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The Journal of Neuroscience, April 15, 2003, 23(8):3186
Independent Sources of Quantal Variability at Single
Glutamatergic Synapses
Kevin M.
Franks1, 2, 4,
Charles F.
Stevens1, 3, and
Terrence J.
Sejnowski1, 2, 4
1 Howard Hughes Medical Institute,
2 Computational and 3 Molecular Neurobiology
Laboratories, The Salk Institute for Biological Studies, La Jolla,
California 92037, and 4 Division of Biology, University of
California, San Diego, La Jolla, California 92093
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ABSTRACT |
Variability in the size of single postsynaptic responses is a
feature of most central neurons, although the source of this variability is not completely understood. The dominant source of
variability could be either intersynaptic or intrasynaptic. To
quantitatively examine this question, a biophysically realistic model
of an idealized central axospinous synapse was used to assess mechanisms underlying synaptic variability measurements. Three independent sources of variability were considered: stochasticity of
postsynaptic receptors ("channel noise"), variations of
glutamate concentration in the synaptic cleft ( q),
and differences in the potency of vesicles released from different
locations on the active zone [release-location dependence
(RLD)]. As expected, channel noise was small (8% of the total
variance) and q was the dominant source of
variability (58% of total variance). Surprisingly, RLD accounted for a
significant amount of variability (36%). Our simulations show that
potency of release sites decreased with a length constant of ~100 nm,
and that receptors were not activated by release events >300 nm away,
which is consistent with the observation that single active zones are
rarely >300 nm. RLD also predicts that the manner in which receptors
are added or removed from synapses can dramatically affect the nature
of the synaptic response, with increasing receptor density being more
efficient than merely increasing synaptic area. Saturation levels and
synaptic geometry were also important in determining the size and shape
of the distribution of amplitudes recorded at different synapses.
Key words:
synaptic variability; glutamate concentration; saturation; synaptic geometry; computational model; Monte Carlo
methods
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Introduction |
Large variability in the size of
miniature postsynaptic potentials or currents (called "minis")
occurs in most if not all central synapses. Mini amplitudes recorded
from single neurons typically have highly skewed distributions and
coefficients of variation (CV) of ~0.5. If the variability measured
at single synapses is small relative to that of the entire cell, then
most of the variability must be attributable to potency
differences between synapses. However, if the mini distributions
measured at individual sites are similar to that of the entire
population, most of the variability must originate at individual
synapses. Whether mini variability is intersynaptic or intrasynaptic
has not yet been definitively answered (for review, see Auger and Marty, 2000 ). Some studies report highly variable, skewed
distributions of mini amplitudes recorded at single synapses that
suggest that the majority of the variability originates within
individual synapses (Bekkers et al., 1990; Raastad et al., 1992;
Frerking et al., 1995; Liu and Tsien, 1995; Liu et al., 1999;
McAllister and Stevens, 2000). However, others have found mini
amplitudes at single synapses to be less variable and have Gaussian
distributions (Tang et al., 1994; Bolshakov and Siegelbaum, 1995;
Silver et al., 1996; Auger and Marty, 1997; Forti et al., 1997).
Finally, a recent report using minimal stimulation of hippocampal
CA3-CA1 synapses found variability in synaptic variability,
with both skewed high-variability synapses and Gaussian low-variability
synapses in the same preparation (Hanse and Gustafsson, 2001).
Three sources of variability in mini amplitude at single synapses are
proposed. The first source of variability is stochastic fluctuations in
the number of activated postsynaptic receptors and in their open times
(Faber et al., 1992; Franks et al., 2002). Presynaptic factors could
also contribute to quantal variability, but only if the receptors are
not saturated by the release of a single vesicle. Indeed, recent
experiments and models suggest that neither AMPA receptors (AMPARs) nor
NMDA receptors (NMDARs) are saturated after quantal release (Holmes,
1995; Liu et al., 1999; Mainen et al., 1999; McAllister and Stevens,
2000; Franks et al., 2002; Ishikawa et al., 2002). Although presynaptic
release resulted in highly variable, skewed distributions of mini
amplitudes, focal iontophoretic glutamate application in which the
quantal size (q) can be assumed to be nearly constant evoked
currents with little variability and Gaussian distributions (Liu et
al., 1999; McAllister and Stevens, 2000), suggesting that variations in
the quantal content of single vesicles (q) account for
much of the observed variability (Bekkers et al., 1990; Frerking et al., 1995; Liu et al., 1999; Hanse and Gustafsson, 2001). This is the
second main source proposed for mini variability.
Hippocampal neuron active zones are closely aligned with the
postsynaptic density (PSD) and typically contain ~10 readily releasable vesicles distributed across the entire active zone (Dobrunz
and Stevens, 1997; Schikorski and Stevens, 1997, 2001; Murthy et al.,
2001). Single action potentials release, at most, a single vesicle
(Stevens and Wang, 1995; Hanse and Gustafsson, 2001) from one of these
locations (but see Oertner et al., 2002). Therefore, if glutamate
equilibrates nearly instantaneously along the cleft, all release sites
should be equally potent. However, if sizeable neurotransmitter
concentration gradients extend across the synapse from the site of
release, then release from different locations within the active zone
will have different potencies (Uteshev and Pennefather, 1996, 1997).
Thus, the third potential source of synaptic variability is the release
from different sites on the active zone, which we call release-location
dependence (RLD).
Using a biophysically realistic Monte Carlo simulation, we show here
that variability at single synapses can be large enough to account for
observed mini distributions and present plausible mechanistic
explanations for the differences in the size and shape of different observations.
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Materials and Methods |
Monte Carlo algorithms for modeling synaptic transmission have
been described and verified previously (Bartol et al., 1991; Stiles and
Bartol, 2001; Stiles et al., 2001). Molecular glutamate diffusion was
modeled using a three-dimensional random walk. A fixed time step of 1 µsec was used throughout this study. Individual unimolecular or
bimolecular kinetic interactions were handled probabilistically on the
basis of macroscopic rate constants. The primary simulation output used
was the time series of receptor states, including the open-conducting
state (see below). Voltage-clamp conditions are therefore assumed such
that the number of open AMPARs scales directly with the AMPA
postsynaptic current. Rate constants were derived from experiments
conducted at room temperature, which we therefore assume for all
simulations. Simulations were run on a cluster of 933 MHz personal
computer workstations running FreeBSD 4.2. It took ~2 min to
simulate 1 sec of real time. Three-dimensional images of MCell output
were rendered with IBM Data Explorer (available at
http://www.opendx.org) using custom written software (DReAMM; Joel
Stiles, University of Pittsburgh, Pittsburgh, PA; available at
http://www.mcell.psc.edu/DReAMM). Data are presented as mean ± SD.
Synaptic and extrasynaptic geometries. The presynaptic
bouton and postsynaptic spine were modeled as two cubes, 0.5 µm on a
side, and separated by a 20 nm synaptic cleft. The spine was connected
to a 1 × 1 × 4 µm shaft of dendrite by a 0.5-µm-long spine neck (0.2 × 0.2 µm in cross section). The neuropil was
4 × 4 × 4 µm, which was built around these structures,
composed of cuboidal elements (0.5 µm on a side), and packed together
with a 20 nm gap of extracellular space surrounding each element
(Franks et al., 2002).
Channel kinetic parameters. Unless stated otherwise, AMPARs
were uniformly distributed at specified densities on the PSD (a 350-nm-diameter disk-shaped structure on the synaptic face of the
postsynaptic spine). AMPARs were modeled using the reaction scheme and
kinetic rate constants from Jonas et al. (1993) as follws:
Here, C0 is the unbound AMPAR; C1 is the single-bound receptor
intermediate; C2 and O are the double-bound closed- and open-conducting channel conformations, respectively; and C3, C4, and C5 are
desensitized states. KXY is the kinetic
rate for the transition from state X to state Y:
KC0C1, 4.59 × 106
M 1sec1;
KC1C0, 4.26 × 103 sec1;
KC1C2, 2.84 × 107
M1sec1;
KC2C1, 3.26 × 103 sec1;
KC2O, 4.24 × 103 sec1;
KOC2, 900 sec1;
KC1C3, 2.89 × 103 sec1;
KC3C1, 39.2 sec1;
KC3C4, 1.27 × 106
M1sec1;
KC4C3, 45.7 sec1;
KC2C4, 172 sec1;
KC4C2, 0.727 sec1;
KC4C5, 16.8 sec1;
KC5C4, 190.4 sec1;
KOC5, 17.7 sec1; and
KC5O, 4 sec1.
NMDA receptors were modeled using the reaction scheme and
kinetic rate constants from Lester and Jahr (1992) and Jonas et al. (1993) as follows:
The nomenclature for rate constants is the same as that with
which AMPARs were modeled: KC0C1,
1 × 107
M1sec1;
KC1C0, 4.7 sec1;
KC1C2, 5 × 106
M1sec1;
KC2C1, 9.4 sec1;
KC2O, 46.5 sec1;
KOC2, 91.6 sec1;
KC2C3, 8.4 sec1; and
KC3C2, 1.8 sec1. There was no voltage-dependent
block of NMDARs, assuming conditions of 0 Mg2+.
Astroglial glutamate transporters (GluTs) are likely widely and
uniformly distributed throughout the neuropil (Bushong et al., 2002) at
densities ~1000-2000 µm2 (Takahashi
et al., 1996; Lehre and Danbolt, 1998). We have shown that AMPAR
activation is insensitive to the degree of uptake (Franks et al.,
2002), which is consistent with experimental observations (Isaacson and
Nicoll, 1993; Sarantis et al., 1993). For computational expediency, we
therefore placed GluTs on all neuropil elements at a density of 10,000 µm2. A simple three-state mechanism
was used for all transporters, as follows:
where T0 and T1 are the unbound- and bound-transporter states,
respectively, and T2 is an intermediate state in which the bound
glutamate is removed from the simulation. The kinetic rates were as
follows: KT0T1, 1.80 × 107
M1sec1;
KT1T0, 180 sec1;
KT1T2, 180 sec1; and
KT2T0, 25.7 sec1 (Geiger et al., 1999).
Glutamate release. Glutamate was instantaneously released as
a point source in the synaptic cleft. In some simulations, a transmitter was always released from the center of the cleft. In other
simulations, a specified number of release locations were randomly
assigned on a plane of specified area that was parallel to and just
below the presynaptic bouton. DGlu was
0.2 µm2/msec unless otherwise stated. In
one set of simulations, glutamate was released by assuming diffusion of
2000 molecules through a fusion pore. The pore (9 nm in length)
connected a vesicle with a diameter of 35 nm and the cleft, and
expanded at a rate of 25 nm·msec1
(Stiles et al., 1996).
Quantal amplitude distribution. Multiple simulations
(n) were performed for each condition to obtain a histogram
for the number of quantal events with a given peak amplitude. The mean
(m) and SD ( ) of each distribution were computed along
with its skewness and defined as follows:
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(1)
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where µ3 is the third-order moment of
the distribution about the mean.
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Results |
To determine quantitatively the relative contributions of these
three sources of synaptic variability ("channel noise,"
q, and RLD), we have used a Monte Carlo simulation
environment to simulate the activation of postsynaptic AMPA receptors
after the release of a quantum of transmitter. Our simulations followed individual glutamate molecules as they diffused through a spatially complex three-dimensional neuropil. Glutamate was released
instantaneously from a point source in the synaptic cleft, which is the
volume defined by the 20 nm separation between the synaptic faces of the presynaptic bouton and the postsynaptic spine. Synaptic glutamate concentrations decayed rapidly because of diffusion of the cleft and
uptake by GluTs distributed across the extrasynaptic membrane surfaces
of the neuropil, whereas in the synaptic cleft, glutamate could bind to
and activate postsynaptic receptors. These results, and a full
description of the model, have been published previously (Franks et
al., 2002).
We simulated the activation of a round PSD (350 nm diameter) populated
with ~200 AMPARs and 20 NMDARs after quantal release, either from the
center of the active zone or one of 10 randomly assigned release
locations on a 350 × 350 nm plane just adjacent to the bouton
(Fig. 1A).
Vesicle-lumen diameters were selected from a normal distribution
( = 25 nm; v = 3.4 nm)
(Schikorski and Stevens, 1997) and filled to a constant concentration
of 0.406 M (Karunanithi et al., 2002), such that
a vesicle with a lumen diameter of 25 nm contained exactly 2000 glutamate molecules. Ensemble-averaged (n = 1000) EPSCs
were simulated by scaling the number of open receptors by their
single-channel conductance (AMPA, 10 pS; NMDA, 45 pS) and a driving
force of  65 mV, and summing the AMPA and NMDA components. The
resulting EPSC had a large rapid phase mediated primarily (>98%) by
the AMPAR component (Fig. 1Bi), which had a 20-80%
rise time of 90 µsec, a rapid decay that could be fit with a single
exponential ( , 2.6 msec). The smaller slow component of the EPSC was
attributable to the NMDA component (Fig. 1Bii).
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Figure 1.
Simulated miniature EPSCs (mEPSCs) are composed of
AMPA and NMDA components. A, AMPA and NMDA receptors
(red icons) were distributed on the top surface of a spine head (gray
cube). A presynaptic bouton (green) was separated from the spine by a
20 nm synaptic cleft. Synaptic vesicles (yellow) were randomly assigned
above the PSD, on a surface adjacent to the bottom of the PSD (blue).
This structure was embedded within a complex three-dimensional tortuous
neuropil (not shown). B, Ensemble miniature EPSCs
(black) showing the AMPA (i) and NMDA
(ii) components (red).
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Synaptic variability distributions typically describe the maximum of
the EPSC current; thus, for simplicity, we equate mini amplitude with
the peak number of open AMPARs and henceforth do not explicitly
consider the NMDAR-mediated component of the EPSC. Figure
2A shows the high
variability in the number of open AMPARs after transmitter release in
four typical trials. Peak mini amplitude was defined as the greatest
number of channels in the open state during that trial. An average
(AMPA) of 20 AMPARs opened at peak,
with an SD (AMPA) of 12 (CV, 0.58). The
distribution of peak amplitudes (Fig. 2B) was skewed
from the normal (skewness,  = 0.87), and could be fitted using
the following:
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(2)
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where P(x) is the probability that a single
trial will have an amplitude x, and m and are
the mean and variance, respectively, of the peak number of open AMPARs.
This relationship was first used by Bekkers et al. (1990) to fit the
measured distribution of mini amplitudes based on the jitter in vesicle
diameter. The number of open NMDARs was 2.1 ± 1.5 (CV, 0.7), and
the distribution had a skewness of 0.69 (data not shown). Our
simulations therefore reproduce experimental measures of quantal
variability. However, we specifically wanted to determine the
individual contribution of the different sources of variability.
Therefore, we isolated each of the three proposed sources of
variability and examined them in the simulations described below.
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Figure 2.
Distribution of synaptic amplitudes at a single
synapse. A, Typical individual traces (thick traces)
plotted with the ensemble average (thin traces; 1100 simulations
averaged together). B, Normalized distribution of peaks
from all 1000 simulations (100 from each of the 11 release locations).
The solid line is a theoretical fit to the data using Equation 2
(r = 0.977).
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Channel noise
We first examined the variability attributable solely to the
probabilistic nature of postsynaptic receptors and to local differences in the three-dimensional distribution of transmitter molecules resulting from their random walk diffusion. These properties, which we
collectively term channel noise, set an upper limit on the fidelity of
the function of a synapse. Channel noise was estimated by always
releasing a quantum of exactly 2000 molecules from a fixed position
above the center of the PSD. Under these conditions, variability was
dramatically reduced (AMPA, 32;
AMPA, 5.2; CV, 0.16) (Fig.
3A), and the distribution of
mini amplitudes was well fitted with a Gaussian distribution (Fig.
3B), consistent with experiments in which fixed amounts of
glutamate were directly applied to single synapses (Liu et al., 1999;
McAllister and Stevens, 2000). Repeated release of exactly 2000 glutamate molecules from the center of the synapse opened 3.0 ± 1.36 (CV, 0.47) NMDARs. Channel noise therefore accounts for the
majority of the variability when the number of receptors is small.
Other simulations have shown that channel noise decreases with
increases in both quantal size and postsynaptic receptor number, and
channel noise is similar for equal numbers of AMPA and NMDA receptors
(Franks et al., 2002).
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Figure 3.
Noise caused by stochastic flicker of receptors.
A, Examples of four typical individual trials. Raw
traces (thick traces) are plotted with ensemble averages (thin traces;
n = 1000) after release of exactly 2000 glutamate
molecules. B, Distribution of synaptic responses. A
normal distribution could be fit to the data (solid line;
r = 0.995). C, Glutamate (Glu)
concentration in a sampling volume within the synaptic cleft for nine
trials (thin gray traces) plotted with the ensemble average of 1000 trials (thick black trace) shows little trial-to-trial variability.
D, Ensemble average of traces with (black) and without
(gray) desensitization states. Inset, Cumulative histogram of
normalized amplitudes with (black) and without (gray)
variability.
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To determine the amount of the channel noise caused by trial-to-trial
variations in local transmitter concentration, we measured glutamate
concentration in a 0.45 al sampling volume positioned in a quadrant of
the cleft. As might be expected, peak concentration within the volume
showed little variability (91 ± 4.2 µM;
n = 500) (Fig. 3C), suggesting that the
major source of channel noise was stochastic fluctuation between
conducting and nonconducting AMPAR states. The kinetic scheme used to
model AMPARs has three desensitized nonconducting states. Stochastic
fluctuations between these and the open conducting state could decrease
mean peak amplitude and add to channel noise. We therefore ran the
simulation using a kinetic scheme that did not include any desensitized
states. Indeed, removal of the desensitized states increased
AMPA to 35 (n = 500) but did not affect the variability (CV, 0.16) (Fig. 3D), suggesting that most channel noise was caused by
stochastic fluctuations between the C2 (closed state) and the O (open
conducting state) (see below).
A transmitter enters the synaptic cleft after the vesicle fuses with
the presynaptic membrane and a fusion pore allows the passage of the
transmitter into the cleft. Stiles et al. (1996) determined that
transmitter escape from a vesicle could be accurately modeled with
passive diffusion through a fusion pore expanding at 25 nm·msec1. We compared mini variability
in simulations in which glutamate was released as a bolus or as a
function of time (Stiles et al., 1996). Slowing transmitter release
slightly decreased the peak activation of receptors but did not affect
the variability (data not shown). We therefore continued to model
transmitter release as an instantaneous process. Note that jitter in
the opening rate of the fusion pore would increase
AMPA, but investigating this issue is beyond
the scope of this study. Channel noise therefore accounts for a small
but significant amount of total observed variability, primarily
attributable to stochastic fluctuations of double-bound receptors
between the closed- and open-conducting states.
Dependence on quantal size
Variability in transmitter concentration has often been assumed to
be the major source of mini variability at central synapses (Bekkers et
al., 1990; Frerking et al., 1995; Liu et al., 1999; McAllister and
Stevens, 2000; Hanse and Gustafsson, 2001). To determine the amount of
variability caused by variations in q, the release location
was held constant at the center of the active zone, and vesicle-lumen
diameters were randomly drawn from a normal distribution with a mean
(v) of 25 nm and SD
(v) of 3.4 nm. Jitter in vesicle size did not
significantly affect mean quantal size ( ) but
resulted in a wide skewed distribution (skewness, 0.82) of q
that was well fitted by Equation 2 (Fig.
4A). The resulting AMPA, 33, was not significantly
different from release with fixed q, but the mini
distribution was significantly more variable (CV, 0.47;
n = 1000; p < 1010; f test) (Fig.
4B). The mini amplitude distribution was also highly
skewed (0.58) and could also be described by Equation 2. Increasing
v increased the variability and skewness of
both q and the distribution of mini amplitudes (Fig.
4C, Table 1). Note that
, and therefore also
AMPA, systematically increased
with increasing v resulting from the lower
bound of no glutamate molecules in a vesicle.
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Figure 4.
Variability in quantal size contributes to most
synaptic variability. A, B, Distribution
of quantal sizes (A) and resulting synaptic
responses with vesicle-lumen diameters set to 25 ± 3.4 nm
(B; n = 1000). Solid lines are
forced fits of q and mini amplitudes to the distribution
predicted by Equation 2. C, Summary of increasing
synaptic variability plotted against increasing variability in vesicle
diameter. D, Dose-response curves for 200 AMPARs at a
350- nm-diameter PSD. The solid line is an exponential fit to the
data Nopen = 172 × (1 e
q/7400) 8.2.
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The two key assumptions used in the derivation of Equation 2 were that
all vesicles were filled to the same concentration (Karunanithi et al.,
2002) and receptors operated on an approximate linear range of the
dose-response curve (Bekkers et al., 1990). We have explicitly
satisfied the first condition and now test the second. Although release
of different-sized quanta produced a saturating nonlinear
dose-response curve, the relationship was approximately linear in the
range of observed q in the simulations described above (Fig.
4D).
The implications of a linear versus nonlinear dose-response curve are
shown in Figure 5. Two sets of
simulations were run, but now with different vesicle concentrations
such that was set to either ~1000 (Fig.
5Ai) or ~4000 (Fig. 5Bi) and the jitter in
vesicle size was the same (25 ± 3.4 nm). The distributions of
q had similar skewness (~0.8) and variability (CV, 0.40).
If the dose-response relationship of AMPARs was linear for both
conditions, then the distributions of peak amplitudes should have
similar shapes (i.e., same skewness and variability). Instead, we found that the distribution of amplitudes resulting from less-concentrated vesicles was highly skewed and very variable (Fig. 5Aii),
whereas the amplitude distribution from highly concentrated vesicles
was Gaussian with a low CV (Fig. 5Bii) caused by partial
receptor saturation for very large q. Therefore, variations
in quantal size can account for most of the observed variability and
skew in mini amplitude distributions, but the size and shape of the mini distributions depend on the degree of receptor saturation. Importantly, saturation levels did not depend on the size of the postsynaptic receptor pool. Variable-sized quanta (n = 1000) with = 2000 were released at synapses
containing 50 (Fig.
6A), 200 (Fig.
6B), or 800 (Fig. 6C) AMPARs. Note that
the variability, skewness, and saturation levels were primarily
insensitive to the number of receptors on the postsynaptic
membrane.
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Figure 5.
The shape of mini amplitude distributions depends
on vesicle concentration. A, Distribution of
q (i) and peak
(ii) amplitudes for vesicles with
= 1000 glutamate molecules.
B, Distribution of q
(i) and peak (ii)
amplitudes for vesicles with = 4000 glutamate molecules. Solid lines in Ai and
Bi are forced fits to Equation 2. Solid lines in
Aii and Bii are Gaussian fits to the
data. Note that for both cases, the shape of the input
(q) was the same, whereas the shape of the output
(peak number of open AMPARs) was drastically different.
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Figure 6.
The shape of mini amplitude distributions does not
depend on receptor number. A-C, Normalized distribution
of mini amplitude after release at synapses containing 50 (A), 200 (B), and 800 (C) AMPARs after release with variable
q. Solid lines indicate the shape of the forced Gaussian
distribution using the mean and SD of the mini distribution. Data in
B are the same as shown in Figure 3B but
normalized to a mean amplitude of 1. Note that the shape, variability,
and saturation levels were similar at synapses with a large range of
receptors.
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Dependence on release location
We next examined the degree to which transmitter release from
different spatially distinct sites above the PSD contributes to the
total variability. To isolate RLD, q was fixed at 2000, and
we considered only the ensemble averages (100 trials per release site),
thus eliminating channel noise. Figure
7A shows the results for seven
of these locations. Note that the release from the center of the active
zone was most efficacious, and that efficacy decreased with increasing
distance from the center. Figure 7B shows the distribution
of amplitudes for the ensemble averages from 51 different release
locations (release from the center of the active zone and 50 randomly
assigned locations; CV, 0.29; skewness, 0.03). Open probabilities
(Popen) were calculated for a single
receptor located different distances from the release site. Release
immediately above the receptor cluster was most efficacious and
decreased dramatically with increasingly misaligned release events
(Fig. 7C). Receptors were essentially unaffected by release
events >300 nm away, and the signal-to-noise ratio decreased
catastrophically as Popen decreased.
(Receptors >300 nm from the release site had CVs of >2.) Note that
this effect depends on the tangential diffusion constant of glutamate,
and RLD would be greater if the cleft was anisotropic.
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Figure 7.
Synaptic efficacy depends on release location.
A, Schematic representation of the synaptic cleft.
Individual AMPARs (red) were distributed across a 350 nm disk atop the
spine (gray). Release sites were distributed across a flat active zone
350 nm on a side (blue) adjacent to the underside of the presynaptic
bouton (data not shown). Yellow traces represent the ensemble average
of simulations released from a single point, whose location is
indicated by the yellow disks. Each trace is plotted with the ensemble
average from all locations (red traces) for comparison with relative
efficacy. B, Distribution of all peak open AMPARs from
ensemble averages 51 release locations (release from the center, 50 randomly assigned locations). C, Decreasing average
probability of activating individual receptors displaced with
increasing radial distance from the site of release. The solid line is
an exponential fit to the data; Popen = 0.42×er/88 nm, where
r is the radial distance from the center of the PSD.
NMDAR efficacy displayed similar spatially dependent properties, with
an e-fold decrement of ~125 nm (data not shown).
Inset, CV increased with increasing radial distance from the site of
release.
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To further demonstrate the RLD, we rendered snapshots of two
simulations with a release from either the center (Fig.
8A) or edge (Fig.
8B) of the active zone. Figure 8Aa
plots the evolution of single- and double-bound AMPAR states after
central release for a single trial. (Double-bound states include the
double-bound closed state and the open conducting state.) Figure 8,
Ab-Ad, shows these data at 1, 40, and 250 µsec after
release. The observer is looking down on the top of the PSD through the
presynaptic bouton and the synaptic cleft. After release, glutamate
rapidly diffused across and out of the cleft. With central release
events, the number of double-bound receptors increased most steeply 40 µsec after release (20-80% rise time, 40 µsec), by which time glutamate had equilibrated across the synapse (Fig.
8Ac). By the time the number of double-bound
receptors had peaked (250 µsec after release), synaptic glutamate
concentration had dropped dramatically, precluding additional
receptor activation, and double-bound AMPARs were distributed
approximately equally across the PSD (Fig. 8Ad).
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Figure 8.
Differences in receptor activation with central
and peripheral release events. A, Release from the
center of the synapse. a, Evolution of single-bound
(dark blue) and double-bound (red) AMPAR states with release at
t = 0. b, Schematic showing the
synaptic cleft and synaptic face of the postsynaptic cell 1 µsec
after release. Glutamate is indicated by small black spheres. The white
disk shows 350-nm-diameter PSD. AMPARs are 60-nm-diameter pentagonal
structures with state-dependent color coding: single-bound, dark blue;
double-bound, red; all other receptor states, including unbound and
desensitized, light blue. c, Forty microseconds after
release, the transmitter had equilibrated across the synapse and the
number of double-bound receptors increased most steeply.
d, By 250 µsec, most of the transmitter had left the
cleft, and the number of double-bound receptors, distributed uniformly
across the synapse, had peaked. B, Release from the edge
of the synapse. a, Evolution of single- and double-bound
AMPARs states. b, Glutamate distribution 1 µsec after
release from the edge of synapse. c, One-half of the
transmitter had left the cleft, although its distribution was not yet
uniform after 40 µsec. Primarily receptors near the release site were
bound. d, Significantly fewer AMPARs, primarily those
close to the release site, were double-bound 250 µsec after
peripheral release.
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Fewer receptors were double-bound (75%) and the rise-time was slower
(139 µsec) when a transmitter was released from the edge of the PSD
(Fig. 8Ba). A gradient of transmitter still extended across the synapse 40 µsec after release, with little glutamate in
the synaptic quadrant opposite release and double-bound receptors restricted to the regions of the PSD proximal to the release location (Fig. 8Bc). After 250 µsec, the synaptic glutamate
concentration was significantly reduced and most of the double-bound
receptors were proximal to the release location (Fig.
8Bd). To summarize, different release sites on the
active zone have different potencies according to their eccentricity
and can therefore add a significant amount of variability to
both amplitude and rise-time distributions.
Signaling at different-shaped PSDs
Although PSD size and shape vary considerably, active zone and PSD
areas are closely aligned across synapses (Schikorski and Stevens,
1997). It has also been suggested that AMPARs are distributed in an
outer ring around NMDARs, which are clustered in the middle of the PSD
(Kharazia and Weinberg, 1997, 1999), and that PSDs <180 nm in diameter
lack AMPARs (Takumi et al., 1999). To explicitly test the effect of
variations in the size and shape of the PSD/active-zone complex or the
distribution of postsynaptic receptors across the PSD, we examined the
activation of AMPARs using three other PSD/active-zone geometries: a
small, round, 200-nm-diameter PSD; a 100 × 314 nm rectangular
PSD; and a larger round PSD with AMPARs restricted to an outer annulus
(inner diameter, 180 nm; outer diameter, 270 nm) (Fig.
9A) [Schikorski and Stevens
(1997), their Fig. 5]. These geometries were selected such that
receptor densities on all three PSD areas were equal. In all cases, the
active zone extended over the area of the spine occupied by the PSD,
with 20 randomly assigned release locations on each active zone, and
quantal size was held constant at 2000. For the annular PSD, the active
zone extended over both the inner receptor-free and outer
receptor-populated regions of the annulus. Because their distribution
across the active zone was uniform, the mean location of all release
sites was still the center of the active zone.
View larger version (58K):
[in this window]
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|
Figure 9.
Signaling properties with different synaptic
configurations. A, Schematic view of the three synaptic
configurations that were used (from left to right): circular PSD,
rectangular PSD, and annular PSD. Note that all PSD areas and receptor
densities are the same. Twenty release locations were randomly assigned
to the release plane (blue) located just below the presynaptic bouton.
B, Ensemble averages (n = 1000; 50 trials from each location) for the three synaptic configurations.
C, Release-location-dependent variability for the three
synaptic configurations. The data shown are variability in the peak
number of open receptors from the ensemble averages for each of the 20 release locations.
|
|
The distances measured from the center of the release plane to the mean
receptor displacement on the PSD ( values) were as
follows: 200 nm disk PSD, 71 nm; rectangular PSD, 86 nm; annular PSD,
229 nm. These correspond to the average efficacies (n = 400) of the synapses: 200 nm disk PSD
(Popen, 0.20) > rectangular PSD (Popen, 0.16) > annular PSD
(Popen, 0.14) (Fig. 9B).
Note that the efficacy of the small disk PSD was greater than the less
densely populated 350-nm-diameter PSD used previously in the model with the same number of receptors (Popen,
0.093), in which was 124 nm. RLD was lowest at
the annular PSD, slightly larger with the 200-nm-diameter PSD, and
largest with the rectangular PSD (Fig. 9C). Moreover, the
distribution of ensemble averages at the 200-nm-diameter PSD was less
variable (CV, 0.094) than the 350-nm-diameter PSD. This was expected
for more clustered PSD/active-zone complexes given that RLD depends on
variable diffusion distances from release sites to the receptor
population. The difference between mean diffusion path-lengths for each
release site at the annular PSD and either the rectangular PSD or the
350-nm-diameter PSD was smaller, because release sites above the inner
ring of the PSD all have similar values, and thus
explain the low CV at the annular PSD. CV at the rectangular PSD was
highest with randomly assigned release locations with little difference
between release sites distributed along the short axis, but there were large differences between those distributed along the long axis (data
not shown). In conclusion, the geometry of and receptor distribution on
the synapse are important determinants of the shape of mini amplitude distribution.
Noise sources are independent
The variability from the three different sources should be
independent, and summing the variances measured for each source should
equal the variance measured with all sources of variability (i.e., the
variability measured in Fig. 2B). Variability in
q could not be separated from channel noise, and the
variance measured from the raw RLD data (as opposed to the ensemble
averages) also contained the variance from channel noise; thus,
if the three sources of variance were independent then,
|
(3)
|
CV  is the normalized variance
attributable to q with release from a fixed location,
CV  is the normalized variance
of the responses measured from all release locations but with fixed
q, and CV  is the
normalized variance caused by channel noise, in which both release
location and q were fixed. For these simulations,
|
(4)
|
which is consistent with the independent contribution of all three
sources to the total observed variance. Thus, for a 350-nm-diameter synapse with ~200 AMPARs and a mean quantal size of 2000 glutamate molecules, 58% of the variability was caused by variations in quantal
size, 36% of the variability was caused by release from different
sites on the active zone, and 8% of the variability was caused by
channel noise.
| |
Discussion |
Independent sources of variability
Our model used three sources of synaptic variability to reproduce
the distribution of mini amplitudes observed in experiments. These
sources are channel noise, release from spatially distinct locations
within the active zone, and variations in synaptic glutamate concentration. The major source of variability underlying channel noise
was stochastic fluctuations of double-bound AMPARs between conducting
and nonconducting states. Tang et al. (1994) found that cyclothiazide,
which blocks desensitization, reduced the variability of the non-NMDA
components of EPSCs. However, cyclothiazide also increases the
glutamate affinity of the receptors leading to AMPAR saturation, which
can explain the dramatic reduction in variability. Blocking
desensitization in our model did not lead to a significant reduction in
quantal variability, suggesting that the results obtained by Tang et
al. (1994) were primarily caused by cyclothiazide-induced receptor saturation.
The largest source of variability at single synapses was caused by the
release of variable amounts of transmitter. We assumed that the
concentration of transmitter was constant across vesicle diameter,
which is supported by genetic experiments with Drosophila in
which there was a linear relationship between quantal size and
vesicular volume (Karunanithi et al., 2002). Because variation in
vesicle diameters produced a third-power variation in vesicle volume,
and therefore q, a normal distribution of vesicle diameters produced a positively skewed distribution of open AMPARs that increased
with the amount of jitter in vesicle diameter, but only when receptors
were not saturated. These results are consistent with distributions of
mini amplitudes measured at many single central glutamatergic synapses
(Bekkers et al., 1990; Raastad et al., 1992; Liu and Tsien, 1995; Liu
et al., 1999; McAllister and Stevens, 2000; Hanse and Gustafsson,
2001).
However, a clear understanding of the nature of quantal variability has
proved elusive, because action potential-evoked synaptic currents at
excitatory synapses have also produced Gaussian distributions (Bolshakov and Siegelbaum, 1995; Forti et al., 1997), and recently, both skewed and Gaussian distributions have been reported at different synapses in the same preparation (Hanse and Gustafsson, 2001). An
important advantage of our model is the ability to specify and isolate
the sources of variability. In particular, action potential-evoked
responses may have small signal-to-noise ratios in which the
contamination of a non-Gaussian signal with a large Gaussian noise
component might give an appearance of a Gaussian signal. An alternative
physiological explanation for Gaussian distributions may be caused by
receptor saturation. Hanse and Gustafsson (2001) observed that the
synapses that had low CVs tended to be of larger amplitude, more
saturated, and have Gaussian distributions similar to those reported by
Tang et al. (1994) and Forti et al. (1997), whereas those that had high
CVs tended to have smaller mean amplitudes, be less saturated, and have
highly skewed distributions.
What determines the degree of saturation at a given synapse? Simply,
larger synapses with more receptors may be less saturated than smaller
synapses with less receptors, but this argument is inconsistent for two
reasons. First, previous modeling studies have shown that saturation
levels depend primarily on quantal size and are primarily independent
of the number of receptors (Faber et al., 1992; Holmes, 1995; Franks et
al., 2002). Second, synapses with fewer receptors would be less potent
and more variable, contrary to the results of Hanse and Gustafsson
(2001). Alternatively, our simulations show that
synapse-to-synapse variations in the mean glutamate concentration in
vesicles can account for these observations. Specifically, we have
shown that for vesicles with low transmitter concentrations, skewed
distribution of vesicle volumes resulted in low potency, highly
variable, and skewed distributions of responses. However, for high
vesicle glutamate concentration, the activation of synaptic receptors
by the tail of very large values in the skewed distribution of
q was compressed because of receptor saturation, resulting
in response amplitudes with a low CV and a Gaussian distribution.
Interestingly, increasing vesicular transmitter concentration, either
by overexpression of vesicle transporters at a cholinergic synapse
(Song et al., 1997) or by increased loading of a transmitter into
vesicles by raising cytoplasmic glutamate concentration (Ishikawa et
al., 2002), resulted in increased mean receptor activation with
narrower, less-skewed amplitude distributions. Evers et al. (1989) also
observed that spontaneous synaptic currents at developing neuromuscular
junctions were initially small with large skewed distributions, whereas
more mature synapses showed larger synaptic currents whose
distributions were less variable and more Gaussian. However, they were
unable to determine whether this was attributable to differences in
q or the extent of close membrane apposition near the
release sites. Thus, differences in either synaptic maturation or
vesicle filling could explain the different distributions reported by
Hanse and Gustafsson (2001) or the large Gaussian distributions reported by Forti et al. (1997). Note also that Forti et al. (1997) recorded from synapses with large elliptical presynaptic varicosities (longitudinal diameter, 1.67 ± 0.60 µm), suggesting that these synapses contained multiple active zones (see below). Occasional simultaneous release of multiple vesicles from these large synapses would result in a large mean response with a high variance but a low CV
and a Gaussian distribution.
Implications of RLD
Although the total active zone area per bouton is linearly related
to the volume of the presynaptic bouton (Streichert and Sargent, 1989;
Yeow and Peterson, 1991; Pierce and Mendell, 1993; Schikorski and
Stevens, 1997), the size of individual active zones is typically <0.2
µm2 and almost never exceeds 0.4 µm2 (Yeow and Peterson, 1991; Schikorski
and Stevens, 1997). Larger boutons appear to produce multiple small
active zones rather than a single large one, suggesting that larger
active zones might not function optimally (Schikorski and Stevens,
1997). We found a dramatic decrease in both the activation and
signal-to-noise ratio of receptors, located increasing distances from
the release site, and that AMPARs >300 nm from the release site were
unable to reliably detect release events. These findings confirm a
previous analysis of concentration gradients across the active zone
(Uteshev and Pennefather, 1997). The more distant release leads to
smaller peak concentrations of glutamate at the AMPARs, thus activating a smaller fraction of them. Thus, the small size and close association typical of the active zone/PSD complex (Schikorski and Stevens, 1997)
suggest that most receptors are able to reliably detect release events
from anywhere on the active zone.
The dynamic regulation of AMPARs has been proposed as a cellular
mechanism to explain long-term synaptic plasticity (Malinow and
Malenka, 2002), and surface expression of AMPARs at central spinous
synapses is constrained to the PSD (Kharazia et al., 1996; Nusser et
al., 1998; Takumi et al., 1999). This allows two methods for regulating
receptor number: receptors can either be inserted or removed from
predefined slots in a PSD of fixed size, thus changing receptor
density, or the size of the PSD can shrink or expand to accommodate
AMPAR removal or insertion, thus maintaining a fixed receptor density.
The latter is consistent with electron microscopy studies (Nusser et
al., 1998; Takumi et al., 1999) and the observation that bigger
synapses produce bigger responses (Andrasfalvy and Magee, 2001;
Matsuzaki et al., 2001). Our simulations predict that the density and
spatial arrangement of receptors at the synapse are important
determinants of receptor activation. Because release sites are
distributed above the postsynaptic area on which receptors are located,
smaller denser synapses will be more efficacious than larger ones with
the same number of receptors. Synapse potency is linearly related to
receptor density (Franks et al., 2002). However, for constant receptor
density, increasing the receptor number requires increasing the synapse
size, which decreases the average receptor efficiency for a given
release event. Thus, a sublinear relationship describes receptor number and activation for constant receptor density and predicts a decrease in
average receptor efficacy with receptor insertion.
Our results show that release events from the side of the active zone
are less potent than those from the center. If the presynaptic Ca2+ sensor responsible for release is located very close
to the Ca2+ channel(s) and/or mobile Ca2+
buffers sharply narrow the distribution of high Ca2+
(Sabatini et al., 2001), release locations should be independent. However, if Ca2+ enters the terminal from
multiple channels distributed uniformly in the active-release zone and
the buffering is weak, the elevated Ca2+
merges at the central release sites, which have higher probabilities than peripheral ones. Thus, in stimulus trains designed to deplete storage pools, higher probability central release sites should release
first, producing an average decrease in potency with increasing stimulus number. However, no change in average potency was seen under
these conditions (Dobrunz and Stevens, 1997; Hanse and Gustafsson, 2002), suggesting that release sites were independent. There is evidence at the calyx of Held for multiple clusters of Ca2+
channels over a range of distances from the release sites of the
vesicles (Meinrenken et al., 2002).
Minimal stimulation paradigms are designed to stimulate only one axon
that makes contact with a postsynaptic cell at a single synapse.
However, the synapse is likely to have ~10 docked vesicles that are
presumably located at the position from which they can be released.
Careful titration of Clostridium toxins could reduce the
number of functional release sites until, ideally, a single docking
site remains, and the distribution of evoked amplitudes could be
measured under these conditions. RLD predicts that evoked PSCs under
these conditions should be smaller than controls.
In conclusion, we have produced a biophysically realistic model of
postsynaptic receptor activation at an idealized central glutamatergic
synapse that reproduces experimentally observed variations in synaptic
responses recorded from single glutamatergic synapses. Although our
simulations demonstrate that the site of transmitter release can affect
synaptic efficacy, we confirm that variations in synaptic glutamate
concentration, arising from anatomically constrained measures of jitter
in vesicle diameter, are sufficient to account for the majority of the
observed variance and distribution skewness. However, some of the key
assumptions underlying our results need to be tested; in particular,
the variation of transmitter concentration among vesicles could also
contribute to the observed variability in quantal amplitudes.
| |
FOOTNOTES |
Received Nov. 14, 2002; revised Jan. 21, 2003; accepted Jan. 22, 2003.
This work was supported by the Howard Hughes Medical Institute and the
National Science Foundation. We thank Thomas Bartol for technical
assistance and Jeffry Isaacson and Richard Weinberg for reading
a previous version of this manuscript.
Correspondence should be addressed to Terrence J. Sejnowski,
Computational Neurobiology Laboratory, The Salk Institute, 10010 North
Torrey Pines Road, La Jolla, CA 92037. E-mail: terry{at}salk.edu.
K. M. Franks's present address: Department of Neurosciences,
University of California, School of Medicine, La Jolla, CA 92093.
| |
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TOP
ABSTRACT
Introduction
Compound via MeSH
