Evaluation of glutamate concentration transient in the synaptic cleft of the rat calyx of Held

Abstract

Establishing the spatiotemporal concentration profile of neurotransmitter following synaptic vesicular release is essential for our understanding of inter-neuronal communication. Such profile is a determinant of synaptic strength, short-term plasticity and inter-synaptic crosstalk. Synaptically released glutamate has been suggested to reach a few millimolar in concentration and last for <1 ms. The synaptic cleft is often conceived as a single concentration compartment, whereas a huge gradient likely exists. Modelling studies have attempted to describe this gradient, but two key parameters, the number of glutamate in a vesicle (N_Glu) and its diffusion coefficient (D_Glu) in the extracellular space, remained unresolved. To determine this profile, the rat calyx of Held synapse at postnatal day 12–16 was studied where diffusion of glutamate occurs two-dimensionally and where quantification of AMPA receptor distribution on individual postsynaptic specialization on medial nucleus of the trapezoid body principal cells is possible using SDS-digested freeze-fracture replica labelling. To assess the performance of these receptors as glutamate sensors, a kinetic model of the receptors was constructed from outside-out patch recordings. From here, we simulated synaptic responses and compared them with the EPSC recordings. Combinations of N_Glu and D_Glu with an optimum of 7000 and 0.3 μm² ms⁻¹ reproduced the data, suggesting slow diffusion. Further simulations showed that a single vesicle does not saturate the synaptic receptors, and that glutamate spillover does not affect the conductance amplitude at this synapse. Using the estimated profile, we also evaluated how the number of multiple vesicle releases at individual active zones affects the amplitude of postsynaptic signals.

Key points

• Spatiotemporal glutamate concentration profile in the cleft is a determinant of the EPSC amplitude and time course.

• Two key parameters required to describe this profile are the number of glutamate in a vesicle (N_Glu) and its diffusion coefficient (D_Glu), both of which are unestablished.

• Using the rat calyx of Held synapse as a model, the distribution of AMPA receptors was mapped with SDS-digested freeze fracture replica labelling and their performance as glutamate sensors was evaluated with outside-out patch recordings.

• Based on these data, synaptic responses were simulated using various combinations of N_Glu and D_Glu, and an optimal range of the N_Glu–D_Glu combinations that could reproduce the recordings was determined.

• Using the estimated profile, we show that release from a single vesicle does not saturate the receptors, glutamate spillover does not affect the synaptic conductance amplitude, and synaptic response increases non-linearly with the number of multivesicular releases.

Introduction

Transmitters released from a vesicle prevalently serve as a medium for transferring signals from one cell to the other. What is unclear is the number of transmitter molecules in a vesicle and how fast they diffuse through the extracellular space once the vesicle undergoes exocytosis. Rapid neuronal communication is generally assumed to be realized locally at synapses. Spatiotemporal profile of the transmitter concentration within the synaptic cleft is one of the major factors determining the amplitude and time course of signal transfer between neurons. One of the issues that needs clarification is whether the release from a single vesicle can provide high enough concentration of transmitter to saturate all of the postsynaptic receptors or not (Tang et al. 1994; Frerking & Wilson, 1996; Liu et al. 1999; Ishikawa et al. 2002; Yamashita et al. 2009). If the postsynaptic receptors are saturated with just a single vesicle release, the magnitude of signal transfer would be binary and the occurrence of the transfer depends solely on the presynaptic release. However, graded levels of signals could be transferred depending on the number of synchronously released vesicles if the postsynaptic receptors are not saturated. Reports suggest that more than one vesicle can be released within each active zone in response to a presynaptic action potential firing at many synapses (Tong & Jahr, 1994; Wadiche & Jahr, 2001; Oertner et al. 2002; Taschenberger et al. 2002). If the spatiotemporal profile of transmitter transient from a single vesicle is resolved, we would be able to understand how the signals from individual vesicle releases within each active zone would summate. In addition, accumulating evidence shows that synaptic transmitter can escape from the release site and affect the neighbouring synapses, a phenomenon termed ‘spillover’ (Trussell et al. 1993; Barbour & Häusser, 1997; Matsui et al. 1998; Budisantoso et al. 2012). Evaluation of the existence and extent of such spillover is important because it would answer whether the independence of signal transmission at each synapse is violated or not.

To determine the spatiotemporal profile of the neurotransmitter glutamate, we chose a simple structure, the calyx of Held synapse. Here, a large presynaptic terminal encapsulates the postsynaptic soma, which limits synaptically released glutamate to diffuse in a narrow space sandwiched by a presynaptic and a postsynaptic plasma membrane. This space could be approximated as a two-dimensional disk with a width of ∼20 nm, and thus a simple analytical solution to the diffusion equation can be applied to estimate the glutamate concentration profile. Current flowing through the postsynaptic AMPA receptor-channels (AMPARs) can reliably be recorded with little distortion compared with synapses at distal dendrites. The receptors on the soma were excised by outside-out patches, and their kinetics in response to various agonist and antagonist applications were characterized. Then we constructed a kinetic model of the AMPARs that act as glutamate sensors. Another advantage of studying this synapse is the shallow curvature of the postsynaptic membrane. This allowed the collection of large continuous profiles of the postsynaptic membrane in freeze-fracture replicas, which would otherwise be impossible. The two-dimensional distribution of the AMPARs within and outside synapses was then assessed by SDS-digested freeze-fracture replica labelling (SDS-FRL). Knowing the space where transmitter diffusion occurs, the performance and distribution of the postsynaptic receptors and the final outcome of the synaptically evoked responses, we attempted to fill in the gap in between, which is the glutamate concentration profile in the synaptic cleft.

Methods

Ethical approval

All procedures in this study were performed according to the Guidelines for Care and Use of Laboratory Animals of the Physiological Society of Japan. Experimental protocols were reviewed and approved in advance by the Institutional Animal Care and Use Committee of the National Institutes of Natural Sciences.

Electrophysiology

Brain slices containing the medial nucleus of the trapezoid body (MNTB) were prepared from young Wistar rats (P12–P16). The animals were anaesthetized by inhalation of halothane before decapitation, and the brain was sliced in ice-cold solution containing (in mm) sucrose, 238; KCl, 2.5; CaCl₂, 0.1; MgCl₂, 3.2; NaH₂PO₄, 1.0; NaHCO₃, 26.2; glucose, 11; myoinositol, 3; sodium pyruvate, 2; ascorbic acid, 0.5 (saturated with 95% O₂–5% CO₂). Slices were cut at 150 μm using a microslicer (PRO7; Dosaka EM, Kyoto, Japan). The slices were then incubated in the above solution with sucrose substituted with 119.0 NaCl and with CaCl₂ and MgCl₂ concentrations substituted to 2.0 mm and 1.3 mm, respectively, at 34°C for 30 min and then stored at room temperature. During the recording, the slices were superfused with the latter solution at room temperature (22–25°C) with the addition of 100 μm picrotoxin and 0.5 μm strychnine hydrochloride to block inhibitory GABAergic and glycinergic synaptic responses, and 50 μm d-(−)-2-amino-5-phosphonopentanoic acid (d-AP5) to block NMDA receptors. When recording miniature EPSCs (mEPSCs), TTX (0.5 μm) was added. In experiments where extracellular divalents were varied, total divalent concentration was kept constant, except for 4 mm Ca²⁺ where 0.5 mm Mg²⁺ was also included.

Whole-cell voltage-clamp recordings were made from visually identifiable postsynaptic MNTB neurons (40× water immersion objective, Olympus upright microscope BX51WI, Tokyo, Japan) using Axopatch 200B patch-clamp amplifier (Molecular Devices, Sunnyvale, USA). Patch electrodes with resistances of 2.5–3.5 MΩ were used with the pipette solution with the following composition (in mm): CsF, 35; CsCl, 100; Hepes, 10; EGTA, 10; pH 7.2 titrated with CsOH. Holding potentials were corrected for the liquid junction potential of −7 mV. Series resistance was typically 5–10 MΩ and was compensated ∼70–80%. Signals were filtered at 2 kHz and digitized at 50 kHz with Digidata 1322A using pClamp 8 acquisition software (Molecular Devices). Electrophysiological data analysis was performed with AxoGraph X (AxoGraph Scientific, Sydney, Australia).

mEPSCs were detected using the template method in AxoGraph X followed by visual inspection. Minimum amplitude of 15–20 pA was typical for the detected mEPSC recordings. EPSCs were evoked by stimulating the presynaptic axon fibre bundles with a bipolar platinum electrode placed near the midline of the slice (10–90 V, 100 μs; used in constant voltage mode; ISO-Flex; A.M.P.I). EPSCs derived from the calyx of Held synapse were identified as those evoked in an all-or-none manner for a graded stimulus intensity and those having amplitude >1 nA at −77 mV (Forsythe & Barnes-Davies, 1993). Stimulus intensity was minimized to accomplish single fibre stimulation.

In outside-out patch experiments, a theta glass flow-pipette mounted on a piezoelectric bimorph was used for rapid agonist/antagonist applications (Jonas, 1995; Matsui et al. 2005). The external solution used in flow-pipettes contained the following (in mm): NaCl, 140.0; CaCl₂, 2.0; MgCl₂, 1.3; Hepes, 5.0; pH adjusted to 7.4 with NaOH. d-AP5 (50 μm) was routinely included to block NMDA receptors. To measure the kinetic properties of AMPARs, excised patches were perfused continuously with control solution flowing from one barrel and rapidly switched to the other barrel with the same solution containing glutamate with or without 2 mmγ-d-glutamylglycine (γDGG) for a designated time. In other words, the control solution never contained γDGG and γDGG was applied along with glutamate. Therefore, upon solution exchange, the receptor initially transits from totally unbound state to either agonist or antagonist bound states, and such race experiments are often used to understand the structure and rates of a kinetic model (Wadiche & Jahr, 2001). Where race experiments were performed, responses to glutamate alone and responses to glutamate with γDGG were always obtained from the same patches. The simulated responses were obtained using the same race experiment situation. However, it should be noted that in order to simulate γDGG blockade to synaptically released glutamate, the kinetic model was pre-equilibrated with γDGG to reproduce the experimental condition. Solution exchange time was measured after each experiment by rupturing the patch, and the junction currents across the open pipette tip were recorded. For measuring the deactivation kinetics, a very brief pulse of glutamate was applied with a half-width time of 350 μs, and the 20–80% rise and decay times of the solution exchange were 130 μs and 140 μs, respectively. For all other patch recordings, the application time was 10 ms with a 20–80% rise and decay time of 130 μs. Patch experiments were also performed at room temperature.

The sources of the chemicals were as follows: glutamate, picrotoxin and strychnine were from Sigma-Aldrich (St. Louis, USA); TTX and γDGG were from Tocris Bioscience (Bristol, UK); d-AP5 was from Ascent Scientific (Bristol, UK).

SDS-FRI

Wistar rats at P14 and 11-week-old Long–Evans rats were anaesthetized with sodium pentobarbital (50 mg kg⁻¹, i.p.) and perfused transcardially with 25 mm PBS for 1 min, followed by perfusion with 2% paraformaldehyde and 15% saturated picric acid solution in 0.1 m phosphate buffer (PB) at pH 7.4 for 12 min. Coronal slices (130 μm thick) were cut using a microslicer (PRO7) in 0.1 m PB. A region of the MNTB and dorsal lateral geniculate nucleus (dLGN) was trimmed from the slice of the Wistar rat and Long–Evans rat, respectively. The trimmed slices were immersed in 30% glycerol/0.1 m PB at 4°C overnight and frozen by a high-pressure freezing machine (HPM010; BAL-TEC, Balzers, Liechtenstein). Frozen samples were then fractured into two parts at −140°C and replicated by deposition of carbon (5 nm thick), platinum/carbon (uni-direction from 60 deg, 2 nm) and carbon (20 nm) in a freeze-fracture replica machine (BAF 060; BAL-TEC). After thawing, tissue debris attached to the replicas was removed with gentle rocking at 80°C for 18 h in a solution containing 15 mm Tris-HCl (pH 8.3), 20% sucrose and 2.5% SDS. The replicas were then washed in 50 mm Tris-buffered saline (pH 7.4) containing 0.05% BSA and blocked with 5% BSA in the washing buffer for 1 h at room temperature. The replicas were incubated with a rabbit primary antibody against GluA1–4 (panAMPAR; E. Molnár, School of Medical Science of the University of Bristol, Bristol, UK) two overnights at 15°C, followed by incubation with anti-rabbit secondary antibody conjugated with 5 nm gold particles (British Biocell International; BBI, Cardiff, UK) overnight at 15°C. The labelled replicas were examined by using a transmission electron microscope (Tecnai-12; FEI, Hillsboro, USA).

Quantification of immunoparticles was done as follows. Images of excitatory postsynaptic specialization identified by the presence of intra-membrane particle (IMP) clusters on the exoplasmic face (E-face) were captured at a magnification of 135,000× with a digital camera (Veleta, Olympus-Soft Imaging System; OSIS). Multiple IMP clusters on a continuous large E-face of a soma indicate MNTB postsynaptic specializations (Fig. 3A). The retinogeniculate postsynaptic specializations in the dLGN were recognized by their typical dense IMP cluster morphology (Tarusawa et al. 2009). The diameter of each E-face IMP apparently associated with panAMPAR immunolabelling was approximately ∼14 nm, and the synaptic E-face IMP clusters, defined as densely packed IMPs at a distance of <14 nm from each other, were demarcated freehand. The size of IMP cluster demarcated by this method was comparable to that of the postsynaptic densities (PSDs) visualized in conventional ultrathin sections and, thus, the demarcation likely represents the extent of postsynaptic specialization well (Tarusawa et al. 2009). The geometrical centroid, also referred as the centre of gravity in this article, was calculated from the shape of the demarcation using iTEM software (OSIS). The areas of these demarcated IMP clusters were also measured. Data from only the complete synapses, where the whole IMP cluster is visible within a continuous fractured plane, were collected from the MNTB. Immunoparticles within a demarcated IMP cluster and those located outside but within 30 nm from the edge of the IMP cluster were regarded as synaptic labelling, considering possible deviation of the immunoparticles from antigens (Budisantoso et al. 2012). Immunolabelling efficiency in the current study was estimated by comparing the immunoparticle density in the retinogeniculate synapses using the current batch of the antibody with the published immunoparticle density measurements obtained in the same synapses, with the same labelling procedures, but using the previous batch (Tarusawa et al. 2009). A calibration factor for the AMPAR labelling efficiency with the current batch of the antibody was obtained based on this comparison.

Figure 3. AMPAR number and distribution of the MNTB synapse.

A, an SDS-FRL image of a large portion of the somatic membrane of the MNTB principal cell. The postsynaptic exoplasmic face (E-face) of the somatic membrane (green) contained multiple IMP clusters representing the glutamatergic postsynaptic densities (PSDs; blue). It also contained several ruptured spots where the corresponding presynaptic protoplasmic face (P-face) membrane was exposed (orange). A cross-fracture of the presynaptic structure indicates the cytoplasm (dark red). B, detailed image of the three highlighted areas. Multiple vesicles (SVs; black arrowheads) were identified in the cross-fractured presynaptic terminal. C, a characteristic IMP cluster on the postsynaptic E-face (demarcated with blue line) labelled for AMPARs (with 5 nm gold particles). D, AMPAR labelling positively correlated with the area of synapses (n= 59 complete synapses). The average synaptic area (CV = 0.60 and 0.78), and the average synaptic number (CV = 0.59 and 0.59) and density of the immunoparticles (with calibration: grey bars) from 2 animals. E, intrasynaptic distribution of AMPARs in a synapse area divided into 5 divisions of equal width using the distance map. An extra division with 30 nm width on the outer rim was added. F, particle density in each division was averaged across all synapses and also calibrated (grey bars). Very few particles were found in the extrasynaptic region (5.8 ± 0.6 particles μm⁻²). One-way repeated-measures ANOVA followed by pairwise comparisons were used. G, concentric rings of 10 nm bins from the centre of gravity of each synapse were defined. H, based on this map, the average AMPAR immunoparticle distribution (with calibration: grey bars) from the centre of gravity was tabulated (n= 65 synapses from one animal). *P < 0.05. Error bars indicate SEM.

AMPAR immunoparticle distribution within the IMP cluster was evaluated by making a distance map (Fig. 3E) from the demarcated border using FIJI software (distributed under the General Public License, GPL). The grey-scale values correspond to the nearest-neighbour distance (NND) of each pixel from the border with the lighter values corresponding to the longer distances. Using this distance map, the IMP cluster area was divided into five equal distances from the border. An additional division outside of the demarcation (outer rim) with 30 nm width was also created to take into account the possible spatial deviation of the immunoparticles from the antigen. Immunoparticle location in this distance map was extracted and the density of immunoparticles falling into each division was tabulated.

Simulations

To simulate synaptic AMPAR responses to releases of glutamate, glutamate diffusion was calculated, and the AMPAR kinetic model described in Fig. 2 was run against the calculated glutamate transient (Tarusawa et al. 2009). Instantaneous release of glutamate was assumed, and the glutamate concentration in the extracellular space as a function of time and distance from release was calculated using the analytical solution to the diffusion equation in a two-dimensional space as below (Uteshev & Pennefather, 1996; Budisantoso et al. 2012):

Figure 2. AMPAR kinetic model simulating AMPAR currents in outside-out somatic patches from the MNTB principal cell.

A, kinetic scheme of the AMPAR model. Rates were as follows (units are m⁻¹ s⁻¹ for k₁, k₂, k₃, k₁₁, k₁₂, k₁₃, k₁₄, and s⁻¹ for the rest): k₁= 18.412 × 10⁶, k₋₁= 4.323 × 10³, k₂= 4.000 × 10⁶, k₋₂= 17.201 × 10³, k₃= 19.863 × 10⁶, k₋₃= 1.168 × 10³, β= 51.690 × 10³, α= 10.082 × 10³, k₄= 885.990, k₋₄= 280.350, k₅= 449.033, k₋₅= 1.944, k₆= 2.797, k₋₆= 39.497 × 10⁻³, k₇= 1.380 × 10³, k₋₇= 421.849, k₈= 848.141, k₋₈= 538.920, k₉= 51.700, k₋₉= 29.164, k₁₀= 939.000, k₋₁₀= 24.463, k₁₁= 105.000 × 10⁶, k₋₁₁= 14.400 × 10³, k₁₂= 26.250 × 10⁶, k₋₁₂= 57.600 × 10³, k₁₃= 92.007 × 10⁺³, k₋₁₃= 4.323, k₁₄= 875.000 × 10⁺³, k₋₁₄= 24.000. B, AMPAR deactivation and desensitization kinetics of patch recordings (Patch) and simulations (Model) exposed to 10 mm glutamate. Deactivation time constant (τ_deact) of Patch and Model is 0.41 ± 0.03 ms (n= 19) and 0.41 ms, respectively. Desensitization time constants and the relative portion of fast constants of Patch were: τ_fast= 0.65 ± 0.04 ms, τ_slow= 2.72 ± 0.28 ms, %fast = 69.2 ± 3.4, τ_weighted (τ_w) = 1.20 ± 0.06 ms (n= 30). Model: τ_fast= 0.71 ms, τ_slow= 2.14 ms, %fast = 62.1, τ_w= 1.25 ms. C, non-stationary noise analysis of the decaying phase during desensitization of the patch responses to 10 mm glutamate (open tip: top trace). Middle trace is the average AMPAR response (dark) of 49 sweeps (grey) with the corresponding ensemble variance shown below. The variance was plotted against the mean current from the same sample patch. A parabolic function was fitted from which the single channel conductance (γ), maximum open probability (P_Omax) and number of channels were deduced (for this patch: γ = 26.4 pS; P_OMax= 0.64; 38 channels). Summarized are the average γ and P_OMax (21.4 ± 1.1 pS (n= 19), P_OMax= 0.61 ± 0.02 (n= 13)). The model produced a P_OMax of 0.61. D, Patch and Model responses to paired 10 ms pulses of 10 mm glutamate with different intervals. Recovery from desensitization was plotted (n= 12). Double exponential curve fit to the PPR recovery with rates as follows: Patch, τ_fast= 20.1 ms, τ_slow= 58.7 ms, %fast = 62.3, τ_w= 34.7 ms; Model, τ_fast= 21.9 ms, τ_slow= 50.0 ms, %fast = 63.9, τ_w= 32.1 ms. E, Patch and Model responses to different concentrations of glutamate. Dose–response relationship of the normalized peak current was plotted. Hill coefficient and EC₅₀ were, respectively, 1.20 and 1242 μm for the Patch (n= 5–12), and for the Model 1.37 and 1343 μm. F, recorded and simulated traces activated by two pulses (duration = 10 ms, interval = 20 ms) of 2 mm or 4 mm glutamate in the presence and absence of 2 mmγ-d-glutamylglycine (γDGG). Application of γDGG blocked the patch current of the first pulse by 71.4 ± 1.8% (n= 9; Model: 70.2%) when combined with 2 mm glutamate. When combined with 4 mm glutamate, the block became 52.6 ± 1.2% (n= 10; Model 54.0%). Errors bars indicate SEM.

where r is the distance from the release site, t is the time from release, h is the width of the extracellular space, N_Glu is the number of glutamate molecules in a vesicle and D_Glu is the diffusion coefficient of glutamate in extracellular space. The calyx of Held can be considered as a large parallel arrangement of multiple active zones aligned to the postsynaptic membrane. Thus, the extracellular space between the presynaptic and postsynaptic membrane was regarded as a plane with no gaps or glial elements with a cleft width of 20 nm (Savtchenko & Rusakov, 2007). The effect of the reduction of free glutamate by the binding of glutamate to AMPARs was not considered as the estimated N_Glu was two-orders of magnitude larger (∼7000) than the number of AMPARs present within a synapse (∼70). Time steps for AMPAR simulations were set to 0.5 μs. Based on N_Glu and D_Glu, the glutamate concentration profile at each receptor location was calculated using the Excel software (Microsoft). An AMPAR kinetic model (Fig. 2A) was run against the glutamate transients to calculate the open probability (P_O) of individual AMPARs using AxoGraph X.

Statistical analysis

Values in text and graph are mean ± SEM. Excel and SPSS (IBM) were used for statistical analysis. One-way ANOVA with post hoc Tukey's test was used for Fig. 1E; one-way repeated-measures ANOVA followed by pairwise comparisons was used for Fig. 3F. Statistical significance with P < 0.05 was expressed as an asterisk in the figures.

Figure 1. Amplitude of AMPAR currents in the absence and presence of γ-d-glutamylglycine (γDGG).

A, spontaneous AMPAR-mediated miniature (m)EPSCs in the presence of 50 μm d-AP5, 100 μm picrotoxin, 0.5 μm strychnine and 0.5 μm TTX in 2 mm[Ca²⁺]_o. B, collected mEPSCs were aligned (grey) and averaged (black). mEPSC amplitude and baseline noise (open and grey bars, 2 pA and 0.2 pA bins, respectively) are plotted in histograms shown below. CV of the peak amplitude was 0.36 for this recording and 0.38 ± 0.02 for all recordings (n= 21). C, summary of average mEPSC amplitude (n= 21). D, recordings of evoked EPSCs normalized at different [Ca²⁺]_o from four cells. Note that the y-axis scale bar is different for each recording. The amount of block after application of 2 mmγDGG varied depending on the P_r. E, the average block by γDGG was plotted against the [Ca²⁺]_o (n= 7–11). *P < 0.05. Error bars indicate SEM.

Results

The amplitude and the γDGG block of the postsynaptic currents produced by synaptically released glutamate

Exocytosis of a synaptic vesicle creates a glutamate transient in the synaptic cleft that in turn activates the postsynaptic AMPARs. This leads to a current flowing through these receptor-channels, which could be detected using whole-cell patch-clamp recording under voltage-clamp mode. Our strategy was to record the EPSC and back-calculate the glutamate transient that caused such current. First, EPSCs in response to single vesicle releases were measured as mEPSCs. Sporadic presynaptic action potential firing that triggers concerted release of multiple vesicles was blocked with TTX (0.5 μm). In this condition, quantal releases of vesicles are considered to occur spontaneously and the resulting mEPSCs were recorded from principal neurons in the MNTB (Fig. 1A). The mean amplitude of the mEPSCs was 41.0 ± 1.8 pA (Fig. 1B and C; n= 21). This quantal size is consistent with several previous studies using the same species at a similar age (Ishikawa et al. 2002; Joshi et al. 2004). Simulations shown later would try to match the amplitude of the recorded mEPSCs.

We also used the amount of block of the evoked EPSC by a low-affinity antagonist for AMPARs, γDGG, as a clue for the estimation of the glutamate transient. It has been shown that the block of the postsynaptic currents by a low-affinity competitive antagonist with rapid dissociation rates depends both on the concentration and the time course of the liberated transmitter transient in the extracellular space (Clements et al. 1992; Diamond & Jahr, 1997; Beato, 2008; Karayannis et al. 2010). For example, if the time course of the concentration transient is the same, the block is generally expected to be higher for lower transmitter concentration transients and lower for higher transmitter concentration transients because high transmitter concentration would compete out the antagonist during the time course of the postsynaptic current. A reliable value of the γDGG block is difficult to obtain from the recordings of mEPSCs due to their small size, which can be buried in the baseline noise after antagonist application. Stimulation of a single presynaptic calyx of Held fibre that contains multiple active zones evokes large EPSCs that result from the release of either a single vesicle (univesicular release; UVR) or multiple vesicles (multivesicular release; MVR) at each active zone. As our initial target was to understand the glutamate transient created by single vesicular releases, extracellular calcium concentrations ([Ca²⁺]_o) were varied in order to manipulate the presynaptic vesicular release probability (P_r) such that UVR conditions were created. Even though the release probability was likely to be lower in 1 mm compared with 1.4 mm[Ca²⁺]_o (paired pulse ratio of the evoked EPSCs at inter-stimulus interval of 50 ms = 1.10 ± 0.05 and 0.97 ± 0.03 at 1 and 1.4 mm[Ca²⁺]_o, respectively; n= 9 and 8, P < 0.05, unpaired t test), the amount of block by applying 2 mmγDGG was similar (Fig. 1D and E). This means that the glutamate concentration transient at each active zone reached the lowest value at [Ca²⁺]_o below 1.4 mm, indicating UVR condition. The block at 1 mm[Ca²⁺]_o was 89.5 ± 0.5% (n= 8), a value that will also be used later to constrain the parameters describing the glutamate transient. MVR likely occurred at 2–4 mm[Ca²⁺]_o as the block became progressively less with higher [Ca²⁺]_o (γDGG block, 83.2 ± 1.2% and 73.6 ± 2.7%, for 2 mm and 4 mm[Ca²⁺]_o, respectively). MVR situations that can reproduce these values will be evaluated with simulations in the later sections. These results implicate that one should be aware that the calyx of Held synapse is featured by UVR at physiological [Ca²⁺]_o at P14 and older (Taschenberger et al. 2002; Lorteije et al. 2009), and by MVR at 2 mm[Ca²⁺]_o, which is commonly used in acute slice experiments.

Construction of a kinetic model of AMPARs from MNTB principal neurons

AMPARs expressed on the postsynaptic cell could be considered as a sensor of the glutamate transient. The performance of this sensor was assessed by excising outside-out patches from the MNTB soma, which were exposed to ultrafast exchanges of solution containing various concentrations of glutamate with or without γDGG using flow pipes mounted on a piezo-electric device (Jonas, 1995; Wadische & Jahr, 2001; Matsui et al. 2005). The calyx of Held synapse is a giant axosomatic synapse harboring many release sites and corresponding postsynaptic specializations (PSDs) on the soma, from which outside-out patches were excised. A kinetic model of the AMPARs was constructed using the basic structure that Häusser & Roth (1997) have made with γDGG binding steps added by Wadiche & Jahr (2001), and the rates were modified to match the outside-out patch responses (Fig. 2A).

First, square pulses of a saturating concentration of glutamate (10 mm) were applied to record deactivation, desensitization and recovery from desensitization rates of the AMPARs on the outside-out patches. The deactivation rate was evaluated by measuring the decay of the AMPAR response after a very brief pulse of glutamate. The AMPAR response decayed mono-exponentially with a rate constant of 0.412 ± 0.032 ms (n= 19; Fig. 2B). During continued presence of glutamate (10 ms pulse), the AMPAR response decayed rapidly. Such desensitization rate was well fitted with a double exponential rather than a single exponential (Fig. 2B; a weighed rate constant, τ_weighted, of 1.20 ± 0.06 ms, n= 30), which was one of the rationale behind the introduction of multiple desensitization states in the original Häusser & Roth (1997) model. By applying double 10 ms pulses of glutamate with different intervals,the time constant of recovery was evaluated. A double exponential function was required again to accurately fit this recovery time course (τ_weighted= 34.7 ms, n= 12). These rates are consistent with previous reports using outside-out patches from MNTB principal neurons (Joshi et al. 2004; Koike-Tani et al. 2005), although a slightly faster rise time (0.097 ± 0.003 ms) and deactivation decay were observed in our case. This difference could be caused by the faster solution exchange time established in this study (see Methods). With these experiments alone, the absolute value of the open probability (P_O) could not be determined. Therefore, non-stationary fluctuation analysis was necessary to limit this parameter of the kinetic model. The decay during desensitization to 10 mm glutamate was repeatedly measured, from which the average and the variance caused by the probabilistic behaviour of the channel openings were calculated. A parabola function was fitted to the mean-variance curve to calculate the single channel conductance (21.4 ± 1.1 pS, n= 19) and maximum open probability (P_OMax, 0.61 ± 0.02, n= 13) of the AMPARs to 10 mm glutamate (Fig. 2C; Sigworth, 1980). The value for the single channel conductance matched with previous reports that performed peak-scaled non-stationary fluctuation analysis of the mEPSCs (Sahara & Takahashi, 2001; Yamashita et al. 2003). This agreement in results suggests that the AMPARs in outside-out patches have similar characteristics as those found in synapses. However, even though the extrasynaptic AMPAR expression was low (Fig. 3F), we were unable to confirm that the AMPARs studied in the outside-out patches were in fact those in the PSDs. We further recorded AMPAR currents in response to different concentrations of glutamate in order to estimate the AMPAR sensitivity to glutamate (Fig. 2E). The pooled data were fitted with the Hill equation with a half-maximal activation concentration of glutamate of 1.2 mm.

In order to evaluate whether the amount of γDGG block of the synaptic response could be used as an index of the glutamate concentration transient, the γDGG binding to AMPARs was studied in a ‘race’ experiment configuration. The outside-out patches were exposed to control solution that was quickly switched to a solution containing either glutamate (2 or 4 mm) alone or glutamate with γDGG (2 mm). Based on these recordings, γDGG binding steps were incorporated in the AMPAR kinetic model (Fig. 2F). During the 2 mm glutamate pulse, the peak amplitude was blocked by 71.4 ± 1.8% (n= 9) with combined application of γDGG and, during the 4 mm glutamate pulse, the amplitude was decreased by 52.6 ± 1.2% (n= 10), consistent with γDGG working as a competitive antagonist.

AMPAR distribution on the postsynaptic membrane

After establishing the performance of the AMPAR as a glutamate sensor, we sought to describe the two-dimensional distribution of these sensors along the postsynaptic plasma membrane using SDS-FRL. High-pressure freezing of the neuronal tissue followed by fracturing exposes the plasma membrane including the postsynaptic membrane specializations. The surface AMPARs were immunolabelled by the application of panAMPAR (GluR1–4) antibody (Nusser et al. 1998). Clusters of IMPs on the E-face represent the postsynaptic membrane specialization of glutamatergic synapses (PSDs; Fig. 3A–C, blue areas and demarcation; Tarusawa et al. 2009). Virtually all E-face IMP clusters were labelled with panAMPAR immunogold particles. Only multiple PSDs found on a large postsynaptic profile were identified as glutamatergic synapses of the MNTB principal neurons and thus included in the analysis (Fig. 3A). These profiles were often accompanied closely by a protoplasmic face (P-face) of the presynaptic terminal, which corresponds to the large axosomatic terminal, the calyx of Held (Fig. 3A and B: orange areas). The identity of this presynaptic profile was supported by the presence of multiple synaptic vesicles in the cross-fracture of the terminal (Fig. 3B, cross-fracture: dark red area; synaptic vesicles: arrows).

PanAMPAR antibody used in our previous studies had superb labelling efficiency with one-to-one detection sensitivity to functional AMPAR channels in SDS-FRL samples (Tanaka et al. 2005). Because no stock of this antibody was left, a different batch was used in the present study. The labelling efficiency of the current antibody was quantified by comparing its labelling density with that of a previous antibody in a well-quantified tissue that was previously used, the retinogeniculate synapses of the dLGN. Using the previous antibody, the labelling density of the AMPAR immunogold particles within retinogeniculate postsynaptic specialization was 1112 particles μm⁻² (Tarusawa et al. 2009), and the current antibody showed 1.89 times less labelling density (588 ± 10 particles μm⁻², n= 2). Therefore, this value was considered as the calibration factor, and the number of AMPAR immunogold particles found in MNTB sample was multiplied by this calibration factor in order to obtain an estimate of the actual AMPAR number.

In the MNTB sample, the IMP clusters were demarcated as illustrated in Fig. 3C, to calculate the area of the postsynaptic specialization, and the number of immunoparticles within this demarcation was counted. The size of the IMP cluster area varied, but a positive correlation between the area and the number of AMPAR immunoparticles was found, signifying a relative constant density of AMPARs in postsynaptic specializations irrespective of the size of the area (Fig. 3D). The average area of the IMP clusters, and the number and density of AMPAR immunoparticles were 0.056 ± 0.002 μm², 37.1 ± 2.1 and 705 ± 6 particles μm⁻², respectively (Fig. 3D; n= 2 animals). Including the calibration factor, the estimated AMPAR number and density were 70.2 and 1334 AMPARs μm⁻², respectively (Fig. 3D, grey bar). Using the remaining highly sensitive panAMPAR antibody from the previous batch, the immunoparticle density in IMP clusters of MNTB principal neurons was quantified as approximately 1400 particles μm⁻² (N. Kamasawa, unpublished observations), which further supports the credibility of the calibration.

Intrasynaptic density of AMPARs relative to the border of demarcation was also largely homogeneous with the density only in the most peripheral of the demarcation being slightly less than the centre (Fig. 3E and F; see Methods). Interestingly, a similar distribution was observed in the retinogeniculate synapse in the dLGN (Budisantoso et al. 2012), suggesting a general feature of synaptic AMPAR distribution, although the centre to peripheral gradient of the AMPAR density was more pronounced in the dLGN (see Petralia et al. 1998; Somogyi et al. 1998 for comparison). The density of extrasynaptic immunoparticles had a small value of 5.8 ± 0.6 particles μm⁻² (n= 74 profiles; with calibration, 11.0 AMPARs μm⁻²; Fig. 3F). This implies a minor contribution of extrasynaptic AMPARs to the synaptic response size, which will be assessed with simulations in the next section. We further characterized the average distribution of the number of AMPAR particles from the centre of gravity as illustrated in Fig. 3G and plotted in Fig. 3H. This provides a map of the distribution of AMPARs that the released glutamate encounters from the point of release. In previous studies (Tarusawa et al. 2009; Budisantoso et al. 2012), we have shown that the exact location of release within the synapse had little impact on the summed response of all AMPARs present in the PSD (see also Trommershäuser et al. 1999). This average distribution will be incorporated in the simulations.

Simulation of AMPAR response to quantal release

Equipped with the kinetic model and distribution of AMPARs, we were ready to perform simulations of the EPSCs in response to single vesicular releases. The pre- and postsynaptic surface of the MNTB synapse illustrates an extracellular space sandwiched by two parallel planes. The uniformity of the cleft width outside the active zone-PSD complex is under debate (Taschenberger et al. 2002), but the irregular shaped plasma membrane observed in ultrathin sections is often considered to be due to artifacts from tissue processings for electron microscopy observations. Studies using high-pressure freezing methods show that in the areas where only two cells contact, the two plasma membranes smoothly parallel each other with a relatively constant width (Zhao et al. 2012). Thus, the diffusion of the released glutamate was considered to occur two-dimensionally in a cleft with a width of 20 nm (Savtchenko & Rusakov, 2007). Analytical solution to the simple diffusion equation in two-dimensional space is given (see Methods) with only two unknown parameters; the number of glutamate molecule packed in a vesicle (N_Glu) and the glutamate diffusion coefficient in extracellular space (D_Glu). We chose N_Glu= 7000 and D_Glu= 0.3 μm² ms⁻¹ for the simulations performed here. The validity of this selection is evaluated in the next section.

A sample synapse was selected with near average size and number of immunoparticles (Fig. 4A). Assuming that the release occurs at the centre of gravity of the IMP cluster demarcation, the glutamate transient at each AMPAR location was calculated (Fig. 4B, example traces in red at location 1–3). When the kinetic model was run against these glutamate transients, the P_O curves of individual AMPARs were generated, reflecting the AMPAR responses at each AMPAR location (Fig. 4B, corresponding traces in black). The attained peak of the P_O of individual AMPARs decreased with increasing distance from the release site (Fig. 4C, red line). The sum of all AMPAR responses in the synapse is the simulated quantal response. Because more AMPARs are present than our current antibody was able to detect, multiplication with the calibration number was necessary to obtain an estimate of the actual number of the open AMPARs. Based on the single channel conductance obtained from outside-out patch experiments (Fig. 2C) and the holding potential in voltage-clamp experiments (−77 mV), the peak of the simulated current for this sample synapse was calculated as 43.9 pA (Fig. 4B). This value corresponded well with the average of the recorded mEPSC amplitude (Fig. 1C; 41.0 pA).

Figure 4. Simulations of AMPA receptor (AMPAR) response to quantal release.

A, glutamate concentration profile (red scale; N_Glu= 7000, D_Glu= 0.3 μm² ms⁻¹) and simulated AMPAR P_O (pseudo-colour) at 0.05 ms after release at the centre of gravity of the sample synapse. B, glutamate concentration transients and corresponding AMPAR responses at location 1–3. The sum of the responses of all AMPARs present in the sample synapse is shown, after multiplication with calibration number (Cal). Conversion from open AMPAR to current was done with the formula shown below. C, average AMPAR immunoparticle distribution from the centre of gravity (grey) was plotted along with the simulated peak P_O of AMPAR at each distance from the release site (red). D, simulation of the summed response of all receptors distributed on an average synapse. Summary of peak open AMPARs from simulation (Model) and recording (Data). E, an example of two neighbouring IMP clusters on the postsynaptic E-face with panAMPAR labelling (5 nm gold particles). F, histogram of nearest-neighbour distances (NNDs) of IMP clusters (50 nm bins, n= 177). Distance versus simulated peak P_O is shown in red. G, illustration of the defined synaptic (centre) and extrasynaptic (yellow) area and the synapse at NND (grey; 780 nm). Extrasynaptic area was divided by 10 nm bins from the synaptic centre (grey lines; 50 nm bins = black lines). The extrasynaptic AMPAR distribution was assumed to be homogeneous. H, simulation of synaptic and extrasynaptic response, and synaptic response at mean NND after a quantal release at the centre of gravity of a synapse. The sum of all responses is shown in green. I, simulated response for an AMPAR located on (@ 0 nm) and at 400 nm (dotted traces) from the centre of release in the presence (blue) and absence (black) of 2 mmγ-d-glutamylglycine (γDGG). Simulated peak P_O and γDGG block versus distance were plotted below. J, average quantal response was simulated in the absence (black) and presence (blue) of 2 mmγDGG. γDGG block from simulation (Model) and recording (Data) was summarized.

Using the average AMPAR distribution from the centre of gravity of IMP cluster demarcations (Figs 3H and 4C, grey plot), the quantal response in an average synapse was simulated. Similar to above, the glutamate transient and the corresponding time course of P_O at each distance from the release site were first calculated. The attained peak of the P_O is plotted in Fig. 4C (red), which shows that, as glutamate concentration transient decreases with distance from release site, the peak P_O progressively decreases. Interestingly, the pattern of AMPAR distribution from the centre of gravity correlated well with the effective range of AMPAR activation from the centre of release (Fig. 3C, red line; 50% cumulative frequency of immunoparticles from centre = 85 nm; half-width half-maximum distance of peak P_O= 125 nm). The time course of the P_O at each distance from the release site was multiplied with the number of particles located at the corresponding distance and then summed for all distances. This provided the time course of the number of open AMPARs in an average synapse that would represent a quantal response. At the peak of this simulated quantal response, 24.9 AMPARs were opened (Fig. 3D). By dividing the synaptic conductance at the peak of the mEPSC with the single channel conductance, open AMPARs in the actual recording were calculated (Fig. 3D, open AMPARs at peak, 24.9 ± 1.1). This experimentally measured value matched with the one obtained by the simulation using the current N_Glu and D_Glu combination.

Even though the concentration of synaptically released glutamate would be substantially diluted by the time it reaches the extrasynaptic space, such spilled over glutamate could affect AMPARs located extrasynaptically and in the neighbouring synapses. To evaluate the contribution of glutamate spillover to the quantal response amplitude, the NNDs between centres of IMP clusters were first quantified on wide fractured planes of the somatic membrane containing multiple postsynaptic specializations in the MNTB principal neurons (Fig. 4E). The mean NND was 782 ± 31 nm (n= 177; Fig. 4F), which was longer than the NND studied with SDS-FRL previously at another multisynapse contact, the retinogeniculate synapse (569 nm; Budisantoso et al. 2012). At this distance, the glutamate concentration was reduced so much that the peak of the P_O reached close to zero (Fig. 4F, red line). Nevertheless, as the average number of AMPARs per synapse is estimated to be as large as 70.2 (Fig. 3D), the total response of the neighbouring synapse reached a substantial level, however, with a markedly slow time course (Fig. 4H). And since the density of extrasynaptic AMPARs was less than 1% of the synaptic AMPARs but not quite zero (11.0 AMPARs μm⁻²), contribution coming from the extrasynaptic AMPARs was also evaluated. We assumed that the extrasynaptic AMPARs distributed evenly on the postsynaptic membrane from 400 to 800 nm from the release site. This area was divided by concentric circles with 10 nm bins and the estimated number of AMPARs in each bin was calculated (Fig. 4G). After multiplication with this number, the time course of P_O of each bin was summed for the whole extrasynaptic region. The number of open AMPARs resulting from spillover into the extrasynaptic space was small (Fig. 4H). Summation of the average synaptic response with the spillover effect at the extrasynaptic space and at the neighbouring synapse did not increase the peak amplitude but only the decay, as the response due to spillover was slow to rise (Fig. 4H, green trace). Note that this simulation was done assuming that the release occurred only at one synapse and no concurrent release occurred at the neighbouring synapse. This finding suggests that the peak of the quantal response is solely determined by the responses from synaptic AMPARs. Thus, spillover only affects the decay of the response from quantal release and possibly the short-term plasticity through desensitization of AMPARs as indicated in our previous study (Budisantoso et al. 2012).

The amount of block of the EPSC by γDGG can also be used as an index of the synaptically released glutamate transient. In previous studies using low-affinity antagonists to evaluate the glutamate concentration transient, the synaptic cleft was treated as a single concentration compartment (Clements et al. 1992; Diamond, 2001; Wadiche & Jahr, 2001; Scimemi & Beato, 2009). However, a huge gradient of glutamate is likely created upon vesicular release and the γDGG block would be affected both by the concentration and the time course of the glutamate transient. Thus, the amount of block could be different depending on the distance from the release site. To illustrate this, the P_O of AMPARs was simulated at different distances from the release site in the absence and presence of γDGG (Fig. 4I). As expected, the γDGG block was larger at a distance corresponding to the edge of an average synapse compared with the centre. The γDGG effect on the total quantal response was evaluated by simulating the P_O in the absence and presence of γDGG for all AMPARs distributed in an average manner. The peak amplitude of the simulated quantal response was blocked by 89.3%, which matched well with the actual evoked EPSCs recorded in 1 mm[Ca²⁺]_o (89.5 ± 0.5%, n= 8; Fig. 4J). This suggests that the current N_Glu and D_Glu combination used in the simulation not only reproduces the mEPSC amplitude but also the amount of γDGG block in UVR condition.

Limiting the range of possible N_Glu and D_Glu combinations

Only two parameters, N_Glu and D_Glu, are necessary to define the glutamate concentration transient in two-dimensional diffusion and, although the experimentally recorded EPSCs were well reproduced with N_Glu= 7000 and D_Glu= 0.3 μm² ms⁻¹, this may not be the sole combination that can reproduce the results. We therefore explored different N_Glu and D_Glu combinations, and simulated the postsynaptic response to single vesicular release, of which the amplitude and the γDGG block were evaluated. As expected, the peak amplitude increased with larger N_Glu and also with lower D_Glu, as a longer dwell time of glutamate would allow more opening of the AMPARs. The peak number of open AMPARs was calculated as 24.9 in an average of mEPSC recordings (Fig. 4D), and a diagonal line was drawn in the N_Glu–D_Glu plot representing all possible combinations that match this value in the simulations (Fig. 5B). The amount of γDGG block also depends on N_Glu and D_Glu. With more glutamate molecules (larger N_Glu) that would compete with γDGG, the block became smaller. A similar effect occurred with a longer dwell time of glutamate (smaller D_Glu), which would allow more replacing of the γDGG with glutamate (Fig. 5C). The average γDGG block in UVR condition of 1 mm[Ca²⁺]_o was measured as 89.5% (Figs 1E and 4J), and another diagonal line in the N_Glu–D_Glu plot was drawn that represents all combination that can reproduce this value with the simulations (Fig. 5C). The two diagonal lines that displayed a different slope crossed at N_Glu= 7000 and D_Glu= 0.3 μm² ms⁻¹, which optimally match both experimental results. However, because the two lines were not orthogonal and a margin of error was expected, 25th to 75th percentile range of both the peak open AMPARs in mEPSC recordings and the γDGG block measurements in UVR conditions was considered (Fig. 5B and C, dotted line). N_Glu and D_Glu combinations that satisfy these ranges would be in the green area in the N_Glu–D_Glu plot (Fig. 5B and C). Therefore, N_Glu and D_Glu combinations such as (5000, 0.2) and (9000, 0.4) were also considered as combinations that closely correlated with the experimental results. The diffusion coefficient of glutamine in aqueous solution was measured as 0.76 μm² ms⁻¹ (Longsworth, 1953), and there is a controversy whether glutamate diffuses as freely in the synaptic cleft or not (Barbour, 2001). However, our experiments and simulations show that, if the diffusion is that fast, the dwell time of glutamate would become so short that tremendous amount of glutamate molecules needs to be released in order to reproduce the mEPSC amplitude or the γDGG block in UVR condition. In addition, the two diagonal lines in the N_Glu–D_Glu plots that match the experimentally measured mEPSC amplitude and the γDGG block become separated at D_Glu= 0.76, suggesting the absence of an unique N_Glu that can reproduce both results. These findings imply that the glutamate molecules in the synaptic cleft may not diffuse as freely as in aqueous solution (Nielsen et al. 2004), although the mechanism underlying such hindered apparent diffusion is uncertain.

Figure 5. Simulations based on a range of N_Glu and D_Glu combinations.

A, simulated synaptic responses at a synapse with an average AMPA receptor (AMPAR) distribution are shown in red. Simulated synaptic responses in the continued presence of 2 mmγ-d-glutamylglycine (γDGG) are shown in blue. γDGG block is calculated as the percentage reduction of the peak amplitude in γDGG (dotted arrow). Results from several N_Glu and D_Glu combinations are shown. B and C, grey scale contour plot of the peak open AMPARs (B) and γDGG block (C) within a range of N_Glu and D_Glu combinations. Black dots indicate the N_Glu and D_Glu combinations that were actually tested with the simulations, and the contour plots were made based on these values. The open circles indicate the N_Glu and D_Glu combinations used for generating the sample traces shown in A. The values of the contour lines are labelled with red and blue numbers in B and C, respectively. Contour lines that match the average values of the experimentally measured peak open AMPARs (24.9) and γDGG block (89.5%) are shown in red bold (B) and blue bold (C) diagonal lines, respectively. Contour lines representing the 25th, 50th and 75th percentile values of the experimentally measured peak open AMPARs and γDGG block are indicated by the dotted lines. The range of N_Glu and D_Glu combinations that lie within the 25th to 75th percentile range of both the peak open AMPAR and the γDGG block is highlighted in green.

Evaluation of MVR

It is reported that a maximum of only one vesicle can be released at each release site upon an action potential invasion at some synapses (Triller & Korn, 1982; Biróet al. 2005), but MVR has also been reported to occur at others (Tong & Jahr, 1994; Auger et al. 1998; Wadiche & Jahr, 2001; Oertner et al. 2002; Taschenberger et al. 2002). Some studies indicate no MVR even though the synapse displays high P_r, such as in the case of olfactory nerve terminals (Murphy et al. 2004), and some indicate MVR at synapses with low initial P_r, such as in the case of the granule cell to Purkinje cell synapses (Foster et al. 2005). The difference between single vesicles released at multiple synapses (UVR) and multiple vesicles released at individual synapse (MVR) is that in the latter case, glutamate concentration transients summate resulting in a higher concentration at individual synapse. The use of a low-affinity antagonist is currently the sole mean to differentiate the two situations electrophysiologically. In the calyx of Held synapse, the γDGG block was significantly lower when the P_r was elevated with 2 mm and 4 mm[Ca²⁺]_o, suggesting that there exists no mechanism that would limit the vesicle release to only one at this synapse. Although MVR likely occurs in 2 mm[Ca²⁺]_o condition, which is typically used in slice experiments, the physiological mode of release is predicted to be UVR at the calyx of Held synapse at P14 and older (Fig. 1D; Taschenberger et al. 2002; Lorteije et al. 2009). However, we decided to use this synapse as a model to examine how the glutamate transients from MVR would overlap in time and space, and affect the amplitude and the γDGG block of the EPSCs. This became feasible because the glutamate concentration transient in UVR condition was established in the previous section.

First, we considered a situation where multiple vesicles are released simultaneously at the centre of the synapse with an average AMPAR distribution (Fig. 6A and B). The AMPARs were not saturated with UVR, consistent with previous reports (Ishikawa et al. 2002; Yamashita et al. 2009). The amplitude progressively increased with increasing number of vesicles released, but this relationship was not linear. The response to two and four MVRs would be 1.5 and 1.8 times the response to an UVR, respectively (Fig. 6B). When the simulation was done in a sample synapse, it was apparent that the majority of the AMPARs reached the P_OMax of ∼0.6 (Fig. 6A) when four vesicles were released, suggesting that the total synaptic response was close to saturation. These results imply that this synapse is capable of differentially encoding several levels of MVR. As expected, the elevation of the glutamate concentration resulting from MVR leads to a reduced block (Fig. 6B, blue line). A γDGG block of 83.2% and 73.6% was found in 2 mm and 4 mm[Ca²⁺]_o in the actual recordings (Fig. 1E), respectively, and two and four vesicle releases were required to reproduce this amount of γDGG block in the simulations, respectively. Similar results were observed with other N_Glu and D_Glu combinations (N_Glu, D_Glu) of (5000, 0.2) and (9000, 0.4) that reproduced the UVR conditions relatively well (Fig. 6B). This further strengthens the estimate of the number of vesicles released.

Figure 6. Evaluation of MVR.

A, schema of release situation assumed is shown on top. Situations with a single vesicle (left) and 4 vesicles (right) simultaneously released at the centre of the synapse with an average AMPA receptor (AMPAR) distribution were simulated. The N_Glu and D_Glu were set to 7000 and 0.3 μm² ms⁻¹, respectively, for all the following simulations unless otherwise noted. Simulated traces of open AMPAR are shown in black (control) and grey (2 mmγ-d-glutamylglycine (γDGG)). P_O of individual AMPAR (pseudo colour) on a sample synapse at 0.05 ms after release for each situation is shown below. B, the peak open AMPARs (left y-axis) in the absence (black) and presence of γDGG (grey) and the percentage γDGG block (blue, right y-axis) were plotted against the number of vesicles released. Simulations based on different N_Glu and D_Glu combinations that could reproduce the quantal response relatively well (Fig. 5) were tested, and the percentage γDGG block was plotted for these combinations as well. C, simulations of asynchronous release of 2 vesicles on an average synapse. Sample traces shown were based on simulations with the releases of 2 vesicles separated by Δt= 0.1 ms. D, percentage γDGG block was plotted against Δt. E, simulations of simultaneous release of 1 vesicle at the centre and the 2nd vesicle at varying distances from the centre (Δd) of a sample synapse. An ellipse was fitted to the demarcation and the 2nd release was assumed to occur along the major axis. P_O of individual AMPAR is shown below for Δd= 0 nm and 160 nm. F, the peak open AMPARs in the absence and presence of γDGG and percentage γDGG block were plotted against Δd. The dotted lines in each colour indicate the expected values of the peak P_O and the percentage γDGG block for single vesicular release. G, left, simultaneous release of 4 vesicles with Δd= 80 nm from the centre along the major axis and Δd= 50 nm from the centre along the minor axis of a sample synapse. P_O of individual AMPAR is shown below and traces of open AMPARs are shown on the right. Right, asynchronous release of 3 vesicles with one in the centre and two at Δd= 80 nm along the major axis. Release rate was calculated by deconvolution of the evoked EPSC with the idealized mEPSC, from which the cumulative release was plotted below. Assuming release at the timing of 25%, 50% and 75% of the total release, the release intervals (green arrows) were calculated. The corresponding open AMPAR traces are shown on the right.

Next, a situation was examined where two vesicles were released with a slight offset in time (Fig. 6C and D). Release asynchrony of 1 ms caused a larger γDGG block than when the two releases occurred simultaneously because the glutamate concentration would summate to a lower value when there is an offset in release. However, release at short time intervals (<300 μs) revealed a slight decrease in the γDGG block (Fig. 6D). Such effect could be explained by the fact that the low-affinity antagonist could save a population of receptors from entering rapid desensitization in response to the first glutamate transient and such receptors would promptly be available for the next instance of glutamate release (Wong et al. 2003; Renden et al. 2005; Chanda & Xu-Friedman, 2010). Such effect was clearly demonstrated in the retinogeniculate synapses where the receptors quickly entered desensitization states from which it took a long time to recover (Budisantoso et al. 2012). Desynchronization of MVR has been suggested to underlie the larger block of the climbing fibre to Purkinje cell EPSCs by a low-affinity antagonist during continuous repetitive stimuli compared with the case where the stimulation was given in isolation (Rudolph et al. 2011). However, our model suggests that a slight offset of release should rather cause a little decrease of the amount of block. Similar results were obtained when running the model of Wadiche & Jahr (2001) against our glutamate transients. We are not arguing against the occurrence of desynchronized MVR but the larger block by the low-affinity antagonist during repetitive stimuli in climbing fibre to Purkinje cell synapses could be better explained by less vesicles being released. In any case, although there are subtle differences in the block depending on the interval between the two releases, our simulations suggest that the γDGG block appeared relatively stable for different intervals within a millisecond timescale (Fig. 6D).

We further evaluated situations where two vesicle releases occurred simultaneously at an offset location of a sample synapse (Fig. 6E and F). One vesicle was assumed to be released at the centre of the synapse with the other released at varying distance from the centre along the major axis of the ellipse fitted to the synapse demarcation. Interestingly, the peak amplitude of the response was little affected by the location of release of the second vesicle. When the P_O of individual AMPARs was examined, it became apparent that a very high P_O was attained for a population of AMPARs close to the centre when the two vesicles were released at the same location (Fig. 6E, Δd= 0, bottom). When the two releases occurred at offset locations, the population of AMPARs with a very high P_O decreased while that with a mid-size P_O increases. Because the synaptic response was the summation of the activity of all AMPARs, the two situations produce nearly identical results. Accordingly, our model suggests that the amount of γDGG block is not much affected by the release location. With the offset vesicle release exceeding the synapse demarcation border, both the size of the synaptic response and the γDGG block approached the value for single vesicular release (Fig. 6F). These results indicate that similar synaptic strength is encoded irrespective of the small variation of the MVR offset both in time and space.

Finally, synchronous and asynchronous MVR were evaluated in a situation that would match the highest P_r condition (4 mm[Ca²⁺]_o), which we tested experimentally. First, simultaneous release of four vesicles at four different locations was simulated based on the γDGG block in Fig. 6B. Although the P_O of individual AMPARs was slightly different from the case when four vesicles were released in the centre (Fig. 6A), the overall amplitude and the γDGG block were similar (open AMPARs, 44.3 and 47.6; γDGG block, 74.0% and 71.7%; for same release location and disperse release locations, respectively) and the simulated γDGG block reproduced the 4 mm[Ca²⁺]_o recordings well (73.6%; Fig. 1E). Next, in order to determine the rate of release asynchrony, an idealized mEPSC waveform was made by fitting the recorded mEPSC with an equation of the form m^xh (Hodgkin & Huxley, 1952; Bekkers & Stevens, 1996), which was further modified to have a double exponential decay. This was used for deconvolution of the evoked EPSC waveform in 1 mm[Ca²⁺]_o, a condition where UVR and linear summation of the quantal responses are assumed (Wadiche & Jahr, 2001). If we assume that asynchrony of release triggered by a presynaptic action potential is not altered by the [Ca²⁺]_o, then the release rate calculated by this deconvolution method could be used to suppose the asynchrony of release within individual synapse in MVR situation. The four releases were assumed at the timing of 20%, 40%, 60% and 80% of the total release based on the cumulative release rate plot (Fig. 6G, bottom right). Thus, the interval between four sequential releases was calculated as ∼100 μs. As expected from the results of Fig. 6D, such asynchronous MVR resulted in less γDGG block than synchronous MVR. In order to reproduce the amount of γDGG block recorded in 4 mm[Ca²⁺]_o, the number of MVR needed to be reduced to three as illustrated in Fig. 6G (release interval at 25%, 50% and 75% of total release = 120 μs). These results show that a MVR of three–four vesicles is required to explain the amount of γDGG block observed experimentally in conditions of high P_r. These simulations indicate that glutamate transients from MVRs markedly overlap if the releases take place within approximately 1 ms interval and within the synapse demarcation. Therefore, each release in MVR conditions should not be considered to produce independent postsynaptic effects and the synaptic conductance appears not to increase linearly with the increasing number of vesicular releases. However, our data suggest that similar synaptic strength is exerted irrespective of the exact synaptic location and timing of the MVR.

Discussion

Many previous studies of the concentration and time course of synaptically released glutamate treated the synaptic cleft as single concentration compartment and estimated a peak concentration of a few mm and a decay time constant of 1 ms or less for single vesicular releases (Clements et al. 1992; Diamond & Jahr, 1997; Wadiche & Jahr, 2001). However, a steep gradient of glutamate concentration is likely created upon exocytosis, and receptors within a synapse would be differentially activated due to the difference in the glutamate transient that they experience (Wahl et al. 1996; Trommershäuser et al. 1999; Franks et al. 2003; Raghavachari & Lisman, 2004; Zheng et al. 2008). In addition, if glutamate transient in the synaptic cleft resembles simple diffusion process, the decay of the glutamate concentration would not be exponential (Rusakov & Kullmann, 1998; Scimemi & Beato, 2009). It is probably valid to express the glutamate transient with two-dimensional diffusion equation in a simple structure such as the calyx of Held where the pre- and postsynaptic plasma membrane sandwich the extracellular space for distances far exceeding individual synapses, although three-dimensional diffusion in a completely reconstructed extracellular space would be more accurate (Sätzler et al. 2002; Cathala et al. 2005). Such two-dimensional assumption likely still holds valid for glutamate transients at and around individual synapses even at 2nd postnatal week when the presynaptic terminal is shaped like an open claw rather than a closed cup-shape (Ford et al. 2009). Multiple synapses are still contained within a presynaptic finger where undisturbed two-dimensional diffusion could continue for long distances. Even though astrocytes that highly express glutamate transporters completely encapsulate the pre- and postsynaptic contact, transporter blockade does not affect the amplitude or the decay of the postsynaptic current (Renden et al. 2005), suggesting that the glutamate sink at the edge of the contact would not considerably affect the glutamate transients at synapses created by single action potentials. Using the simple assumption of two-dimensional diffusion, glutamate transient can be expressed by assigning a value to each of the two free parameters; the number of glutamate in a vesicle and the glutamate diffusion coefficient. Neither of the values has been experimentally measured in active synapses. We varied the two parameters in our simulations to find a combination that would match both the mEPSC amplitude and the γDGG block. The two parameters have a compensatory relationship as high N_Glu and high D_Glu combination would produce similar activation of AMPARs as with low N_Glu and low D_Glu combination (Diamond, 2001; Scimemi & Beato, 2009). Therefore, it was difficult to pinpoint a single combination that would reproduce the synaptic response. Nonetheless, we were able to limit the range of combinations that describes the characteristics of the effective glutamate transient.

Our optimal estimate of N_Glu = 7000 may appear a bit too large, but so far no direct estimation of the vesicular glutamate content at central synapses has been obtained (Scimemi & Beato, 2009). By iontophoretic application of transmitter acetylcholine, the number of acetylcholine molecules in synaptic vesicles of the frog neuromuscular junction was estimated as 10000 (Kuffler & Yoshikami, 1975); however, this should be considered as an overestimation. By using carbon fibres as electrochemical detectors, 5000 molecules of neurotransmitter, serotonin, from individual synaptic vesicles were estimated to be released from cultured neurons (Bruns & Jahn, 1995). Previous studies that isolated synaptic vesicles with purification protocol (Riveros et al. 1986) and assessed synaptic vesicle structure (Harris & Sultan, 1995; Zampighi & Fisher, 1997; Takamori et al. 2006) proposed a vesicular glutamate content of 2000–4000 molecules. If we rely on these previous estimates and assume that the ∼5000 estimate is the upper limit of the N_Glu, then our D_Glu estimation would be limited to a smaller value of less than ∼0.2 μm² ms⁻¹.

It is of interest to point out that the D_Glu in aqueous solution could not reproduce our experimental observations. It has been shown that increasing the viscosity of extracellular fluid by application of macromolecule dextran could enhance the EPSC amplitude and slow the spillover-mediated synaptic currents (Nielsen et al. 2004). However, the slowness of diffusion in the synaptic cleft in control condition may not be due to the large viscosity of endogenous extracellular fluid in synapse, but could be due to the geometrical diffusion barriers introduced by molecules crowding the synaptic cleft and/or due to the attraction of the glutamate molecules to synaptic molecules. It is possible that, microscopically, 0.76 μm² ms⁻¹ should still be used as the diffusion coefficient, but a new factor that can explain the slow diffusion needs to be introduced. However, we can conclude that the diffusion is somehow slowed compared with a simple aqueous solution, and an apparent diffusion coefficient of 0.2–0.4 μm² ms⁻¹ appears to describe the glutamate transient (Nielsen et al. 2004).

Although theoretical studies have realized that a steep gradient of glutamate concentration is created within the synapse (Trommershäuser et al. 1999; Franks et al. 2003), to understand the effect of such a gradient on postsynaptic response, knowledge of the distribution of the receptors within the cleft was needed. Even SDS-FRL could provide only a fragmented view of the whole postsynaptic specialization if the synapses are made on structures that display a strong curvature such as the spines. The calyx of Held synapse was advantageous as the AMPAR distribution on whole synapses could be visualized and collected with relative ease. Corresponding to the steep glutamate gradient, the P_O of individual AMPARs was highly variable within the synapse. However, as the synaptic response is the summation of the activity of all AMPARs present, the exact location of release had negligible impact on the amplitude of the synaptic response as has been discussed previously (Tarusawa et al. 2009). If the P_O of the AMPARs drops very sharply with increasing distance from the release site, one would expect that responses from MVR might add more or less linearly (Raghavachari & Lisman, 2004). In other words, if the effects of multiple releases within individual synapses are independent of each other, MVR would be no different from UVR at multiple synapses. However, our data suggest that this is not the case at least in the calyx of Held synapses. The size of an individual synapse is small enough that when MVR occurs, glutamate concentration transients from each vesicle would overlap and exert an effect on the postsynaptic AMPARs that would not be affected by the small differences in the exact release locations. Our simulations imply that postsynaptic AMPARs are not saturated with UVR, consistent with previous experiments (Liu et al. 1999; Ishikawa et al. 2002; Yamashita et al. 2009), suggesting that an individual synapse is capable of encoding more than binary information. However, the number of presynaptic vesicular release and the summed postsynaptic response had a non-linear relationship (Fig. 6B). If the size of the vesicle or the glutamate content within a vesicle is much smaller at other CNS synapses, less saturation and more linear summation with MVR could occur.

After establishing the parameters describing the glutamate transient, the effect of glutamate spilling over from the synapse could be evaluated. In principle, spillover of glutamate could exert its effect on extrasynaptic receptors (Matsui et al. 1998; Clark & Cull-Candy, 2002) and/or receptors on neighbouring synapses (Barbour & Häusser, 1997; Budisantoso et al. 2012). In the calyx of Held, the density of extrasynaptic AMPARs was very low but not negligible. And, as the glial processes with glutamate transporters do not intervene the glutamate diffusion for some distance, the spilled over glutamate would be exposed to a large area of extrasynaptic membrane. However, the accumulating effect of the spillover glutamate on the extrasynaptic AMPARs is extremely low due to the dilution of the glutamate with longer distance from the release site. Thus, the extrasynaptic AMPARs do not contribute to the peak of the synaptic conductance but do contribute to the slight slowing of the decay. As the calyx of Held synapse is a multisynapse contact, the NND of synapses was measured, which was on average 782 nm. When the spilled over glutamate travels this far, it is faced with a sudden increase in the number of AMPARs encountered. Even though the glutamate concentration is extremely low by the time it reaches this distance, the total effect of glutamate spillover on the neighbouring synapse would be substantial. However, we found that the AMPAR conductance at this neighbour rose so slowly that it also did not add to the peak of the total synaptic conductance but rather only to the decay. Such slow-rising EPSCs resulting from spillover have been recorded in cerebellar mossy fibre–granule cell synapses (DiGregorio et al. 2002). The low concentration glutamate resulting from spillover could exert an effect on the desensitization of the AMPARs, which could affect the responses to subsequent releases (Budisantoso et al. 2012). However, it has been suggested that AMPAR desensitization does not occur in response to high-frequency stimulation at mature calyx synapses (Renden et al. 2005), which implies that spillover effects are minimal at these synapses. Although NMDA receptors are mostly absent in mature calyx synapses, these receptors have high affinity for glutamate and, thus, such receptors would be strongly affected by the low concentration of glutamate resulting from spillover at other synapses (Matsui et al. 1998; Barbour, 2001).

Generally, cell-to-cell communication uses the extracellular space as a medium for signal transfer. Insights to the properties of the diffusion in this space would help us also understand about characteristics of communication other than the glutamatergic synaptic transmission. At least from the current study, we can assume that the synaptic cleft has properties that slow the diffusion of glutamate molecule. Many pharmacological agents are also delivered through this extracellular space as well. Knowing the exact concentration and spread of endogenously released transmitter molecule could help us design the effective concentration of the pharmacological agent that would have just the right amount of action on modifying receptor and transporter function.

Glossary

AMPAR

AMPA receptor

CV

coefficient of variation

d-AP5

d-(−)-2-amino-5-phosphonopentanoic acid

D_Glu

diffusion coefficient

dLGN

dorsal lateral geniculate nucleus

E-face

exoplasmic face

γDGG

γ-d-glutamylglycine

IMP

intra-membrane particle

mEPSC

miniature EPSC

MNTB

medial nucleus of the trapezoid body

MVR

multivesicular release

N_Glu

number of glutamate molecules

NND

nearest-neighbour distance

P-face

protoplasmic face

P_O

open probability

P_r

release probability

PB

phosphate buffer

PSD

postsynaptic density

SDS-FRL

SDS-digested freeze-fracture replica labelling

UVR

univesicular release

Author contributions

K.M. designed and supervised the study, and T.B. collected electrophysiological, morphological and simulation data. K.M. devised methods for the analysis of the data and modelling. K.M. and T.B analysed and interpreted the data, and wrote the paper with contributions from the other authors. Refinement and optimization of the replica labelling were done by H.H., N.K., Y.F. and R.S. as well as supervision of all morphological observations. All authors approved the final version.

Authors’ present addresses

N. Kamasawa: Electron Microscopy Facility, Max Planck Florida Institute, Jupiter, FL 33458–2906, USA.

Y. Fukazawa: Department of Anatomy and Molecular Cell Biology, Nagoya University Graduate School of Medicine, Nagoya 466–8550, Japan.