorentzian function because there is
some optical signal that appears to contribute to the “tails” of this distribution. The signal
sampled by one pixel does not derive exclusively from a single point source (a single open
Ca2+ channel centered below the pixel), but rather there are likely neighboring sources that
contribute some elevated signal because we predict that several spatially distributed Ca2+
channels likely open within one active zone after each action potential. Given the anatomical
organization of active zones and considering our 1 ms illumination timed with action
potential invasion (which limits time for diffusion), a pixel that is positioned over one active
zone will likely not sample significant signal derived from calcium channel flux originating
within neighboring active zones. However, within the sampling region detected by one
pixel, we do not have a good method for determining the heterogeneity in contribution that
might arise from different Ca2+ channels that might be at slightly different distances from
the center of one pixel.
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During acquisition, images were collected in sets of 20. Within each set, the first 10 were
acquired without nerve stimulation to obtain resting (background) fluorescence, whereas
each of the second 10 followed nerve stimulation at 5× threshold to obtain action potentialdependent fluorescence. A delay of 1.5 ms between stimulation and illumination was used to
account for nerve conduction delay in this preparation. In most experiments, 10 sets of trials
were performed sequentially to obtain a total of 100 background images interleaved with
100 images after stimulation. Between sets, we confirmed or adjusted focus based on αBTX staining (which allowed a characterization of active zone distribution and focal plane)
and discarded image sets from analysis if they showed noticeable z-axis drift or significant
changes in average background fluorescence. In some experiments, the preparation
subsequently was exposed to the potassium channel blocker 3,4-diaminopyridine (DAP) (5
μM for 30 min), and another 10 sets of images were obtained in the continued presence of
DAP. Because there is active propagation of action potentials along the length of motor
nerve terminals (Katz and Miledi, 1965, 1968; Braun and Schmidt, 1966; Mallart, 1984),
DAP treatment will block presynaptic potassium channels, prolonging the duration of the
action potential (Kirsch and Narahashi, 1978; Durant and Marshall, 1980), without altering
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propagation within the nerve terminal. As such, this treatment will indirectly increases the
probability (p) that Ca2+ channels open after nerve stimulation but leave the number of
channels (n) unchanged. This differential effect allows subsequent analysis of fluorescence
fluctuations across repeated trials to determine p and n on a per pixel basis (see below).
Image registration and analysis
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Before analysis, all images collected from individual terminals were registered to the first
image to correct for slight fluctuations in the x–y (or lateral) position of the preparation
during data collection. Registration software was written at the National Resource for
Biomedical Supercom-puting (www.nrbsc.org) at the Pittsburgh Supercomputing Center. To
avoid aligning on background features, we sampled the most prominent aspects of the
background (including any artifacts) and subtracted this background from the images. We
then used the raw calcium-dependent fluorescence to create a mask that represented the
detailed shape of the nerve terminal in each image. With this approach, we used customwritten nonlinear registration software to warp each image in a time series to the first image
of that series. Although the software was capable of generalized rotational and nonlinear
corrections, virtually all of the adjustments necessary for these experiments were simple
interpolated translational movements of one pixel or less. Stimulus-dependent changes in
fluorescence intensity were small (typically 3– 4% above background; see Results), and so
the registration step brought the shape of the nerve terminal into alignment without being
confounded by large and variable changes in signal strength within regions of nerve
terminals. Analysis of registered images was performed using MATLAB. To create
difference images showing stimulus-dependent fluorescence changes (ΔFs) for each pixel,
we calculated the average background fluorescence of each pixel ( ),subtracted it from the
fluorescence (fs) obtained after a stimulation trial, and then normalized the resulting
differences to , i.e., per pixel
. Resulting difference images were displayed in
pseudo-fb color. For subsequent calculation of n and p (see below), analysis for each pixel
also included calculation of the background variance ( ), the mean fluorescence ( ) and
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variance ( ) after nerve stimulation, and the mean fluorescence ( ) and variance ( )
after stimulation combined with DAP treatment. Within image sets from individual
terminals, the variance of background fluorescence arises from dark noise and photon shot
noise and, under our experimental conditions, was dominated by Gaussian shot noise.
Conversely, background photoelectron counts from different visualized nerve terminals
varied according to differences in geometry and dye loading and ranged from 1500 to 6000
per pixel. With resting photoelectron counts this high and stimulated fluorescence changes
that were <15%, the contribution of differences in shot noise between resting and stimulated
measurements to our final results would have been very small (<1%) and were thus ignored.
Determination of n and p
Over the course of repeated stimulation trials, the mean fluorescence intensity
is expected
to exceed the mean background level for pixels that overlie a subregion of an active zone
and periodically detect Ca2+ influx through one or more open Ca2+ channels. We limited our
subsequent analysis to those pixels within active zone regions that reported significant
action potential-evoked fluorescence signals under control conditions. We evaluated a range
of criteria for significance to rule out sampling effects on our results as much as possible.
For most of our analyses, we settled on using the criterion that the stimulus-dependent mean
fluorescence (Δfs; see below) be greater than the SD of background fluorescence σb (SD
criterion). We demonstrated that the choice of selection criterion had little or no effect on
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our estimates of n and p by comparing results using this criterion with a Student’s t test
using different levels of significance (Table 1) (see Figs. 6 and 7).
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We calculated n and p for selected pixels using two measurable ratios, RF and RCV (Sabatini
and Svoboda, 2000). The mean of the stimulus-dependent fluorescence signals before and
after DAP treatment are as follows:
1
2
We define RF as the ratio of stimulus-dependent fluorescence signals before and after DAP
treatment:
3
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Similarly, the coefficient of variation (CV) in the stimulus-dependent fluorescence signals
before and after DAP treatment are as follows:
4
5
RCV is defined as follows:
6
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To calculate n and p from the experimental RF (Eq. 1c) and RCV (Eq. 2c) values, we assume
that each Ca2+ channel acts independently and opens during an action potential with
probability p before DAP treatment and pD after DAP treatment. The corresponding
probabilities of remaining closed are (1 − p) and (1− pD), respectively. Under each
condition, the number of channels that open from trial to trial is expected to follow a
binomial distribution. From standard binomial theory, in a sub-active zone region containing
n channels, the average number that will open (μ) before DAP treatment is given by:
7
Assuming a linear detection system (see Results), the mean fluorescence arising from Ca2+
entering through open channels (ΔFs; Eq. 1a) will be proportional to μ, thus
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8
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Similarly, after DAP treatment, the mean fluorescence arising from entering Ca2+ (ΔFDs;
Eq. 1b) will be proportional to the average number that will open μD after DAP treatment:
9
The mean stimulus-dependent fluorescence signals before and after DAP treatment should
be governed by the number of Ca2+ channels opened by an action potential.
From Equations 1c, 5, and 6, we now have
10
where we assume that DAP treatment does not affect the number of functional Ca2+
channels n as well as the amount of Ca2+ flux through single open channels (see Results).
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Again from standard binomial theory, the predicted variance for channel opening before
DAP treatment σ2 is
11
The SD (σ) is thus:
12
Using Equations 3 and 8, the CV in the number of open channels is
13
14
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If all of the variance in measured stimulus-dependent fluorescence arises from the random
openings of channels from trial to trial, then from Equations 2a and 7,
15
and from Equations 2a and 9b,
16
Similarly, after DAP treatment,
17
Therefore, from Equations 2c, 11, and 12, we have
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18
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where again we assume that DAP treatment does not affect the number of Ca2+ channels n
as well as the amount of Ca2+ flux through single open channels.
In Equations 6 and 13, we have the two measured ratios RF and RCV, as well as the two
unknown probabilities p and pD. Rearranging Equation 6 for pD yields the following:
19
After using Equation 14 to substitute for pD in Equation 13, algebraic rearrangement now
provides an expression for p that includes only the measured ratios RF and RCV:
20
Equation 15 was therefore used to calculate p, and Equation 14 was used to calculate pD.
Finally, a rearranged form of Equation 11 was used to estimate n:
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21
Computational modeling of action-potential-triggered Ca2+ fluorescence Generation of
action potentials
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Action potentials were generated with a standard Hodgkin–Huxley model using the
NEURON simulation environment (release 7.1.) (Hines and Carnevale, 1997; Carnevale and
Hines, 2006). The parameters for the Hodgkin–Huxley model were chosen based on two
criteria for the resulting action potentials. First, because adult motor nerve terminals are not
accessible to direct recordings of action potential shape, we based our assumptions for AP
shape on experimentally measured synaptic action potential waveforms from embryonic
cultured motor nerve terminals, which are very narrow. Second, when used within our
computational model of action-potential-triggered Ca2+ influx (see below), we aimed for a
Ca2+ channel open probability p under control conditions of ~0.2 (AP1, 0.18; AP2, 0.20). In
choosing modeled APs for our analysis, we sought to use one AP shape that was very
similar to the recorded AP from embryonic cultured motor nerve terminals (AP2). Because
we cannot be sure of the exact shape of the AP at adult frog motor nerve terminals and to be
more rigorous in our analysis, we also considered a second AP (AP1) with a distinctly
different AP shape but still subject to the same constraints on open probability p for Ca2+
channels. The two thus generated action potential waveforms AP1 and AP2 are depicted in
Figure 3A. Figure 3B shows both action potentials together with an experimentally recorded
action potential recorded from cultured embryonic Xenopus nerve–muscle synapses (Pattillo
et al., 2001).
The effect of DAP on action potential shape was modeled by reducing the gk,max value of
the potassium gating particles in the Hodgkin–Huxley model. The resulting broadening of
the action potentials (see Fig. 3A) led to an increase in the Ca2+ channel open probability p,
and gk,max was chosen to yield a p value of ~0.6 (AP1, 0.56; AP2, 0.65). It is important to
point out that the values we chose for p were arbitrary (but very close to experimental
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observations) because our computational validation procedure only seeks to establish the
ability of SPOFA to estimate the values of p and n regardless of their actual values.
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Monte Carlo simulations of action-potential-triggered Ca2+ influx
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To test whether SPOFA is able to estimate p and n from measured fluorescence data, we
developed a computation model of action-potential-triggered Ca2+ influx through voltagegated Ca2+ channels. All simulations were performed with M Cell version 3 (Monte Carlo
Cell) (Stiles et al., 1996; Stiles and Bartol, 2001; Kerr et al., 2008) and were typically run on
a desktop computer running the Linux operating system. MCell allows one to perform
continuous time stochastic simulations of action-potential-triggered Ca2+ channel opening
and subsequent Ca2+ ion flux into the presynaptic nerve terminal through the channel. We
created several simulation models each containing a fixed number of Ca2+ channels (1, 10,
15, 20, 30, and 40 Ca2+ channels, respectively) embedded in a membrane. During each
simulation, Ca2+ channels opened stochastically driven by the action potential and
permeated Ca2+ ions according to the kinetic scheme depicted in Figure 3C consisting of
three closed states, one open state, and voltage-dependent rates between states. The driving
force kflux for Ca2+ through the open channels is shown in the bottom of Figure 3A. Rates
were chosen such that the model reproduced the experimentally known single-channel
conductance (2.6 pS in 2 mM extracellular Ca2+) (Church and Stanley, 1996) and the
experimentally measured whole-cell currents (see Fig. 3B) and Pattillo et al. (2001). For
each model containing a given number of Ca2+ channels and action potential AP1 and AP2,
we ran 10,000 simulations under control and DAP conditions. The resulting Ca2+ currents
were recorded and then used as a proxy for fluorescence in our SPOFA procedure assuming
a linear relationship between Ca2+ influx and resulting fluorescence (as determined
experimentally; see below). In addition, the models containing a single Ca2+ channel were
used to compute the distribution of channel open latencies and open times as shown in
Figure 4.
Results
Spatial resolution of data acquisition
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Adult frog NMJs are characterized by long linear nerve terminals containing numerous
active zones and thus allow simultaneous imaging of multiple clearly defined active zones
subsequent to nerve stimulation (Wachman et al., 2004). Each active zone is ~1 μm long, is
oriented perpendicular to the long axis of the terminal, overlies a postsynaptic junctional
fold containing densely packed nicotinic acetylcholine receptors, and is separated from
adjacent active zones by ~1 μm (shown schematically in Fig. 1A,B, left). Approximately
200–250 intramembraneous particles (denoted active zone proteins in Fig. 1B, left) include
N-type voltage-gated Ca2+ channels, are arrayed in parallel double rows running the length
of the active zone, and are bordered by 25– 40 docked synaptic vesicles. For Ca2+ imaging
(Fig. 1B, right), terminals were loaded with Calcium Green-1 Dextran (3000 molecular
weight, KD ~540 nM), and postsynaptic acetylcholine receptors were labeled with Alexa
Fluor 594-conjugated α-bungarotoxin. Regions of terminals containing well-focused active
zones were identified by receptor fluorescence before initiation of low-frequency nerve
stimulation (0.5 Hz) and acquisition of Ca2+ fluorescence.
To determine the effective optical resolution of our imaging system, we measured its PSF
using sparsely distributed 20 nm fluorescent beads. Figure 1C shows that the results were
well fit by a Gaussian function and that the full width at half-maximum amplitude was 450
nm. This distance, as indicated schematically in Figure 1B (left), is approximately two to
three times larger than the pixel size of our cameras (see Materials and Methods) and
approximately half the length of an active zone. Thus, we concluded that each pixel selected
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for analysis (see below) actually sampled an area approximately equivalent to one-half of an
active zone. To confirm this conclusion with Ca2+-dependent fluorescence imaging from a
dye-loaded frog nerve terminal, we performed cross-correlation analysis of stimulusdependent signals detected by adjacent pixels within active zones. As shown in Figure 1D, a
Lorentzian fit of our results gave a half-width of 410 nm, very close to the value obtained
for the PSF. We therefore reasoned that our high-speed fluorescence acquisition system (1.5
ms delay after stimulation, 1 ms acquisition window; see Materials and Methods) captured
signals primarily limited by the optical PSF and not by spatiotemporal spread of the Ca2+
fluorescence. Together, our PSF and cross-correlation results provide strong evidence that
subsequent findings from variance analysis correspond to a space approximately equivalent
to one-half of an active zone.
Selection of active zone pixels
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We have shown previously that action potential-evoked Ca2+ signals in this preparation are
detected in active zones of nerve terminals and arise exclusively from Ca2+ entry through Ntype Ca2+ channels, with no contribution from Ca2+-induced Ca2+ release (Wachman et al.,
2004). During low-frequency stimulation, large trial-to-trial variability in Ca2+-dependent
fluorescence signals was evident in different active zone regions of the nerve terminal.
Figure 1E shows α-bungarotoxin labeling of postjunctional membrane underlying four to
five active zones, and Figure 1F shows variability in Ca2+-dependent fluorescence images
captured for the same field of view after six different stimuli selected at random from a train
of ~100 (see Materials and Methods).
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Highly variable fluorescence signals can result from detection of a small number (n) of Ca2+
channels that function independently and have a small probability (p) of opening during an
action potential. In principle, binomial fluctuation analysis can provide estimates of n and p
under such conditions, using two independent experimental measurements from which to
calculate the two unknowns. For example, early binomial analysis of quantal
neurotransmitter release (Del Castillo and Katz, 1954) was based on determination of the
failure rate together with the frequencies of single (quantal) and multiple responses. In the
present case, however, failures and quantal responses cannot be determined with certainty
because the signal-to-noise ratio is very low, i.e., the difference between stimulus-dependent
Ca2+ fluorescence and resting background fluorescence is very small. Therefore, a different
approach must be taken and we followed previous reports of optical fluctuation analysis
(Sabatini and Svoboda, 2000), using two ratios of values (fluorescence intensity and the
squared coefficient of variation; see below) measured before and after an experimental
manipulation that specifically increases p. In this way, one then can calculate p and n
without direct determination of the failure rate or the size of a quantal response (see
Materials and Methods).
Over the course of repeated trials, the stimulus-dependent mean fluorescence ( ) (Fig. 2C)
and the variability of fluorescence (e.g., σs) are expected to exceed the corresponding
background levels [ (Fig. 2B) and σb, respectively] for pixels that periodically detect Ca2+
influx through one or more open Ca2+ channels. To apply fluctuation analysis to data
obtained from individual pixels (SPOFA), we first had to identify those pixels that
responded to repeated stimulation with both a statistically significant percentage increase in
mean fluorescence(
) (Fig. 2D) and also an increase in the variance
of fluorescence intensity (
). As expected, increasingly restrictive criteria for
statistical significance reduced the number of pixels selected for analysis. In addition, and
again as one would expect, the remaining pixels were increasingly restricted to regions
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directly over active zones (Figs. 1B, right, 2A,E). In fact, we could predict how the results of
fluctuation analysis would be influenced by the choice of criterion for statistical
significance, particularly with respect to the apparent number (n) of functional Ca2+
channels “seen” by selected pixels. To test our prediction and confirm interpretation of our
results, we repeated our analysis using a wide range of significance levels and characterized
the impact on calculated values of n and p (see subsequent discussion of Table 1 and Fig. 6
below).
To illustrate one highly selective criterion, Figures 1B (right) and 2 show pixel selection
based on a 1 SD method, i.e., for a given pixel to be included in additional analysis, the
mean fluorescence after stimulation had to be at least 1 SD above the average background
fluorescence (SD criterion,
). As shown, pixels selected by the SD criterion
overlie active zone locations identified by postsynaptic acetylcholine receptor staining. As
introduced above, SPOFA also requires the use of coefficient of variation values
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, and Figure 2F shows the distribution obtained from a representative
nerve terminal using pixels that met the SD criterion. In this example, the median value was
0.45, and similar CVs values were obtained from a total of seven nerve terminals (0.44 ±
0.08, mean ± SD; range, 0.32–0.54).
Numerical validation of SPOFA
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We wanted to determine p and n based on observed changes in both mean fluorescence and
the variability of fluorescence subsequent to an experimental manipulation that specifically
increases p. As detailed in Materials and Methods, we treated the terminal with DAP, which
blocks a fraction of voltage-gated potassium channels and thus increases the size and
duration of the action potential. Our calculation of n and p from fluorescence measurements
is based on the assumption that fluctuations in fluorescence are attributable to a binomial
distribution of n channels that open with probability p. However, in reality, other sources of
variability contribute to the stimulus-dependent fluorescence signal. For example, the
amount of Ca2+ flux through an open channel varies because of the distribution of times to
channel opening (opening latencies) as well as the distribution of open durations. Through
both of these effects, the size and timing of single-channel Ca2+ signals (total, or integrated,
single-channelcurrents) may be affected. Furthermore, because the duration of individual
Ca2+ signals may exceed the image acquisition window and may do so by differing
amounts, the fraction of total signal captured before and after DAP treatment may also
change. Thus, to estimate p and n accurately and establish error estimates for their values,
these additional contributions may need to be taken into account.
To assess the possible impact of all these factors on our ability to calculate p and n via
binomial analysis, we used computer simulations to investigate the Ca2+ flux through
individual channels in response to action potentials (NEURON and MCell simulations; see
Materials and Methods). We could then use SPOFA to calculate the values of p and n based
on the simulated fluorescence, compare directly with the known values of p and n chosen for
the simulation, and then determine error estimates to be used with binomial analysis of our
experimental fluorescence measurements.
Figure 3A shows two representative action potentials (AP1 and AP2) under control
conditions and in the presence of DAP generated via the NEURON simulation environment
(Carnevale and Hines, 2006). As shown in Figure 3B, the generated action potentials agree
well with experimental recordings from cultured Xenopus nerve–muscle synapses (Pattillo
et al., 2001). We used these action potentials in MCell simulations (Stiles et al., 1996; Stiles
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and Bartol 2001; Kerr et al., 2008) to drive stochastic voltage-dependent changes in Ca2+
channel conformation, as well as stochastic voltage-dependent Ca2+ ion flux through the
channel while it was in the open state. Figure 3C shows corresponding closed-to-open and
open-to-closed transitions obtained over the course of repeated trials (cases in which the
channel did not open at all are not shown). In the same figure, instances of Ca2+ ion flux
through the open state (single, or rarely, multiple ions) during discrete time intervals are also
indicated, and it is evident that such permeation events were more likely when the driving
force for Ca2+ entry was high. In Figure 3B, we compare computed whole-cell Ca2+ currents
with recordings from cultured Xenopus nerve–muscle synapses (Pattillo et al., 2001). Both
simulated action potential waveforms give rise to currents that match the time course of
experimental data well, particularly AP2.
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To estimate the amount of Ca2+ signal that would be detected experimentally as mean
fluorescence, we chose a 1 ms time window corresponding to our experimental image
acquisition time and then summed all Ca2+ ions that passed through channels before and
during the acquisition window. Because experimentally we do not know precisely where
within the duration of the action potential our 1 ms acquisition window falls, we used two
different modeling scenarios to bracket the behavior of the system. In the first, the
acquisition window starts shortly after action potential onset after the integrated Ca2+
current has reached 5% of its maximum value. We call this early acquisition. In the second,
acquisition starts only after the integrated Ca2+ current has reached 50% of its maximum
value. Here, our 1 ms acquisition window captures most of the total Ca2+ signal entering the
terminal during the action potential. We call this second scenario late acquisition.
Initially, we simulated models containing a single Ca2+ channel. To illustrate the data
obtained over repeated trials, Figure 4 shows histograms of channel opening latencies (Fig.
4A), channel open times (Fig. 4B), and total single-channel Ca2+ ion passage (current
integral, Fig. 4C obtained via late acquisition) obtained during repeated trials for the two
action potential waveforms AP1 and AP2. The mean channel open times under control
conditions (AP1, 0.56 ± 0.3 ms; AP2, 0.65 ± 0.35 ms) and in the presence of DAP (AP1,
0.77 ± 0.34; AP2, 0.91 ± 0.4) are below 1 ms, indicating that our 1 ms acquisition window is
sufficient to capture most of the Ca2+ signal particularly in the late acquisition scenario
(however, see discussion of current distribution below). Figure 4C depicts the Ca2+ current
distributions generated with AP1 and AP2 under control and DAP conditions. Overall, the
current distributions under both conditions are similar. The fact that, in the presence of DAP,
we sample slightly lower maximum current values is attributable to the prolonged action
potential duration and correspondingly lower driving force combined with a fixed 1 ms
acquisition window.
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Our next step in modeling studies was to use multiple Ca2+ channels in each simulation and
to determine the time course of the summed Ca2+ signal for different combinations of action
potential waveform, number of channels, and with or without DAP treatment. For each set
of conditions, we ran thousands of simulations and obtained the average number of
permeant Ca2+ ions as a function of time (data not shown). The resulting Ca2+ currents were
then used to compute values for p and n according to the SPOFA procedure outlined in
Materials and Methods. We used the number of Ca2+ ions summed over a 1 ms acquisition
window as proxy for measured fluorescence. As an example, Table 2 gives values for
summed Ca2+ ions, CV values, RF, RCV, and calculated values of p for a system driven by
action potential AP1 under an early acquisition scenario for simulation systems containing 1,
10, 15, 20, 30, or 40 Ca2+ channels. The computed value of p across all these systems was
fairly consistent with a mean of p of ~0.16, in good agreement with the actual value of p =
0.18 used in the simulations. The last column in Table 2 gives the corresponding values for
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n computed via Equation 11 using the computed average p value. Thus, in this particular
scenario, SPOFA underestimates the true values of n by ~25%.
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Finally, in Table 3, we summarize the relative errors in the computed values of p and n for
models driven by action potential waveforms AP1 and AP2 under both early and late
acquisition scenarios. Based on these results, we can infer that the early acquisition scenario
provides good estimates of p but tends to underestimate n by up to 30%. Conversely, the late
acquisition scenario tends to underestimate the value of p by up to 30% but results in good
estimates of n. Because our experimental acquisition window lies somewhere between these
two extremes, we can thus argue that SPOFA applied to our experimental data provides
reliable estimates of both p and n and will at most underestimate either one by ~30%. These
findings are consistent for both action potential waveforms studied, suggesting that the
predictive power of our SPOFA method is independent of the detailed shape of the
underlying action potential when it is within these ranges.
The probability (p) that Ca2+ channels open during an action potential
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Our use of SPOFA to determine p and n from single-pixel fluorescence measurements was
based on the use of two ratios, for which each component value was measured before and
after an experimental manipulation that specifically increased p. Preparations were treated
with 5 μM DAP for 30 min to block potassium channels selectively and, as a result, broaden
the action potential (Bostock et al., 1981; Thomsen and Wilson, 1983; Augustine, 1990) and
secondarily increase p (Augustine, 1990).
Figure 5, A and B, shows Ca2+ imaging data from a representative nerve terminal before and
after DAP exposure. Using our SD criterion to select pixels, we calculated per pixel values
of ΔFs and CVs under both conditions, and Figure 5, C and D, shows the corresponding
frequency distributions. Although DAP exposure strongly increased ΔFDs, it simultaneously
decreased CVDs compared with control, and both of these effects are consistent with an
increase in p according to standard binomial theory. In brief, if n Ca2+ channels are detected
by a pixel and open independently with an average probability p during an action potential,
the expected number of open channels per trial will follow a binomial distribution. The
mean of a binomial distribution μ is given simply by np, and so an increase in p will clearly
increase μ, or, in our case, the mean value of ΔFs. The binomial variance σ2 and coefficient
, respectively. From the latter, an increase
of variation CV are given by (1 − p)np and
in p will decrease CV, or CVs in our experiments.
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To estimate p, we used the ratio of ΔFs and ΔFDs, together with the ratio of
and
,
measured before and after DAP treatment. These calculations allow us to obtain values for p
both before (control) and after the DAP treatment (see Eqs. 14 and 15 in Materials and
Methods). Figure 5E shows the distribution of control values obtained from the data shown
previously for a representative nerve terminal in Figure 5A–D. Because the distribution was
not Gaussian, we used the median value (0.22) as our estimate of the mean opening
probability (p) for Ca2+ channels in this nerve terminal. After DAP treatment, the estimated
mean opening probability increased to 0.72. Similar results were obtained from four nerve
terminals for which we pooled all the single-pixel data and generated a frequency histogram
for p under control conditions (Fig. 5F). The median value was 0.24 for the pooled data.
Taking into account our numerically derived error estimates (see above, Numerical
validation of SPOFA), we can derive a lower limit of 0.23 and an upper limit of 0.37 for p
with the actual value likely to be somewhere between.
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The number (n) of Ca2+ channels in active zones
We based our initial estimates of n on pixel data obtained from the four nerve terminals used
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in the DAP studies out-lined above. For each terminal, the median p and
values were
used to calculate a value of n (see Eq. 16 in Materials and Methods; pixel selection was
performed using the SD criterion). Using this approach, we found that n ranged from 14 to
24 across the four terminals, with a mean ± SD value of 18.3 ± 4.8. When values of n were
calculated individually for each pixel and then averaged together, the results were not
significantly different.
In addition, we analyzed the seven nerve terminals not treated with DAP discussed
previously (see above, Selection of active zone pixels). Because these terminals were not
exposed to DAP, we did not have an independent estimate of p. Instead, we used the median
value (p = 0.24) determined from the DAP experiments on the initial four terminals. Using
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this value for p, together with the median
value for each untreated terminal, we
calculated values of n, which ranged from 11 to 31, with a mean ± SD value of 18.0 ± 7.5.
This average was not significantly different from the result obtained with the DAP-treated
terminals (unpaired Student’s t test, p = 0.9). Thus, we pooled the data from all 11 nerve
terminals to obtain a final estimate of n, 18.1 ± 6.4 (mean ± SD). From our previous
characterization of the PSF and pixel correlation analysis (Fig. 1), we estimated that single
pixels sample spatial regions approximately equivalent to one-half of an active zone. Thus,
our data indicate that each active zone has ~2n, or only ~36 Ca2+ channels that are capable
of opening in response to an action potential (functional channels). Taking into account our
numerically derived error estimates (see above, Numerical validation of SPOFA), we can
compute a lower limit of 34 and an upper limit of 53 for the number of Ca2+channels, with
the actual value likely falling somewhere between. Presumably, these functional channels
are distributed among the 200–250 intramembraneous particles described in freeze-fracture
replicas.
The impact of pixel selection on estimates of p and n
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Given that we used up to 100 nerve stimuli during image acquisition and also that individual
pixels sampled an area of approximately half an active zone, we had two primary
expectations regarding the selection of pixels for analysis. First, notwithstanding the low
signal-to-noise ratio, a relatively low level of statistical significance should be able to
differentiate between pixels that overlie the nerve terminal as opposed to the surrounding
tissue. Second, as the criterion for statistical significance became more restrictive and fewer
pixels were selected, those remaining should be completely restricted to the nerve terminal,
and, in addition, should be increasingly restricted to positions centered over active zones
(and therefore over functional Ca2+ channels). We then reasoned that values calculated for n
should be smaller with less restrictive selection criteria, because an increasing fraction of
pixels would “see” an area on the periphery of an active zone and therefore would detect a
fluorescence signal originating from fewer channels. Conversely, values calculated for p
should remain fairly constant over a wide range of selection criteria, assuming that
functional channels have identical gating characteristics regardless of their location in the
active zone, or that any possible heterogeneity of gating function occurs over a spatial scale
much smaller than the resolution of our optical system.
Figure 6 and Table 1 summarize the results that verify our predictions for the impact of pixel
selection on estimates of p and n. Whereas the data shown in Figure 6 are based on a single
terminal treated with DAP, Table 1 includes final average values of p and n calculated from
multiple DAP-treated terminals (additional analysis of the data presented previously in Fig.
5). Figure 6A (top) shows that a significance criterion as permissive as p < 10−2 (Student’s t
test) selected an appreciable number of pixels that lay beyond the borders of the nerve
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terminal itself (compare position of red and white dots to fluorescence image of postsynaptic
bungarotoxin stain in Fig. 6D). Values of CVs and p were widely scattered (Fig. 6B,C, top),
although clustering was still apparent and indicated a midrange value for p of ~0.2. When
more restrictive criteria were used to determine significance (p < 10−3, 10−6, or 10−9, or
using our SD criterion instead), the number of pixels selected for analysis decreased (Fig.
6E), the pixels were increasingly restricted to the nerve terminal and active zones (Fig. 6A,
top to bottom), and clustering of CVs and p values became evident (Fig. 6C, top to bottom).
The number of selected pixels converged toward an apparent minimum obtained with either
p < 10−9 (Student’s t test) or our SD criterion (Fig. 6E; recall that the SD criterion was
highly restrictive because inclusion of a pixel required that its average fluorescence was
greater than the average background value by more than 1 SD). Figure 6, A and E, also
shows how pixels were subdivided into those that had increased (white) or decreased (red)
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variance compared with background variance levels ( vs ), despite the prerequisite
increase in average fluorescence. Although the presence of pixels with decreased variance at
first may seem counterintuitive, in fact it is expected because of the very small absolute size
of the stimulus-dependent fluorescence signal (ΔFs of only several percent) (Figs. 1, 2, 5).
Unlike a system at the opposite extreme, in which there is a clearly discernible quantal
response, here, because of the low open probability p and correspondingly small increase in
fluorescence, one expects only a small excess of pixels with increased variance, whereas the
remainder may show decreased variance simply by random chance. An examination of the
total number of pixels with increased (white squares) and decreased (red squares) variance
shown in Figure 6E reveals that this was the case for our data, and careful inspection also
shows a minor trend toward a higher fraction of pixels with increased variance as the
criterion for selection became more restrictive. Limiting our analysis to selected pixels with
increased variance, we found, as predicted, that average values obtained for p were virtually
indistinguishable regardless of the pixel selection criterion (Table 1). Table 1 also shows
that, as predicted, average values obtained for n increased as the criterion for pixel selection
became more restrictive, until nearly identical results were obtained with the two most
selective criteria.
Control measurements
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Our SPOFA depends on a linear relationship between ΔFs and Δ[Ca2+]. To confirm the
linearity of our measurements, we varied extracellular Ca2+ and measured the resulting
change in fluorescence. After doubling extracellular Ca2+ concentration (from 1.8 to 3.6
mM, enhancing Ca2+ influx per open channel), the Ca2+ signal detected within active zone
regions of the nerve terminal increased by 102 ± 2% (n = 4 terminals). In contrast, the CVs
value obtained with high extracellular Ca2+ was not significantly different from that
obtained with normal extracellular Ca2+ (p > 0.05, one-way ANOVA with Tukey’s post hoc
test) (Fig. 6A). This doubling in Ca2+ signal, coupled with an unchanged CVs, supports the
conclusion that the reduced CVs obtained after DAP exposure was indeed caused by an
increase in p and not by a potential saturation of measured fluorescence. Based on this
analysis, we can also conclude that the concentration of extracellular Ca2+ (and thus the
magnitude of Ca2+ influx through open channels) does not alter our quantitative analysis of
variability in presynaptic fluorescence signals. Therefore, this experiment serves as a control
for the validity of our fluctuation analysis.
A lack of significant dye saturation during low-frequency stimulation might be expected
given the ordered geometry of adult frog NMJ active zones (long, linear arrays of
presynaptic Ca2+ channels distributed spatially at some distance from one another) (Fig. 1),
combined with the prediction that there are few Ca2+ channel openings within each active
zone during a single action potential (Wachman et al., 2004; this study). The absence of
significant dye saturation under similar imaging conditions at this synapse was also reported
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by Shahrezaei et al. (2006). The linearity of fluorescence and Ca2+ signal in our experiments
is fortuitous, and both fluorescence detection and calcium-sensitive dye interactions with
calcium ions are expected to saturate outside our experimental conditions.
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Finally, to further validate our fluctuation analysis, we also examined the effects of exposure
to a submaximal concentration of ω-conotoxin GVIA (CgTX) (100 nM). This treatment is
known to completely and irreversibly block (over the course of our experiments) a subset of
N-type Ca2+ channels without affecting the probability of opening for channels that remain
unblocked (Kerr and Yoshikami, 1984; Stocker et al., 1997). Exposure to 100 nM CgTX
blocked total action-potential-evoked Ca2+ entry in the nerve terminal by 70 ± 5.9% (mean
± SD, 5 nerve terminals). As a result, the stimulus-dependent fluorescence signals were very
weak, and we had to use a less restrictive pixel selection criterion to be able to select a
sufficient number of pixels for analysis. Using a Student’s t test to select active zone pixels
(p < 0.01) (Fig. 7, Table 4), the average CVs after CgTX treatment increased significantly
above control to a value of 0.67 ± 0.11 (one-way ANOVA with Tukey’s post hoc test, p <
0.05; mean ± SD, 5 nerve terminals). Using the estimated p (0.24) determined above (CgTX
does not affect the gating properties of unblocked channels) and the CVs from CgTX-treated
nerve terminals, the average n (n = 7.5 ± 2.1) was significantly decreased compared with
control (one-way ANOVA with Tukey’s post hoc test, p < 0.05). The difference in
magnitude of CgTX-mediated reduction of total Ca2+ indicator fluorescence (~70%) and the
reduction in calculated Ca2+ channel number (~33%) is attributable to the following. When
measuring total Ca2+ indicator fluorescence, we observe the change in the total stimulusdependent fluorescence within the entire nerve terminal area. This includes some active zone
regions of the nerve terminal in which all Ca2+ channels were completely blocked by the
CgTX treatment and others in which some Ca2+ channels remained unblocked after
exposure to CgTX. In contrast, our SPOFA analysis can only consider pixels in which some
signal remains after CgTX treatment. Under these conditions, the SPOFA analysis
underestimates the reduction in n that occurs because there are some pixels that sample
active zone regions of the nerve terminal in which n drops to zero after CgTX treatment, and
these are not included in the SPOFA analysis. Regardless of this quantitative difference, a
decrease in n is consistent with the expected effects of CgTX. Therefore, our method of
variance analysis is sensitive to treatments known to alter either p (DAP) or n (CgTX),
because the measured CVs values vary as expected (Fig. 7).
Discussion
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In this study, we have combined variance analysis with high-resolution Ca2+ imaging
techniques and Monte Carlo simulations to estimate the number and probability of opening
of Ca2+ channels within presynaptic active zones. Our results predict that a single active
zone at the frog NMJ contains a relatively small number of Ca2+ channels, each with low
probability of opening during an action potential.
The opening probability of active zone Ca2+ channels during action potential stimulation
The probability that presynaptic Ca2+ channels open in response to a single action potential
is primarily determined by the activation kinetics of Ca2+ channels and the shape of the
action potential. This is distinct from the probability that a channel opens in response to a
prolonged voltage step (Po), which typically is calculated as the steady-state fraction of time
that the channel is in the open state. Here we are interested in the likelihood that a Ca2+
channel will open during a brief action potential depolarization. Indeed, by broadening the
action potential with DAP, we have shown that the opening probability of presynaptic Ca2+
channels increase significantly. In a limited number of cases, it has been possible to estimate
the opening probability of presynaptic Ca2+ channels from patch-clamp recordings of Ca2+
current. At the squid giant synapse (Augustine, 1990), the chick ciliary ganglion calyx
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(Bertram et al., 1996), and cultured Xenopus neuromuscular varicosities (Poage and
Meriney, 2002), it has been estimated that opening probability is relatively small (0.1– 0.3).
In contrast, evidence from the rat calyx of Held (Borst and Sakmann, 1998), hippocampal
mossy fiber boutons (Bischofberger et al., 2002), and cerebellar granule cell synapses onto
Purkinje neurons (Sabatini and Regehr, 1997) indicate that action potentials activate a large
fraction of available Ca2+ current (0.7–0.9). Thus, it is likely that the proportion of
presynaptic Ca2+ channels that open with action potential stimulation may be variable
between synaptic preparations. Furthermore, Ca2+ channels have characteristic gating
kinetics that depend on Ca2+ channel type, splice variant, and auxiliary subunits (Jones and
Marks, 1989; Lin et al., 1997, 1999). In fact, striking differences in the rate of activation
(~15-fold) have been observed when comparing isoforms of the α N-type Ca2+ 1B channel
derived from rat brain (Stea et al., 1999). Therefore, Ca2+ entry during an action potential
can vary widely when examined across synapses and model preparations, even within the
same family of Ca2+ channels. Despite these differences between synaptic preparations, our
data are consistent with previous work at the frog neuromuscular junction that support the
conclusion that the probability of Ca2+ channel opening during an action potential is very
low. Using SPOFA, we were able to calculate the opening probability p in our experimental
preparation to be 0.24, in agreement with previous estimates (Wachman et al., 2004).
Furthermore, based on error estimates taken from extensive computer simulations, we show
that the opening probability p in our sample is likely somewhere in the range of 0.23–0.37.
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Our analysis approach assumes that all Ca2+ channels we sampled have the same probability
of opening during an action potential. Thus, our calculation of the probability of opening
during an action potential represents an average of the actual values for individual Ca2+
channels. It would be interesting to know how much variability in p exists among individual
active zone Ca2+ channels. Furthermore, it is likely that the probability of Ca2+ channel
opening during an action potential can be modulated under different conditions (i.e., disease,
altered synaptic activity, or pharmacologic treatment). In particular, this characteristic may
be one that is modulated under conditions that trigger presynaptic mechanisms for
transmitter release homeostasis (Wang et al., 2004; Frank et al., 2009).
The number of Ca+ channels within single active zones of the motor nerve terminal
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Despite previous work presenting evidence that the ~200–250 active zone
intramembraneous particles observed in freeze-fracture active zone replicas include the
voltage-gated Ca2+ channels that trigger vesicle release (Pumplin et al., 1981; Robitaille et
al., 1990; Cohen et al., 1991) as well as Ca2+-activated potassium channels (Robitaille et al.,
1993), it remains unknown how many of these active zone intramembraneous particles
actually represent presynaptic Ca2+ channels. Furthermore, the stoichiometric relationship
between presynaptic Ca2+ channels and the docked synaptic vesicles that line both sides of
the active zone is unknown. In our experiments, an average of ~18 Ca2+ channels was
reported by individual imaging pixels positioned over active zone regions of the nerve
terminal. When we extended this single-pixel estimate to the number that would be expected
to be present in an entire active zone (based on the optical resolution of the system) (Fig. 1),
we estimate that each active zone has only ~36 voltage-gated Ca2+ channels along its entire
length. Because we used the measured variance of fluorescence signal to calculate the
number of Ca2+ channels in the active zone, other sources of variance (i.e., fluctuating Ca2+
flux through single channels) can influence this estimate. Based on error estimates for our
SPOFA procedure obtained by extensive Monte Carlo simulations (see Results and Table 3),
we predict that the number of voltage-gated Ca2+ channels per active zone is somewhere in
the range of 34–53.
Therefore, our results suggest that the number of active Ca2+ channels in an entire active
zone constitutes only a small proportion (~20%) of total intramembraneous particles (200–
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250) observed in freeze-fracture replicas. Because there are ~25–40 docked synaptic vesicles
per active zone, our data raise the interesting possibility that each docked synaptic vesicle is
tightly associated with only one voltage-gated Ca2+ channel (Fig. 8). Although this idea is
consistent with the highly ordered Ca2+-regulated release machinery at the active zone
(Harlow et al., 2001), we are unable to exclude the possibility of a heterogeneous
distribution of Ca2+ channels along the active zone.
Of course, our analysis only estimates the number of functional presynaptic Ca2+ channels
present in the active zone. There may be additional Ca2+ channels present that are “silent” as
a result of some form of modulation such that they do not open during our experiments. A
“silencing” of ion channels has been observed for potassium channels as a result of
sumoylation (Rajan et al., 2005; Wilson and Rosas-Acosta, 2005), and something similar
could occur with synaptic Ca2+ channels using any of a variety of potential mechanisms
(Pun et al., 1986; Lipscombe et al., 1989; Faber et al., 1991; Voronin and Cherubini, 2004;
Toselli et al., 2005). Variability in the number of active Ca2+ channels in an active zone then
could be explained by some mechanism that underlies a “silent” to “functional”
interconversion. Under this scenario, it is possible that some of the particles identified in
freeze-fracture replicas of the frog neuromuscular junction may be silent Ca2+ channels.
The Ca2+ channel–vesicle release relationship
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The question of how many Ca2+ channels must open to trigger a single release event is
particularly intriguing and contributes to our understanding of how Ca2+ regulates synaptic
vesicle fusion in the nerve terminal. Historically, at some synapses, it has been proposed that
many Ca2+ channels normally open to provide the Ca2+ trigger for vesicle fusion (Wheeler
et al., 1994; Mintz et al., 1995; Borst and Sakmann, 1996; Wu et al., 1999), whereas at
others it appears that one or only a few Ca2+ channels open to trigger each vesicle fusion
event (Yoshikami et al., 1989; Augustine et al., 1991; Stanley, 1993; Brandt et al., 2005;
Gentile and Stanley, 2005; Shahrezaei et al., 2006; Bucurenciu et al., 2010). Within
individual active zones of the frog motor nerve terminal, our experimental data lead us to
predict that an average of approximately nine Ca2+ channels open after an action potential
(in which the range might be 8–18 based on Monte Carlo simulations of predicted error),
whereas vesicles are released with a probability of only ~0.5. Therefore, there appears to be
a relatively low probability that these Ca2+ channel openings trigger vesicle fusion. One
possible explanation is that each vesicle release event requires the summed Ca2+ flux
through many open Ca2+ channels. However, previous studies at this synapse have
suggested that Ca2+ flux through only one to two Ca2+ channels normally trigger transmitter
release (Yoshikami et al., 1989; Shahrezaei et al., 2006). If only a few Ca2+ channel
openings are required to trigger vesicle fusion, it is possible that these openings need to
occur in close proximity to one another in the active zone to be effective at evoking
transmitter release. The probability that two channel openings would occur in close
proximity is low, which could therefore limit the occurrence of vesicle fusion from each
active zone. Alternatively, each vesicle fusion event might be controlled predominately by
one tightly associated Ca2+ channel positioned nearby but that Ca2+ flux through these
single open channels might only trigger vesicle fusion with a low probability (5–10%). In
this case, the release probability within individual active zones would be determined by both
the number of open Ca2+ channels and the probability that a single open Ca2+ channel
triggers vesicle fusion.
Acknowledgments
This work was supported by National Institutes of Health Grant R01 NS043396 (S.D.M.), R01 GM068630, P41
RR06009, and P20 GM065805 (J.R.S.), and F32 GM08347301 (M.D.) and National Science Foundation Research
Grant 0844604 (S.D.M.). We thank Greg Hood for writing the image alignment routine, Robert Poage for
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assistance with some early experiments, and Soyoun Cho and Kate Cosgrove for their comments on previous
versions of this manuscript.
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Figure 1.
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Pixel and optical resolution for calcium imaging in the adult frog neuro muscular junction.
A, Diagram of the adult frog neuromuscular junction. B, Magnified active zones (boxed
region in A) with highly organized active zone proteins, which include voltage-gated Ca2+
channels, and docked synaptic vesicles. The estimated relationship between active zone
dimensions, pixel size, and optical resolution are also shown (left). For comparison, a
composite image that includes fluorescent staining of postsynaptic acetylcholine receptors
(background, grayscale) overlaid with Ca2+-evoked fluorescent signals after nerve
stimulation (foreground, false color) is shown on the right. Scale bar, 1μm. C,
Experimentally measured point spread function of the optical system from a fluorescent
bead with diameter of 0.02μm. The Gaussian fit (red) has a width at half-amplitude of
0.45μm. We thus estimated that approximately half the length of a single active zone can be
resolved optically. D, Correlation coefficient of neighboring pixels that detected AP-evoked
fluorescence signals after repeated low-frequency nerve stimulus tightly depends on the
distance between pixels. The Lorentzian fit (red) has a width at half-amplitude of 0.41 μ m
(points represent mean ± SD; n = 4361 pixels). These data are fit best with a Lorentzian
function, rather than a Gaussian, likely because of the presence of some signal contributing
from neighboring sites, especially at the tails of the distribution. E, Predicted active zone
regions of a representative frog motor nerve terminal identified by labeling the postsynaptic
acetylcholine receptor clusters with Alexa Fluor 594–α-bungarotoxin.F, Representative
difference images showed a large trial-to-trial variability in the spatial distribution of Ca2+
entry evoked by single APs. Scale bar, 2μm (applies to E, F).
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Figure 2.
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Method used to define active zone regions of the nerve terminal within which action
potential-evoked Ca2+ influx is restricted. A, Acetylcholine receptor distribution determined
using Alexa Fluor 594-conjugated α-bungarotoxin. B, Resting fluorescence image of a frog
motor nerve terminal averaged over 100 trials. C, Fluorescence image of the nerve terminal
after a single AP stimulation averaged over 100 trials. D, Average (100 trials) Ca2+ influx
with in active zone regions of the nerve terminal evoked by a single AP. The pattern of Ca2+
influx averaged over 100 stimulus trials decorates nerve terminals with fluorescence signals
that can visually identify active zone regions. E, Masking the active zone regions with the
criterion that pixels have a mean stimulated fluorescence intensity exceeding 1 SD above
resting fluorescence (SD criterion). Scale bar, 5μm. F, Histogram distribution of CVs over
100 stimulus trials for all pixels selected by the criterion shown in E.
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Figure 3.
Simulated action potentials and computational model of action-potential-triggered Ca2+
influx. A, Simulation program NEURON generated action potentials AP1 and AP2 under
control conditions and in the presence of DAP. The bottom panels show the Ca2+flux kflux
through the open Ca2+ channels proportional to the driving force Vm − ECa. B, Comparison
of AP 1 (blue) and AP 2 (red) with an experimentally recorded action potential from
cultured Xenopus nerve–muscle synapses (black) (Pattillo etal., 2001) and the corresponding
whole-cell Ca2+ currents simulated (blue and red) and recorded from a presynaptic cultured
neuromuscular junction varicosity (black) (Pattillo et al., 2001). C, The top depicts a
schematic diagram of our kinetic Ca2+ channel model with three closed and one open state.
The open state conducts Ca2+ ions according to the driving force given by kflux (see also A).
Below, we show plots of the channel open duration for five representative simulations. In
addition, the first plot gives the number of Ca2+ ions conducted per unit time interval.
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Figure 4.
Properties of M Cell Ca2+ channel model. Shown are distributions of channel open latencies
(A), channel open times (B), and Ca2+ current integrals (C) for AP1 and AP2 under both
control and DAP conditions using the late acquisition scenario (see Results). The “dimples”
observed in the DAP plots for C are an artifact of our 1 ms acquisition window and the
decrease in driving force for DAP-modified APs that depolarize to potentials closer to the
modeled calcium channel equilibrium potential, followed by a slightly later return to a
strong driving force as the AP repolarizes.
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Figure 5.
Opening probability of Ca2+ channels during an action potential. A, Averaged AP-evoked
Ca2+ influx under control condition (90 trials). B, Averaged AP-evoked Ca2+ influx after 5
μM 3,4-diaminopyridine treatment (90 trials). Scale bar, 5 μm. C, Histogram distribution of
the fluorescence intensity reported by individual pixels before (blue) and after (red)
exposure to DAP. D, Histogram distribution of the stimulus-dependent coefficient of
variation of individual pixels before (blue) and after (red) DAP exposure. E, Histogram
distribution plotting opening probability of Ca2+ channels during an action potential
calculated from individual pixels for the example control terminal shown in A. F, Histogram
distribution plotting the average opening probability of Ca2+ channels during an action
potential calculated from individual pixels pooled from a total of four control nerve
terminals.
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Figure 6.
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Varying the criterion for pixel selection does not bia sour estimate for the probability that
Ca2+ channels open during an action potential. A, Mask for the pixels selected after using
different criteria, i.e., SD criterion, or a Student’st test using different significance levels (p
< 10−2, 10−3, 10−6, or 10−9). All pixels selected are shown in either red or white; only the
pixels shown in white could be used to derive a meaningful p value (i.e., 0< p < 1). B,
Histogram distribution of opening probability calculated from the selected pixels under each
criterion. C, In each graph, CVs is plotted against opening probability to reveal subsets of
the data that are selected under each criterion. Comparing B and C demonstrates that the
distribution of opening probability of Ca2+ channels during an AP is not changed as more
restrictive criteria eliminate a subset of the data. D, Predicted active zone regions of the
example nerve terminal identified by labeling the postsynaptic acetylcholine receptor
clusters with Alexa Fluor 594–α-bungarotoxin. Scale bar, 5 μm (also applies to the images
in A). E, Plot of the total number of pixels selected by each criterion (yellow) and the
corresponding subset of these pixels that either do (white) or do not (red) resolve a
meaningful p value (i.e., 0 < p < 1).
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Figure 7.
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Effects of CgTX on CVs measured using a variety of pixel selection criteria and the
summary data for measured CVs values and calculated n values under different treatment
conditions. A, Distribution of CVs values (left) and mask for the pixels selected after using
different criteria (right), i.e., SD criterion, or a Student’s t test using different significance
levels (p < 10−2, 10−3, or 10−6) from a representative nerve terminal under control
conditions. The gray scale image at the bottom represents the predicted active zone regions
of the nerve terminal identified by labeling the postsynaptic acetylcholine receptor clusters
with Alexa Fluor 594–α-bungaro toxin. B, Distribution of CVs values (left) and mask for the
selected pixels from the same nerve terminal a sisA after treatment with 100nM Cg TX for
30min. C, Summary plot of the calculated CVs values (mean ± SEM) for pixels sampling
active zone regions of control nerve terminals (ctrl), those exposed to 100 nM CgTX, 5μM
DAP, or elevated extracellular Ca2+ (3.6 mM; high Ca2+) when using either the SD criterion
(gray bars) or a Student’s t test (p < 0.01; white bars). D, Summary plot of the calculated
number of Ca2+ channels (n) sampled by active zone pixels (mean ± SEM) under control
conditions (ctrl), after exposure to 100 nM CgTX, and after increasing extracellular Ca2+ to
3.6 mM (high Ca2+) when using either the SD criterion (gray bars) or a Student’s t test (p <
0.01; white bars). *p < 0.05, significantly different from control, one-way ANOVA with
Tukey’s post hoc test.
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Figure 8.
Conceptual model of a single active zone showing graphically the stoichiometric and
functional relationship between Ca2+ channels and docked synaptic vesicles. Replica from a
freeze-fractured frog neuromuscular junction (adapted from Heuser and Reese, 1981)
showing a linear array of intramembraneous active zone particles. Superimposed on this
image is a graphic representation of the hypothesized number and position of associated
synaptic vesicles (white circles), voltage-gated Ca2+ channels (black circles), and the
number of these voltage-gated Ca2+ channels that are predicted to open after stimulation by
a single action potential (filled black circles).
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Table 1
The impact of pixel selection on average values of p and n
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Pixel selection criteria
p
n
p < 10−2
0.26 ± 0.11
12.1 ± 2.8
p < 10−3
0.26 ± 0.11
14.1 ± 3.0
p<
10−6
0.25 ± 0.10
17.7 ± 4.2
p<
10−9*
0.24 ± 0.10
18.4 ± 1.2
0.24 ± 0.11
18.3 ± 4.8
SD criterion
Pixels were selected for analysis based on a Student’s t test (p values) or our SD criterion (see Materials and Methods). Values shown are mean ±
SD for four or three (asterisk) nerve terminals, and the values for p correspond to the control (pre-DAP treatment) condition.
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Table 2
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n
Ca2+ count
control
Ca2+ count
DAP
RF
CV2
CV2DAP
R CV 2
p
n
1
44
144
0.306
6.96
1.25
5.57
0.15
0.74
10
443
1407
0.315
0.72
0.13
5.56
0.17
7.18
15
660
2122
0.311
0.49
0.09
5.69
0.16
10.59
20
889
2821
0.315
0.35
0.06
5.58
0.17
14.56
30
1339
4248
0.315
0.24
0.04
5.47
0.16
21.88
40
1770
5676
0.312
0.18
0.03
5.74
0.17
28.37
Avg.
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Statistical properties of computational calcium channel model
0.16
Shown are data from a model driven by a NEURON-generated AP (AP1) (Fig.3) and ours to chastically gated channel model shown in Figure 3. The actual open probabilities in the model are p = 0.18 and
pDAP = 0.63 for control and after DAP treatment, respectively. The data were acquired with a 1 ms sampling window, and data collection started after the current integral reached 5% of its maximum value
(early acquisition; see Results).
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Table 3
Average relative errors for calculated values of p and n with respect to the known values
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Average relative
error in p
Average relative
error in n
AP1 (early acquisition)
−0.091
−0.278
AP1 (late acquisition)
−0.343
−0.019
AP2 (early acquisition)
0.032
−0.326
AP2 (late acquisition)
−0.351
0.068
Simulation type
Each row corresponds to a simulation using one of the two action potential wave forms. Positive and negative values for relative errors signify over
and underestimates obtained via optical fluctuation analysis, respectively.
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Table 4
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Pixel selection criteria and their impact on our estimates of CVs and n in CgTX-treated nerve terminals
Pixel selection criteria
CVs
n
Student’s t test, p < 10−2
0.67 ± 0.11
7.5 ± 2.1
Student’s t test, p <
10−3
0.58 ± 0.09
10.0 ± 2.8
Student’s t test, p <
10−6
0.48 ± 0.11
15.9 ± 8.1
0.51 ± 0.05
12.6 ± 2.6
SD criterion
Figure 7B displays the impact of these selection criteria on the number of pixels selected for analysis in a representative nerve terminal (values
represent mean ± SD; n = 5 terminals).
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