A Monte Carlo analysis has been made of calcium dynamics
in submembranous domains of active zones in which the calcium
contributed by the opening of many channels is pooled. The kinetics of
calcium ions in these domains has been determined using simulations for channels arranged in different geometries, according to the active zone
under consideration: rectangular grids for varicosities and boutons and
lines for motor-nerve terminals. The effects of endogenous fixed and
mobile buffers on the two-dimensional distribution of free calcium ions
at these active zones are then given, together with the extent to which
these are perturbed and can be detected with different affinity calcium
indicators when the calcium channels open stochastically under an
action potential. A Monte Carlo analysis of how the dynamics of calcium
ions in the submembranous domains determines the probability of
exocytosis from docked vesicles is also presented. The spatial
distribution of exocytosis from rectangular arrays of secretory units
is such that exocytosis is largely excluded from the edges of the
array, due to the effects of endogenous buffers. There is a steeper
than linear increase in quantal release with an increase in the number
of secretory units in the array, indicating that there is not just a
local interaction between secretory units. Conditioning action
potentials promote an increase in quantal release by a subsequent
action potential primarily by depleting the fixed and mobile buffers in
the center of the array. In the case of two parallel lines of secretory
units exocytosis is random, and diffusion, together with the endogenous
calcium buffers, ensures that the secretory units only interact over
relatively short distances. As a consequence of this and in contrast to
the case of the rectangular array, there is a linear relationship
between the extent of quantal secretion from these zones and their
length, for lengths greater than a critical value. This Monte Carlo
analysis successfully predicts the relationship between the size and
geometry of active zones and the probability of quantal secretion at
these, the existence of quantal versus multiquantal release at
different active zones, and the origins of the F1 phase of facilitation
in synapses possessing different active zone geometries.
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INTRODUCTION |
There is considerable evidence to suggest that
secretory units may be the units of quantal secretion at some terminals
but not at others (see the accompanying paper, Bennett et al., 2000
). For example, quantal secretion from the calyx terminal of the rat
medial nucleus is attenuated by introduction of the relatively slow
buffer ethylene glucol-bis(
-aminoethyl
ether)-N,N,N',N'-tetraacetic acid (EGTA), which is only
slightly less efficient than
1,2-bis(2-aminophenoxy)ethane-N,N,N,N-tetraacetic acid
acetoxymethyl ester (BAPTA) in reducing secretion (Borst and Sakmann,
1996). This observation suggests that it is the slower accumulation of
calcium from many channels in the vicinity of the calcium sensor,
rather than just a strategically placed channel within the secretory
unit, that is responsible for triggering secretion. The contribution of
calcium from many channels at the presynaptic membrane forms a
"submembranous calcium domain" that extends over the region of
calcium entry into the terminal (Klingauf and Neher, 1997). In contrast
to the microdomain, in which the calcium dynamics is dominated by
diffusion rather than buffering, the opposite is the case in the
submembranous domain. Furthermore, the calcium concentration in this
domain is, in addition to the endogenous buffers, determined by the
spatial layout of the calcium channels in the domain, that is, in the
arrangement of channels in the active zone of the nerve terminal. The
two most distinct geometries of active zones are those found on the one
hand in the amphibian motor nerve terminal, in which the docked
vesicles and channels occur on a line (Heuser and Reese, 1973;
Robitaille et al., 1990), and on the other hand in boutons in which
they appear to be arranged in a regular two-dimensional array
(Pfenninger et al., 1972). A Monte Carlo analysis has therefore been
carried out on the dynamics of calcium movement in submembranous
domains associated with active zones possessing either of these two
geometries, in the presence of both mobile and fixed endogenous buffers
and either low- or high-affinity indicators, when calcium channels open
under an action potential. Consideration is also given as to how this
calcium interacts stochastically with the different spatial
distributions of docked vesicles that are found in the active zones of
varicosities, boutons, and motor-nerve terminals. This further Monte
Carlo analysis then provides estimates of the probabilities of quantal
release at these synapses.
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METHODS |
The application of the Monte Carlo simulation method to the
influx, diffusion, and binding of calcium in a terminal for the case
where only one calcium channel opens has been given in detail in the
accompanying paper (Bennett et al., 2000, hereafter referred to as I.)
The extension required here is to the case where multiple calcium
channels can open under an action potential.
The way in which a single channel opens under a Hodgkin-Huxley action
potential was investigated in detail in Bennett et al. (1997). There,
the opening and closing times, topen and
tclose, were modeled as nonhomogeneous Poisson
processes with rate parameters that depended on the action potential,
and hence were functions of time. The single-channel calcium current,
ic(t), was also expressed as a
function of the potential. All parameter values were based on the
N-channel data of Delcour et al. (1993). The problem is how to
incorporate multiple channels into the Monte Carlo scheme. To include
the full details would make the simulation extremely complicated and
time-consuming: each channel would open and close stochastically and
the currents through the open channels would have to be continuously
varied during the course of the action potential. However, to assume
all channels open synchronously and admit constant current would be a
serious distortion of the true situation. A compromise is to divide the
time of the action potential into subintervals of length
t, to estimate the proportion of channels that are open
in each subinterval, and to assume the single-channel current has a
constant value through a subinterval. The proportion of channels open
in a given subinterval can be estimated from simulations using the
continuous theory as given in Bennett et al. (1997). In addition, the
total charge q through a typical channel in a given
subinterval [nt, (n + 1)t] can be found from
simulations using the formula
|
(1)
|
where ic(t) is the single
channel current and g(t) is 1 if the channel is open and 0 otherwise; from this one calculates the average current per channel in
the subinterval [nt, (n + 1)t] as
q/t. The results of this calculation, using
t = 0.5 ms, are given in Table
1; the parameters used in the simulations are the same as in Bennett et al. (1997), except that the
single-channel calcium current ic(t)
has been reduced to half the value given there (see the discussion of
parameter values in Paper I). Also shown in Table 1 are the actual
number of open channels assumed if a total array of 64 channels is
used. Another approximation made in the use of this scheme is that the
channels open in any subinterval are chosen at random from the total
array of channels; that is, no attempt is made to track the opening
behavior of individual channels across subintervals. The effect of this
is to give fewer long openings than actually occur under an action
potential. To estimate the error caused by this approximation, a number
of runs were also done where it was assumed that if a channel is open in a given interval t, it has double the normal
probability of being open in the next interval (with, however, still
the same total number of channels open in a given interval). This
caused only a small increase in the number of exocytotic events
occurring, and it is concluded that this approximation is in keeping
with the general level of approximation made elsewhere.
The parameter values for the kinetics of quantal secretion are the same
as those given in Table 1 of Paper I (Bennett et al., 2000). The
attachment rate for calcium binding to the sensor protein
(ka; 15 × 106 M
1
s1) and the conformational change in the protein (;
2000 s1) are similar to those for the kinetics of
secretion at retinal bipolar cell synapses (14 × 106
M1 s1 and 2000 s1;
Heidelberger et al., 1994) as well as for secretion from neuroendocrine cells (14 × 106 M1 s1 and
1000 s1; Heinemann et al., 1994). The detachment rate
(kd; 750 s1) used in this study is
drawn from a range of synapses and cell types (see Table 2 in Bennett
et al., 1997). The application of our kinetic model with these
parameters to experimental data from neuromuscular synapses is
contingent on the quantal release process at these synapses possessing
similar kinetics and parameter values as those appropriate for bipolar
synapses and neuroendocrine cells.
| |
RESULTS |
The Monte Carlo results are divided into two main sections. The
first of these investigates the calcium transients at the presynaptic
membrane when there are multiple calcium channel openings, as occurs
under an action potential. The second section is concerned with using
the information provided by the previous section to establish how
calcium transients from different arrays of channels affect the
triggering of vesicle exocytosis following an action potential, when
these vesicles are arranged in different configurations with respect to
the channels. In all cases the terminal contains a mobile buffer with
the characteristics of calmodulin and a fixed buffer with the
characteristics of calbindin (see Table 1 in Paper I). In addition, a
calcium indicator is sometimes present, which is either furaptra,
representative of a low-affinity indicator, or fura-2, representative
of a high-affinity indicator. Unless otherwise mentioned, all values of
free calcium and of calcium bound to the various buffers are the means
of at least five simulation trials. It is made explicit when the
standard deviations of these are given.
Ca2+ transients under an action potential
In varicosities and boutons
A submembranous calcium domain refers to a volume at the active
zone of a terminal within which the pooled calcium, arising from the
opening of a number of channels in the zone under an action potential,
may be sufficient to trigger the exocytosis of vesicles whether or not
they possess a nearby channel that is opened by the action potential.
Monte Carlo calculations have therefore been made to determine the
spatial distribution of the mean and variance of the peak free calcium
concentration at the presynaptic membrane of a varicosity or bouton in
such a submembranous domain. A volume of cytosol in a terminal was
considered that was made up of a 1 µm × 1 µm square base of
presynaptic membrane and taken to a height of 30 nm from the membrane
(Fig. 1). In the absence of quantitative
information concerning the spatial arrangement of calcium channels in
boutons (see Westerbroek et al., 1995), channels that occupied the
active zone region were arranged in the middle of this presynaptic
membrane. Given that there is some knowledge concerning the spatial
distribution of vesicles in the active zones of boutons, and that
according to the secretory unit hypothesis these vesicles are
associated with calcium channels, the active zone has been modeled as a
square array of vesicles and their associated channels placed on a
regular grid (Fig. 1; see also Fig. 7 A). The separation
between the channels has been set at 70.7 nm (giving a diagonal
separation of 100 nm) and two array sizes have been used, containing
5 × 5 and 9 × 9 channels, respectively.
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FIGURE 1
The Monte Carlo simulation typically uses a cubic box
with 1000-nm sides. The plasmalemma is represented by the 1 µm × 1 µm base; vesicles and their associated calcium channels are
placed in a regular array in the central region of this area (the
figure shows a 9 × 9 array). Calcium pumps are situated on all
six walls of the box. The submembranous domain is taken to extend to a
height of 30 nm above the plasmalemma, as shown by the dotted line.
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The boundaries of the presynaptic membrane, that is, the other five
sides of the varicosity or bouton, were closed by walls of membrane
incorporating pumps, as described under Methods in Paper I. Previous
calculations have shown that 0.46 of the N-type channels open on
average under an action potential (Bennett et al., 1997), so this has
been taken as the frequency in the present case. The spatial
distribution of open channels occurs at random in each time interval of
0.5 ms during the action potential, and this has been arranged in such
a way as to give a frequency distribution of open times that is similar
to that expected for channels under an action potential (for details,
see Methods above).
Fig. 2 shows the mean of the spatial
distribution of the calcium ions at the time of peak calcium
concentration in the volume under consideration. This is the average of
the results for five action potentials. Two cases have been considered,
one in which an active zone possesses a small array of channels (5 × 5; Fig. 2, A and C) and the other a large
array (9 × 9; Fig. 2, B and D). At this
time, the average number of calcium ions at any particular site (taken
to be a cube of side 30 nm with one face in the presynaptic membrane)
is generally much less than one, except at the middle of the zone (Fig.
2, Aa and Ba). This is mainly because of the removal of the calcium ions by the fixed buffer (Fig. 2, Ac
and Bc), and to a lesser extent by the mobile buffer (Fig.
2, Ab and Bb). Even though the average number of
calcium ions per site in the middle of the array is still only about
one, this amounts to a calcium concentration of ~40 µM. The
standard deviations of these calcium distributions were higher toward
the edges of the active zones, as would be expected, with values
comparable to the mean at the center of the zone and much greater than
the mean toward its edges (Fig. 2, Ca and Da).
This was much the same for the calcium bound to the mobile and fixed
buffers, except that the standard deviation was substantially less than
the mean at the center of the zones (standard deviations for each of
the cases in Fig. 2, A and B are shown in the
corresponding panels in Fig. 2, C and D,
respectively). Increasing the number of calcium ions that enters
increases the number of calcium ions found in any region of the active
zones as well as the number outside the zones, but the qualitative role
of the mobile and fixed buffers remains the same as shown in Fig. 2:
the endogenous buffers maintain a very small free calcium concentration
in any region of the active zones.
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FIGURE 2
The spatial distribution of the mean and
standard deviation of the calcium concentration at the presynaptic
membrane of a varicosity or bouton following an action potential. The
membrane has area 1 µm2 and concentrations are calculated
in the submembranous domain, taken to extend to a height of 30 nm above
the membrane. The channels are spaced 100/  70 nm apart
and arranged in a square grid in the middle of the presynaptic
membrane, with 0.46 of these randomly activated during an action
potential. The method for specifying the open time of the channels is
described under Methods. The distributions are shown at the time when
the average free calcium concentration is at its maximum. (In practice,
this involved running the same simulation twice, once to get the peak
and then to get the full spatial distribution. Typical times are 2.5 ms
for the 5 × 5 array and 4.5 ms for the 9 × 9 array.)
(A) Results for a 5 × 5 array of channels.
(B) Results for a 9 × 9 array of channels. In each
case, panels a-c give the concentrations of free calcium
([Ca2+]), of calcium bound to the mobile buffer
([CaBm]), and the calcium bound to the fixed buffer
([CaBf]), respectively. These graphs show the mean of
five calculations, each using the same pattern of channel openings, but
with different random initializations of the Monte Carlo simulation.
The coordinate system is such that the x and y
axes are in the plane of the presynaptic membrane with the origin at
one corner of the presynaptic membrane plane. The z
coordinate gives the mean number of particles in the xy
plane (to a depth of 30 nm), using a bin size of 30 nm square. The
parameters used in the calculations are given in Table 1 of the
accompanying article. (C, D) Standard deviations for the
corresponding graphs in (A) and (B).
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Next, the effects of a low-affinity indicator such as furaptra and of a
high-affinity indicator such as fura-2 on the spatial distribution of
calcium ions in the square-shaped active zones after an action
potential were considered. For both small (5 × 5) and large
(9 × 9) active zones the effect of the fura-2 was to decrease the
number of free calcium ions to much the same extent across the entire
active zone, so that the small number normally observed at the edges is
substantially reduced (compare Figs. 3
Aa and 2 Aa; also Figs. 3 Ba and 2
Ba) as well as that of the fixed buffer, which now
principally only catches the calcium at the middle of the active zone
(compare Figs. 3 Ac and 2 Ac; also Figs. 3
Bc and 2 Bc), with much now being taken out of
this region by the indicator (compare Fig. 3 Ad and 2
Ab; also Fig. 3 Bd and 2 Bb). This was
the case, as the principal effect of the indicator is to act as an
additional mobile buffer, decreasing the effect of the endogenous
mobile buffer (compare Figs. 3 Ab and 2 Ab; also
compare Figs. 3 Bb and 2 Bb). Although the
effects of using a low-affinity indicator like furaptra were
qualitatively the same as those for fura, they were quantitatively very
different, as the former changed the effects of the endogenous buffers
by <10%: see Fig. 3, C and D for the spatial
distribution of calcium ions in the cases of a small (5 × 5) and
a large (9 × 9) active zone, respectively, in the presence of the
indicator furaptra.
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FIGURE 3
The spatial distribution of the mean of the calcium
concentration at the presynaptic membrane of a varicosity or bouton in
the presence of a calcium indicator following an action potential. The
indicator used in (A) and (B) is fura-2, and that
in (C) and (D) is furaptra. (A) and
(C) give results for a 5 × 5 array of channels,
(B) and (D) give results for a 9 × 9 array
of channels. The details are as for Fig. 2, A and
B with the addition that panel d in each case
gives the concentration of calcium bound to the indicator
([CaBi]).
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In motor nerve terminals
Submembranous domains of calcium have also been considered for the
case of active zones, such as those at motor nerve terminals, that
possess calcium channels and vesicles on a line (Fig.
4; see also Fig. 8 A). A
volume of cytosol made up of a square area of 1 µm × 1 µm of
presynaptic membrane and taken to height of 30 nm from the membrane was
again considered. In this case, calcium channels that occupied the
active zone region were arranged along two parallel lines 30 nm apart,
with the channels 50 nm apart on each line. The boundaries of the
presynaptic membrane were again taken as enclosed by walls
incorporating pumps, as given in the Methods section of Paper I. The
frequency of N-channel opening under an action potential and the random
spatial distribution of open channels were calculated as for Fig. 2.
Fig. 4 shows the mean over five action potentials of the spatial
distribution of the calcium ions at the time of peak calcium
concentration in the volume under consideration. It will be noted that
the mean number of calcium ions in any 30 nm is highest along the
parallel line of channels (compare Fig. 4 A with Fig. 2
Aa). Although the average number of calcium ions is
maintained at a low level by the fixed buffer (Fig. 4 C) and
to a lesser extent by the mobile buffer (Fig. 4 B), these
ions still amount to a high concentration, of the order of 50-100
µM, along the parallel lines of channels.
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FIGURE 4
The spatial distribution of the mean of the calcium
concentration at the active zone of an endplate's motor nerve terminal
of area 1 µm2 to a depth of 30 nm when calcium channels
are arranged on two parallel lines in the middle of the presynaptic
membrane, with the lines 30 nm apart and the channels 50 nm apart along
the lines (cf. Fig. 8 A below) and 0.46 of these are
activated in a spatially random array during an action potential. The
density of the channels is thus 40 per 1000 nm. (A) The
concentrations of free calcium ([Ca2+]). (B)
The concentration of calcium bound to the mobile buffer
([CaBm]). (C) The concentration of calcium
bound to the fixed buffer ([CaBf]). The remaining details
are as for Fig. 2 A.
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During facilitation
The fixed buffer will gradually release its calcium after an
impulse, allowing it to be transferred by diffusion or by the mobile
buffer to the calcium pump at the plasma membrane. It was of interest
to see what effect this would have on the calcium concentration at the
presynaptic membrane due to a subsequent test impulse, especially given
that the fixed buffer may be partially saturated by the calcium from
the conditioning impulse, allowing more free calcium in the regions of
the channels after a test impulse.
Fig. 5 shows the results for Monte Carlo
calculations of the calcium after a test impulse (Fig. 5 B)
10 ms after a conditioning impulse (Fig. 5 A), in the
presence of a low-affinity indicator, such as furaptra, that does not
excessively disturb the calcium dynamics. The active zone under
investigation is that of a bouton or varicosity, similar to that in
Fig. 2. At 10 ms there is clearly more free calcium present in the
active zone (compare Fig. 5 Ba with Aa) due to
the residual free calcium contribution by the conditioning impulse,
even though the extent of calcium bound by the mobile buffer (compare
Fig. 5 Bb with Ab) and that by the fixed buffer
(compare Fig. 5 Bc with Ac) is slightly elevated. This increase in free calcium ions after the test impulse is reflected in the calcium bound to the furaptra indicator (compare Fig.
Bd with Ad). The relative contributions of the
mobile and fixed buffers to residual calcium will be further commented
on below in relation to the effects of these on facilitation.
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FIGURE 5
The spatial distribution of the mean of the calcium
concentration at the presynaptic membrane of a varicosity or bouton in
the presence of the calcium indicator furaptra after conditioning and
test action potentials. The test action potential follows 10 ms after
the conditioning action potential, and a different random choice of
calcium channels was used in the test action potential from that used
in the conditioning action potential. (A) Results for the
conditioning action potential. (B) Results for the test
action potential. The remaining details are as for Fig. 3
C.
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The effects of a conditioning impulse on the free calcium to be found
at the active zones of motor-nerve terminals, with their parallel rows
of channels, after a subsequent test impulse 10 ms later, are given in
Fig. 6. It is apparent that there is
residual calcium in the active zone, even when channels are restricted to two parallel lines, at the time of the test impulse (compare Fig. 6
Ba with Aa). Both the mobile buffer (compare Fig.
6 Bb with Ab) and fixed buffer (compare Fig. 6
Bc with Ac) restrict the free calcium within the
active zone for the conditioning and test impulses.
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FIGURE 6
The spatial distribution of the mean of the calcium
concentration at the active zone of an endplate's motor nerve terminal
in the presence of a calcium indicator after conditioning and test
action potentials. The array is as for Fig. 4 and the remaining details
are as for Fig. 5.
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Exocytosis due to Ca2+-submembranous domains in
varicosities, boutons, and endplates
As mentioned in the Introduction, the concept of submembranous
domains arises when there is nonindependence of exocytosis from
secretory units. In this case, there is a superposition of effects
arising from the summed contributions of calcium from several open
channels within secretory units. In this section, the stochastic
analysis of exocytosis in such submembranous domains is considered for
different spatial distributions of secretory units, calcium channels,
and synaptic vesicles in the active zones.
Arrays of secretory units
Active zones of varicosities and boutons. In this case,
secretory units have been arranged into square arrays of the
same kind used for the analysis of the free calcium in the
submembranous region of nerve terminals in the previous section. Thus
the vesicles of secretory units occupy arrays of from 5 × 5 up to
9 × 9 in the center of a 1 µm × 1 µm presynaptic
membrane, as for the calcium channels in Fig. 2 (see Fig. 7
A). Two different secretory
unit geometries are then considered: one in which the calcium channel is located 25 nm from its synaptic vesicle in the secretory unit and
the other in which it is located 50 nm away (see Fig. 7 A, upper and lower dotted boxes, respectively). The
spatial distribution of free calcium ions in the submembranous domain
was then determined for these arrays after an impulse in the same way
as before. In this case further Monte Carlo calculations were carried
out to ascertain the extent of exocytosis in each region due to the
rise in calcium in the domain.
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FIGURE 7
The frequency of secretion of quanta from a set of
secretory units in a varicosity or bouton on the arrival of an action
potential. (A) A set of 64 secretory units arranged at the
presynaptic membrane in a square array, with the secretory units
separated by 70 nm along the x and y axes. The
vesicles are shown as open circles, and the dotted boxes also show the
channels for the two cases of offset placement (channel-vesicle
distance of 25 nm) and symmetric placement (channel-vesicle distance of
50 nm). (B) Two examples of the spatial distribution of
vesicles that have undergone exocytosis (filled circles) or
that have bound one (single circle) or two
(overlapping circles) calcium ions. (Up to four calcium ions
can be bound, but there are no three- or four-binding cases in these
examples.) Results are shown at a time of 5.5 ms after the initiation
of the action potential. (C) The relation between the size
of the active zone (given as the total number of secretory units) and
the extent of quantal secretion (given as the average number of
exocytotic events or mean quantal release) from the array after an
action potential. Panel a gives the quantal secretion for
standard calcium current and for when the secretory units possess
calcium channels at 25 nm from the vesicle [open square;
see "offset placement" in (A)] or at 50 nm from the
vesicle [filled square; see "symmetric placement" in
(A)]. Panel b gives the corresponding results
for twice the standard calcium current. In each case, the results are
the mean of five Monte Carlo simulations, each using a different random
selection of channel openings as given under Methods. Standard
deviations are shown. The parameters used in the calculations are given
in Table 1 of the accompanying article.
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After calcium influx, only about one or two vesicles on average
underwent exocytosis of the 64 in the case of an 8 × 8 array (Fig. 7 Ca), and two examples of this for two individual
impulses are shown in Fig. 7 B. These examples indicate that
while many calcium-sensor proteins in the array bound one or two
calcium ions, only one or two bound four and triggered exocytosis.
Exocytosis occurs throughout the array of vesicles (Fig. 7,
Ba and Bb), reflecting the high free calcium in
the region of the array (see Fig. 2). It was found that the spatial
distribution of exocytosis within the active zone and the extent of
exocytosis were little affected by the position of the channels in the
secretory units. The extent of exocytosis for the case in which
channels were 50 nm away from a synaptic vesicle in an array (Fig. 7
Ca, closed squares) was much the same as that for the
usual case in which this distance was 25 nm (Fig. 7 Ca,
open squares).
The question of how the extent of exocytosis changes with the size of
the array that constitutes the active zone was also addressed. Fig. 7
Ca shows that as the active zone increases from an array of
5 × 5 secretory units to one of 9 × 9 secretory units, the
average quantal release increases from near zero to ~3.5. This
increase is steeper than linear, indicating a nonlinear relation between quantal release and the size of the active zone, which is to be
expected if the secretory units use pooled and local calcium. (This is
further analyzed below.) Quantal release is thus primarily determined
for active zones consisting of a rectangular array of secretory units
by the submembranous calcium concentration. It should be noted,
however, that when the distance between the channel and the vesicle in
the secretory unit is increased from the standard value of 25 nm to 50 nm, the average quantal release from an active zone of a given size is
slightly smaller (Fig. 7 Ca, where the open squares are for
25 nm and the filled squares are for 50 nm). Such a result is to be
expected if the pooled calcium from all the open channels in the active
zone makes by far the major contribution to the calcium concentration
at a vesicle's calcium-sensor, but that of a nearby open channel may
be considered to make a special contribution.
Doubling the calcium influx allowed through channels produces an
extremely high level of exocytosis, in which on average ~12 vesicles
undergo exocytosis in the 8 × 8 case (Fig. 7 Cb).
Virtually all calcium sensors in the 8 × 8 array bind a calcium
ion, with many binding two and three, and ~12 binding four and going
through to exocytosis. Again, there is a nonlinear relation between the size of the active zone, or number of secretory units in an array, and
the extent of quantal secretion (Fig. 7 Cb). This emphasizes that there is a nonlocal interaction between the secretory units in
these active zones.
Active zones of motor nerve terminals. In the case of an
active zone of a motor nerve terminal, the vesicles are arranged on two
parallel lines, separated by 80 nm, with the vesicles spaced 50 nm
apart along the lines; calcium channels are also spaced 50 nm apart on
lines parallel to the vesicle lines and separated from them by 25 nm,
as shown in Fig. 8 A. Thus, in
this case secretory units are restricted to two parallel lines 80 nm
apart with the calcium channels that belong to a secretory unit 25 nm
from its vesicle-associated protein (Fig. 8 A).
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FIGURE 8
The frequency of secretion of quanta from a set of
secretory units at the active zone of an endplate on the arrival of an
action potential. (A) A set of secretory units arranged at
the presynaptic membrane along two parallel lines in the middle of the
presynaptic membrane of 1 µm × 1 µm, so that there are 40 secretory units present if the active zone extends across the entire
width of the presynaptic membrane. The vesicles are shown as open
circles in two lines 80 nm apart and the dotted box shows also the
channels in two lines 30 nm apart, thus giving a channel-vesicle
distance of 25 nm. (B) Two examples of the spatial
distribution of vesicles that have undergone exocytosis (details as for
Fig. 7 B). (C) The relation between the length of the active
zone (given as the total number of secretory units, or active zone
size) and the extent of quantal secretion (given as the average number
of exocytotic events) from the array after an action potential. Panel
a gives the quantal secretion for standard calcium current.
Panel b gives the results for twice the standard calcium
current. In each case, the results are the mean of up to 50 Monte Carlo
simulations, using different random selections of channel openings.
(More runs were required than for Fig. 7 because the different geometry
increased the stochastic variability of the results.) The broken lines
show linear fits to the points: see Eq. 2.
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This geometry of secretory units and calcium channels conforms to the
most likely arrangement to be found in amphibian motor-nerve terminals
(see Introduction), in which the lines of secretory units can extend
across the entire width of the presynaptic membrane of up to 1 µm. An
active zone of this length possesses 40 vesicle-associated proteins
that bind one or more calcium ions (Fig. 8 B), but only on
an average of 62% of occasions did an impulse trigger exocytosis of a
vesicle, although there were double and even triple exocytotic events,
giving rise to a mean quantal release of ~1.0 (Fig. 8 Ca).
For active zone lengths >~16 secretory units the relation between
the average quantal release from an active zone and the length of the
active zone was approximately linear; for shorter active zones the
quantal release was near to zero (Fig. 8 Ca). Thus the
quantal release from an active zone was approximately proportional to
the number of secretory units for length >16 secretory units, in
contrast to the case of active zones, in which the secretory units are
organized into rectangular arrays, in which case the increase in
quantal release with the size of the active zone is steeper than linear
(compare Figs. 8 Ca and 7 Ca). If the calcium current through the channels is increased by a factor of two, while
keeping the same frequency distribution of channel open times under an
action potential, then the much greater flux of calcium ions leads to
almost an order of magnitude increase in the extent of exocytosis
(compare Fig. 8 Cb with Ca). In this case, the
near-linear relation between the quantal release and active zone length
is evident for the endplate (Fig. 8 Cb) as is the nonlinear
increase in quantal release with the size of the active zone in a
bouton or varicosity (Fig. 7 Cb). It is interesting to
note that the mean quantal release for active zones consisting of 40 secretory units on a double line is about the same as that for 40 secretory units in a rectangular array (compare Figs. 8 C
and 7 C).
The secretory units in the motor-terminal active zones
clearly do not act completely independently in the line case. If they did, the response (mean quantal release) for a line containing 2n secretory units would be Rn = 
0n, where 0 is a constant
(equal to the response from one pair of secretory units) and thus this line should pass through the origin, which it clearly does not in Fig.
8, Ca and Cb. Two effects can be present: one is
the overlap between the calcium domains of neighboring pairs of
secretory units; the other is the necessity for a certain level
of calcium before appreciable exocytosis can occur. This suggests an
expression of the form
|
(2)
|
where 1 is the response from a secretory unit pair
with one neighboring pair, 2 is the response from a
secretory unit pair with two neighboring pairs, and 
is a
"threshold" term. (Eq. 2 holds if the right-hand side is greater
than zero, otherwise Rn is zero.)
Rn as given by Eq. 2 involves three parameters,
1, 2 and , and these cannot be
uniquely determined by a linear fit to the data in Fig. 8 C.
For the purposes of demonstrating that a choice of parameters is
possible, assume that k = 0 + k
0, k = 1, 2, where is some
number in the range 0 < < 1. Making the specific choice
= 0.25 gives the linear fits shown by the broken lines in Fig.
8 Ca (0 = 0.0403, = 0.2692) and Fig. 8 Cb (0 = 0.2763, = 1.5574).
In the planar case, similar reasoning (allowing for
calcium overlaps between neighbors and for a threshold term) leads to the response from an n × n array being
|
(3)
|
where k is the response from a secretory unit with
k neighbors. (Again, this equation only holds for
n sufficiently large so that the right-hand side is
non-negative.) Thus, for a large enough array the response is of the
form
|
(4)
|
where A = n2 is a measure of the area
of the receptor patch and i are constants. For any
reasonable values of the parameters, the 
term
does not cause much departure from linearity: certainly nowhere near as
much as shown in Figs. 7 C and 9
C. For example, assuming
k = 0 + k0, taking = 0.25 and fitting to
the symmetric placement data points at n2 = 25 and n2 = 81, gives the broken lines
shown in Fig. 9, Ca and Cb. Over this range (Eq. 3) shows almost no departure from linearity, indicating that the
nonlinearity in these figures does not arise from local overlap
considerations. Instead, it appears to arise as a consequence of the
pooled calcium from a large number of secretory units throughout the
active zone contributing to the effects at each individual secretory
unit.
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FIGURE 9
The frequency of secretion of quanta from a set of
secretory units in a varicosity or bouton on the arrival of an action
potential when there is an excess of vesicles over secretory units.
(A) A set of 64 secretory units arranged at the presynaptic
membrane in a square array, with the secretory units separated by 70 nm
along the x and y axes, together with an extra
three rows of vesicles around the perimeter; these extra vesicles
possess calcium-sensor proteins and the capacity for exocytosis, but do
not have associated calcium channels. The vesicles are shown as open
circles, and the dotted boxes also show the channels for the two cases
of offset placement (channel-vesicle distance of 25 nm) and symmetric
placement (channel-vesicle distance of 50 nm). (B) Two
examples of the spatial distribution of vesicles that have undergone
exocytosis (details as for Fig. 7 B). (C) The relation
between the size of the active zone (given as the total number of
secretory units) and the extent of quantal secretion (given as the
average number of exocytotic events) from the array after an action
potential. Panel a gives the quantal secretion for standard
calcium current and for when the secretory units possess calcium
channels at 25 nm from the vesicle [open square; see
"offset placement" in (A)] or at 50 nm from the vesicle
[filled square; see "symmetric placement" in
(A)]. Panel b gives the corresponding results
for twice the standard calcium current. The broken lines show an
attempt to fit the points using Eq. 3.
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Excess vesicles over secretory units
Active zones of varicosities and boutons. The possible
effects of an excess of vesicles, with their associated proteins for exocytosis but without calcium channels, over secretory units in the
active zone has also been investigated. Calculations have been
performed for the situation in which vesicles are packed around a
secretory unit array in an active zone with the same density as
secretory units within the array, and this occurs over the entire
presynaptic membrane of 1 µm × 1 µm (Fig. 9 A). In this case, there was no secretion outside the secretory unit array even
though many calcium sensors associated with the vesicles outside of the
array bound one or two calcium ions (Fig. 9 B). Undoubtedly
this restriction of exocytosis to within the array was due to the
action of the endogenous buffers restraining the high levels of
submembranous calcium to within the active zone (Fig. 2). The spatial
distribution of exocytosis over the presynaptic membrane in this case
was then the same as that in the absence of an excess of vesicles. The
quantal release then increased with an increase in the size of the
active zone array of secretory units in the same way for the case of
excess vesicles as in the absence of such an excess (compare Fig. 9
Ca with Fig. 7 Ca). This was so even when the
calcium current through the channels was increased by a factor of two
(compare Fig. 9 Cb with Fig. 7 Cb).
Some mention should be made here of the possibility that the form of
the nonlinearity of the relationship between quantal release and the
size of the secretory unit array depends on the extent to which the
submembranous calcium is removed from the edges of the array by the
endogenous buffers (see Fig. 2). It is possible that as the array size
changes the extent of removal of calcium at the edges of the array is
such as to give a proportionally smaller removal of calcium ions, and
hence a larger number of vesicles in the array are exposed at the edges
to calcium, giving a larger quantal release. To some extent a test of
this proposition is provided by the case of excess vesicles: such an
excess does not give rise to any additional exocytosis at the edges of
the secretory unit array, with secretion still maintained within the secretory unit array as noted above (Fig. 9 B), presumably
because vesicles at the edge of the array, at the time of peak
submembranous calcium, interact with relatively few calcium ions (Fig.
2). These results suggest that the nonlinear relationship between the
extent of quantal release and active-zone size arises from the
interaction between the pooled calcium from the open channels within
the array and the individual vesicle-associated calcium sensor proteins.
Active zones of motor nerve terminals. The effect on
exocytosis of excess sets of vesicles and their associated
vesicle-associated proteins, devoid of calcium channels, in the active
zones of motor nerve terminals has also been calculated. These excess
vesicles were placed on lines parallel to those in the active zone, as shown in Fig. 10 A. The
existence of these vesicles did not much affect the extent of
exocytosis (Fig. 10 B; also compare Fig. 10 Cc
with Ca) as expected, given that the secretory units tend to only interact locally in the active zone, and calcium from an open
channel in a secretory unit is unlikely to have a significant impact at
the calcium-sensor in one of the excess vesicles, given that the
nearest such vesicle is 105 nm away. However, doubling the current
through the channels did give a marginal increase in the extent of
exocytosis (compare Fig. 10 Cd with Cb), so that in these circumstances some of the increased calcium influx does have
an impact on the calcium sensors of the excess vesicles.
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FIGURE 10
The frequency of secretion of quanta from a set of
secretory units at the active zone of an endplate on the arrival of an
action potential when there is an excess of vesicles over secretory
units. (A) A set of secretory units arranged at the
presynaptic membrane along two parallel lines in the middle of the
presynaptic membrane of 1 µm × 1 µm, so that there are 40 secretory units present (cf. Fig. 8 A), together with an
extra two rows of vesicles placed an equal distance on either side;
these extra vesicles possess calcium-sensor proteins and the capacity
for exocytosis, but do not have associated calcium channels. The
vesicles are shown as open circles, and the dotted box also shows the
channels. (B) Two examples of the spatial distribution of
vesicles that have undergone exocytosis (details as for Fig. 7
B). (C) The mean number of exocytotic events after an action
potential; a and b are for the case of no excess
vesicles (as in Fig. 8 A) with standard calcium current and
double calcium current, respectively; c and d are
the corresponding results when excess vesicles are present.
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Excess channels over secretory units
Active zones of varicosities and boutons. The effect of
the presynaptic membrane possessing an excess of N-type calcium
channels outside of those belonging to secretory units in the array of the active zone has also been considered. Two extra rows of channels were placed in the presynaptic membrane outside of the active zone and
with the same spacing as the secretory units within the active zone
(Fig. 11 A). In this case,
exocytosis occurred at the edges of the active zone and in the middle
50% of the zone (Fig. 11 B). This is to be expected, as the
submembranous calcium now extends well beyond the edges of the zone
(Fig. 2). Under these conditions, even the smallest array of secretory
units considered, namely 5 × 5, gave relatively large average
quantal releases under an impulse (~2) compared with this array size
in the absence of an excess of channels (~0; compare Fig. 11 D,
e and g with a and c). For the
larger array of 8 × 8 this quantal release in the presence of an
excess of channels reached ~7 (Fig. 11 C, e and g) compared with the control in the absence of such an
excess of ~2 (Fig. 11 C, a and c). Such quantal
releases are unrealistic when compared with experimental data (see
Discussion) and suggest that it is unlikely that there is an excess of
calcium channels outside of the active zone. This becomes even more
obvious when the calcium current is doubled through the channels, in
which case quantal releases of between 10 and 40 are reached for active zone sizes of 5 × 5 and of 8 × 8, respectively (Fig. 11
D, f and h; Fig. 11 C, f and
h).
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FIGURE 11
The frequency of secretion of quanta from a set of
secretory units in a varicosity or bouton on the arrival of an action
potential when there is an excess of N-type calcium channels over
secretory units. (A) A set of 64 secretory units arranged at
the presynaptic membrane in a square array, with the secretory units
separated by 70 nm along the x and y axes. In
addition, there are an extra two rows of calcium channels around the
perimeter, placed either in the offset position (upper dotted
box) or symmetrically (lower dotted box).
(B) Two examples of the spatial distribution of vesicles
that have undergone exocytosis (details as for Fig. 7 B).
(C) The mean number of exocytotic events from an 8 × 8 array
of secretory units after an action potential; a and
b are for the case of no excess channels with offset
placement of the calcium channels (Fig. 7 A, upper dotted
box) with standard calcium current and double calcium current,
respectively; c and d are the corresponding
results for symmetric placing of the channels (Fig. 7 A,
lower dotted box); e and f are the
corresponding results for excess channels and offset placing of the
channels (A, upper dotted box); g and
h are the corresponding results for excess channels and
symmetric placing of the channels (A, lower dotted
box). (D) The same as for (C), except that
the array of secretory units is reduced to 5 × 5.
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Active zones of motor nerve terminals. The case was also
considered of an excess of calcium channels outside the lines of secretory units that constitute the active zones of motor-nerve terminals. Excess channels were placed throughout the presynaptic membrane, either along lines parallel to those of the existing channels
within the active zone (Fig. 12 A, upper dotted box)
or interspersed between the existing channels (Fig.
12 A, lower dotted box). After an action potential there was an enormous increase in
the quantal release over the case of the active zone without excess
channels from a mean of 1.0 to a mean of ~8 (compare Fig. 12
Cc or Ce with Ca). This average
quantal release in the presence of excess channels is so large compared
with the experimentally determined quantal release that it suggests
that such excess channels do not exist. This proposition is emphasized
by consideration of the case when the calcium current through the
channels is doubled (compare Fig. 12 Cd or Cf
with Fig. 10 Cb).
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FIGURE 12
The frequency of secretion of quanta from a set of
secretory units at the active zone of an endplate on the arrival of an
action potential when there is an excess of N-type calcium channels
over secretory units. (A) A set of 40 secretory units
arranged along two parallel lines in the middle of the presynaptic
membrane of size 1 µm × 1 µm (cf. Fig. 8 A), together
with 40 extra calcium channels placed either as two rows at an equal
distance on the other side of the vesicles (upper dotted
box) or interspersed between the existing channels (lower
dotted box). (B) Two examples of the spatial
distribution of vesicles that have undergone exocytosis for the case of
two extra rows of channels (details as for Fig. 7 B). (C)
The mean number of exocytotic events after an action potential;
a and b are for the case of no excess channels
(as in Fig. 8 A) with standard calcium current and double
calcium current, respectively; c and d are the
corresponding results when excess channels are present as extra rows;
e and f are the corresponding results when
excess channels are interspersed between the original channels.
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Test-conditioning sequences of impulses
Active zones of varicosities and boutons
It has been noted that after an action potential there is not only
a residual free calcium concentration in the submembranous region that
is removed from the cytosol by calcium pumps but also a transient
occupation of the endogenous buffers by calcium ions in this region
(Fig. 5). This last effect results in a large increase in the free
calcium ions in the submembranous region if a subsequent test action
potential occurs during this transient occupation of the endogenous
buffers (Fig. 13 A), an
increase well above that produced in the submembranous region by the
conditioning action potential. The consequences of this for the release
of quanta by the test action potential have been explored (Fig. 13
B). If the conditioning/test sequence occurs at an interval
of 10 ms, then the average quantal release increases from 2.2 to 5.1 for a secretory unit array of 8 × 8, giving a facilitation of
1.32 (Fig. 13 Ca). If the calcium current through the
channels is increased, as would occur with an increase in the external
calcium concentration, then there is a decrease in the extent of
facilitation, which in the case of the 8 × 8 array is from 1.32 in standard calcium to 1.06 in double calcium for offset calcium
channels, and from 2.08 in standard calcium to 1.4 in double calcium
for the centered channels. Such decreases in facilitation with an
increase in external calcium concentration are observed
experimentally.
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FIGURE 13
The frequency of secretion of quanta from a set of
secretory units in a varicosity or bouton due to a test action
potential arriving 10 ms after a conditioning action potential. The
distribution of secretory units is the same as that given in Fig. 7
A. (A) The submembranous calcium concentration (given as the
average concentration of free calcium ions in the 1 µm × 1 µm × 30 nm box) during the conditioning and the test impulse
for both the case of standard calcium current (lower curve)
and for twice that current (upper curve). (B) The
extent and timing of exocytosis that accompanies these two different
calcium currents for the conditioning and test action potentials.
(C) The mean number of exocytotic events that occur as a
result of the conditioning and test action potentials. Results shown
are for 10 simulations: a and b are for the case
of offset calcium channels (see Fig. 7 A, upper dotted
box) for standard and double calcium current, respectively;
c and d are the corresponding results for
symmetric placement of the calcium channels (see Fig. 7 A,
lower dotted box). In each case the dark shaded region shows
the contribution from the conditioning impulse.
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Fig. 14, which is for the case of
double calcium influx, shows that this facilitation is primarily due to
the partial saturation of both the mobile (Fig. 14 B)
and fixed (Fig. 14 C) buffers at the time of the test
action potential, together with the saturation of the calcium pump at
this time (Fig. 14 D) which continues to pump out calcium
(Fig. 14 E). There is only a small contribution from the
residual free calcium remaining from the conditioning pulse (Fig. 14
A) and virtually none from the buffering effects due to the
vesicle-associated calcium sensors binding calcium ions (Fig. 14
F).
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FIGURE 14
The distribution of calcium as a function of time due
to a conditioning action potential followed by a test action potential
10 ms later. The details are as for Fig. 13 for the case of twice
standard calcium current and offset placement of calcium channels. In
each case the ordinate gives the concentration of either free or bound
calcium ions in the submembranous region. (A) The number of
free calcium ions. (B) The number of calcium ions bound to
the mobile buffer. (C) The number of calcium ions bound to
the fixed buffer. (D) The number of calcium ions bound to
the pumps. (E) The number of calcium ions pumped out.
(F) The number of calcium ions bound to the
vesicle-associated proteins (not including those that have undergone
exocytosis).
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Active zones of motor-nerve terminals
Fig. 15 shows the corresponding
results for active zones consisting of secretory units on a line. The
behavior is similar to that shown for the 8 × 8 square array in
Fig. 13, with a reduction in the mean quantal release, because now
there are only 40 secretory units compared to 64 in Fig. 13. Fig. 15
C shows that there is facilitation from this process of 2.4 in low calcium and of 0.93 in high calcium. Fig.
16, which is for the case of double
calcium influx, gives the details of binding to buffers and pumps
(compare Fig. 14).
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FIGURE 15
The frequency of secretion of quanta from a set of
secretory units at the active zone of a motor nerve terminal due to a
test action potential arriving 10 ms after a conditioning action
potential. The distribution of secretory units is the same as that
given in Fig. 8 A. The remaining details are as for Fig.
13.
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FIGURE 16
The distribution of calcium as a function of time at
the active zone of a motor nerve terminal due to a conditioning action
potential followed by a test action potential 10 ms later, for the case
of twice standard calcium current (Fig. 15 A, upper
curve). The remaining details are as for Fig. 14. (The scales on
the ordinates have been kept the same as in Fig. 14 to facilitate
comparison.)
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DISCUSSION |
Calcium in the submembranous domain after the opening of multiple
channels
Klingauf and Neher (1997) developed the concept of submembranous
calcium in the context of their examination of how the relatively slow
secretion of catecholamines occurs from chromaffin cells. One mechanism
that might accomplish this involves most of the granules to be secreted
not being located strategically close to a calcium channel, so that the
pooled calcium from many open channels must reach the calcium sensor of
the granules before exocytosis is triggered. This pooled calcium then
constitutes the submembranous domain. In this case, rather than the
microdomain of calcium dominated by fast diffusion dictating the
temporal characteristics of the secretion process, the submembranous
domain dominated by the slower buffering processes may determine the temporal characteristics of secretion. The submembranous domains of
interest in the present work are those associated with varicosities and
boutons, modeled on the assumption of rectangular arrays of channels in
their active zones (Pfenninger et al., 1971), and those associated with
amphibian motor-nerve terminals, possessing arrays of channels that are
confined to two parallel lines in their active zones (Robitaille et
al., 1990).
Deterministic solutions of the reaction-diffusion equations for
rectangular arrays of channels show that there is a relatively high
calcium concentration associated with the microdomains of each channel,
superimposed on a lower calcium concentration due to the submembranous
pooling of calcium from the different channels outside of the
microdomains at the time of channel closure [see, for example Figs. 7
and 8 in Roberts (1994) and Fig. 3 in Klingauf and Neher (1997)].
However, when allowance is made for the stochastic opening of channels
in the active zone under an action potential, the microdomains are not
as distinct at the end of the action potential as in a deterministic
solution, so that it is difficult to distinguish the microdomains from
the submembranous calcium (see, for example, Fig. 3). This arises
because many of the channels that open under the action potential do so
for such a short time or at a time when the driving force on the
calcium ions is so small that their microdomains are relatively small.
However, as these are numerically the dominant kind of channel, they
contribute significantly to the submembranous calcium, which then
becomes comparable to the microdomains formed by the more effective channels.
There are very few submembranous calcium ions at the edge of the
rectangular array of channels, with the mobile buffer carrying the ions
out of the active zone region, as has been emphasized by Roberts
(1994). However the "time averaged" simulation in his work giving
rise to a "frozen" landscape of calcium concentration in the active
zone consisting of microdomains associated with each open channel
superimposed on a submembranous calcium according to a deterministic
analysis, does not occur if a stochastic solution is obtained [compare
Fig. 7 in Roberts (1994) with Fig. 2 A in this work]. The
Monte Carlo analysis shows that the submembranous calcium is of the
order of 50 µM in the middle of the rectangular arrays of channels,
which is probably sufficient to activate the calcium sensors for
exocytosis (Südhof, 1995). When the channels are arranged on a
line, as in the active zone of motor-nerve terminals, the submembranous
calcium is still significant compared with that of the microdomain calcium.
The temporal changes in increased efficacy of quantal release that
occur at a nerve terminal when a test impulse follows a conditioning
impulse at intervals of <~50 ms is referred to as F1 facilitation.
The effect of a conditioning action potential on the spatiotemporal
distribution of calcium in the submembranous domain after a subsequent
test action potential within ~10 ms is to elevate the free calcium
ions in this domain. This arises principally as a consequence of the
fixed and mobile buffers in the middle of the rectangular array of
channels still retaining ions from the conditioning action potential,
so that they are unavailable for binding ions entering during the test
action potential (see also Klingauf and Neher, 1997). There is also
some residual free calcium in the submembranous domain at this time
from the conditioning action potential, but this adds only a small
amount to that from the test action potential. The additional calcium after the test action potential due to part saturation of the buffers
would contribute to the F1 phase of facilitation (Tanabe and Kijima,
1992).
Surprisingly, the additional free calcium ions available after a test
action potential at motor-nerve terminals due to part-saturation of the
buffers after the conditioning impulse are also significant. The
microdomain calcium does not dominate the submembranous calcium at the
active zones of endplates more than it does for the active zones of
boutons and varicosities. The failure of the calcium chelator BAPTA to
affect F1 facilitation at crayfish motor-nerve terminals (Winslow et
al., 1994) or amphibian motor-nerve terminals (Robitaille and Charlton,
1991) is explained by the fact that it is the part-saturation of the
endogenous buffers by the calcium influx due to the conditioning
impulse rather than any residual free calcium from this impulse that is
mainly responsible for F1 facilitation, together with the binding of
calcium ions to calcium-sensor proteins that did not trigger exocytosis
after the conditioning action potential (Bennett et al., 1997).
One question that arises is whether rectangular arrays of channels
belonging to adjacent active zones can pool their calcium ions. Such an
effect could lead to the nonindependence of adjacent active zones in
the process of exocytosis (Bennett et al., 1998). Some deterministic
calculations have been made that suggest that this might happen if the
zones are within ~200 nm of each other and there is no mobile buffer
(Cooper et al., 1996). The Monte Carlo simulations suggest that this is
unlikely to occur in the presence of an endogenous mobile buffer,
because the edges of the channel arrays are virtually devoid of any
calcium ions as the buffer carries the ions away. The answer to the
question of nonindependence then depends on whether there is a mobile
buffer present.
The discovery that fast-acting buffers like BAPTA can modify
transmitter release at motor-nerve terminals, whereas slower buffers
such as EGTA cannot (Robitaille et al., 1993; Losavio and Muchnik,
1997) is explained by the fact that it is the high-concentration calcium microdomains dissipated primarily by diffusion that trigger transmitter release at these terminals, so that only BAPTA can modify
them. However, if transmitter release is primarily through two-dimensional arrays of channels, then the submembranous calcium domains play a main role in triggering diffusion, and so EGTA can have
an effect on these (Borst and Sakmann, 1996).
Quantal release at calcium submembranous domains
When there is a relatively large rectangular array of channels in
the active zone, buffers ensure that calcium ions are found infrequently at the edges of the array after an action potential (Bennett et al., 1998). As a consequence, exocytosis is confined to the
center of the array, and the addition of extra vesicles outside the
array makes no difference to the extent of quantal release. In this
case there is no independence of the secretory units, as foreshadowed
in Paper I when considering the four secretory unit case, as with about
half the channels opened the calcium-sensor within any one secretory
unit can bind calcium ions from several of the surrounding open
channels, these ions constituting the submembranous calcium. Thus, with
an increase in the number of secretory units in the array there is a
disproportionately larger increase in the number that undergo
exocytosis. The probability of secretion at adjacent varicosities of
sympathetic nerve terminals varies considerably (Lavidis and Bennett,
1993; Bennett, 1994). Measurements of the calcium transients in these
adjacent varicosities after an impulse show that these also vary to a
large extent, suggesting different size active zones with different
numbers of secretory units in the adjacent varicosities (Brain and
Bennett, 1997). However, there has been no comparison between the size of the active zones in the varicosities, identified, for example, by
the relatively high concentrations of syntaxin found there (Brain et
al., 1997), and the probability of secretion that would allow for a
check of the proposal that this is highly nonlinear.
Multiquantal release at synapses
Whether the calcium microdomain is the sole source of calcium for
triggering exocytosis, or whether contributions from the submembranous
calcium must be considered, there is no limit in the present
simulations on the possibility of multiquantal secretion from a synapse
in the present models. The possibility that only one quantum might be
capable of secretion from a synapse on the arrival of an action
potential was first raised in the context of secretion at autonomic
preganglionic nerve terminals for which the maximum number of quanta
released from a single terminal during high calcium exposure was of the
same order as the number of synapses formed by the terminal; that is,
the number of boutons that it formed on a single ganglion cell (Bennett
et al., 1976). Recently this proposal has been especially promoted in
relation to the release of quanta from boutons formed by hippocampal
neurones in culture (Stevens and Wang, 1994; 1995; Murthy et al.,
1997). Although there is considerable evidence for autoinhibitory
mechanisms controlling quantal release due to the action of, for
example, adenosine at motor-nerve terminals and preganglionic nerve
terminals (Bennett et al., 1991; Bennett and Ho, 1991; van der Kloot,
1988), these do not autoinhibit quantal release within a single action potential, but rather during trains of action potentials. A study of
whether there is an inhibitory mechanism for quantal release within an
action potential, such that an early released quantum is followed by a
refractory period during which later releases are inhibited, has not
been found for quantal release at active zones of amphibian motor-nerve
terminals (Thomson et al., 1995). Indeed, there is evidence for
multiquantal spontaneous release measured with loose-patch electrodes
over single varicosities of sympathetic nerve terminals (Bennett et
al., 1996) and at single cerebellar boutons (Vincent and Marty, 1996).
Given these caveats, a refractory mechanism for quantal release has not
therefore been incorporated into the present simulations because there
is an absence of direct experimental evidence for its existence.
and
TOP
ABSTRACT
INTRODUCTION
