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Actions of the excitatory neurotransmitter glutamate inside and outside the synaptic cleft determine the activity of neural circuits in the brain. However, to what degree local glutamate transporters affect these actions on a sub-micron scale remains poorly understood. Here we focus on hippocampal area CA1, a common subject of synaptic physiology studies. First, we use a two-photon excitation technique to obtain an estimate of the apparent (macroscopic) extracellular diffusion coefficient for glutamate, ~0.32 μm2/ms. Second, we incorporate this measurement into a Monte Carlo model of the typical excitatory synapse and examine the influence of distributed glutamate transporter molecules on signal transmission. Combined with the results of whole-cell recordings, such simulations argue that, while glutamate transporters have little effect on the activation of synaptic AMPARs, this does not rule out the occurrence of up to several dozens of transporters inside the cleft. We further evaluate how the expression pattern of transporter molecules (on the 10-100 nm scale) affects the activation of NMDA or metabotropic glutamate receptors in the synaptic vicinity. Finally, we extend our simulations to the macroscopic scale, estimating that synaptic activity sufficient to excite principal neurons could intermittently raise extracellular glutamate to ~1 μM only at sparse (microns apart) hotspots. Greater rises of glutamate occur only when <5% of transporters are available (for instance, when an astrocyte fails). The results provide a quantitative framework for a better understanding of the relationship between glutamate transporters and glutamate receptor signaling.
The activation of ‘classical’ ionotropic receptors outside the synaptic cleft has emerged as an important mode of neural signaling (1-3). Activity-dependent extrasynaptic actions of the inhibitory neurotransmitter GABA can modulate cell excitability and neuronal gain (4-7). Less is understood about similar actions exerted by the excitatory neurotransmitter glutamate. In hippocampal area CA1, synaptically released glutamate is rapidly taken up by high-affinity transporters expressed in abundance by astrocytes (8-12). The uptake keeps the average ambient glutamate concentration low, at ~25 nM in quiescent tissue (13). However, transporter-enriched glial membranes represent only ~13% of cell membranes in area CA1 (14) and approach only 30-40% of an average synaptic circumference (15). Indeed, synchronous and/or relatively strong afferent activation leads to significant activation of extrasynaptic glutamate receptors (16-18). The existence of neuronal, in particular intra-synaptic glutamate uptake is a subject of debates. Although the blockade of glutamate transporters has little effect on AMPAR (AMPAR) mediated synaptic currents (19,20), the amount of glutamate released inside the cleft may dwarf the numbers of local transporters thus rendering their influence on AMPAR activation undetectable. The role of transporters in shaping the extracellular landscape of glutamate on different scales remains therefore incompletely understood.
An important determinant of extrasynaptic communication is the degree of extracellular diffusion retardation R relative to a free medium. The values of R assessed with a well-established iontophoretic technique (21) in area CA1 vary considerably: from 2.07-2.16 (22) to 2.92 (23). To measure this value in our conditions, we applied an alternative approach based on two-photon excitation of a fluorescent indicator ejected from an instantaneous point source (24). Although a related integrative-imaging approach exploiting a diffusion source (22,25) and indicator photobleaching (26,27) have previously been used, the main advantage of two-photon excitation is the ability to collect fluorescence exclusively from a thin focal plane. This provides direct readout of concentration (24,28), avoiding potential errors inherent to de-convolution techniques. In addition, quasi-instantaneous point-source release deals with a small amount of the fluorescent probe, reducing concomitant effects of the residual fluorescence accumulated in the tissue (see below).
We incorporate diffusivity measurements into a Monte Carlo model of the typical synaptic environment to test the roles of unevenly distributed transporters on the activation of local AMPA, NMDA or metabotropic glutamate receptors by synaptically released glutamate. By extending simulations to the macroscopic (inter-synaptic) scale, we also assess cooperative glutamate actions exerted by the quasi-physiological activity of multiple synapses.
Transverse hippocampal slices (300 μM) were obtained from adult male Sprague-Dawley rats using a vibratome (VT1000S, Leica Microsystems, Germany). The slicing solution, ice-cold and bubbled with 95%O2-5%CO2, contained (mM): 75 sucrose, 70 NaCl, 2 KCl, 1 NaH2PO4, 26.2 NaHCO3, 5.6 MgCl2, 0.5 CaCl2, and 25 glucose, pH 7.4, 295-297 mOsm. Slices were stored in an interface chamber in a 0.5 mM CaCl2, sucrose-free solution for >1 hour before starting the electrophysiological recordings. The perfusion solution included (mM): 119 NaCl, 2.5 KCl, 1.3 MgCl2, 2 CaCl2, 26.2 NaHCO3, 1 NaH2PO4, 22 glucose, pH 7.4, 295-297 mOsm. Whole-cell patch clamp recordings were obtained from CA1 pyramidal cells identified under differential interference contrast, using a pipette filled with (mM): 117.5 Cs-gluconate, 17.5 CsCl, 10 HEPES, 0.2 EGTA, 8 NaCl, 2 Mg-ATP, 0.3 GTP, and 5 QX314Br, pH 7.2. The series resistance was monitored throughout the experiment using a 3 mV step command and cells were rejected if this changed more than 20%. Miniature EPSCs were recorded from pyramidal cells voltage-clamped at −60 mV in the presence of picrotoxin (100 μM) and TTX (1 μM). To evoke single-synapse responses in CA1 pyramidal cells, we used minimal stimulation of presynaptic Schaffer collateral fibers (29), as detailed in our previous study (30). Experiments were performed at 33-35°C. Chemicals were purchased from Sigma (St Louis, MO), except from TTX (Alomone Labs, Israel).
To evaluate extracellular diffusion, we used the technique based on two-photon excitation of a small soluble fluorescence indicator diffusing from a point source (24). In essence, this method takes advantage of the fact that multi-photon excitation occurs only within a thin (~1 μm) focal layer of the illuminated tissue volume (31). This layer is normally much wider than extracellular gaps while being much thinner than the region of measurement (50-100 μm), implying that recorded fluorescence provides direct readout of the indicator concentration profile (sampled in the focal plane) evolving in space and time.
We used a patch pipette (~1.0 μm tip diameter) filled with the water-soluble cell-impermeable indicator Alexa Fluor 350 (hydrazide, sodium salt, Molecular Probes, MW 349; 0.2 mM in bath medium inside the pipette). The pipette was connected to a pressure line (PicoPump, WPI) and lowered into the stratum radiatum, 30-50 μm beneath the surface, in a transverse hippocampal slice kept submerged in a recording chamber (Fig. 1A). The chamber was part of a multi-photon microscopy installation comprising a Radiance 2100 imaging system (BioRad-Zeiss) connected to an infrared femtosecond pulse laser MaiTai (SpectaPhysics-Newport) (32). The indicator was excited at λx = 790 nm, with an average beam power under the objective of <1 mW, to ensure that no detectable photobleaching occurs (this was tested separately by recording 1-2 s line scans of Alexa fluorescence inside cells; not shown). The fluorescence profile recorded on the scale of 50-100 μm therefore reflected diffusion from a point source.
The pipette tip was brought into focus (Fig. 1 A, arrow), and the holding pressure was adjusted to eliminate any detectable leakage of the fluorescent indicator from the tip. In control trials, continuous pressure application exerted a concentric fluorescence increase, as expected from the point source diffusion (Fig. 1, A and C). We then ejected the indicator using a 5 or 10 ms pressure pulse and recorded the time course of the fluorescence profile using a line-scan (rate 500 Hz) positioned near the point of ejection (Fig. 1, B and D): because of limited elasticity of the pressure system, this pulse duration was required to achieve a minimal detectable ejection of the indicator from the pipette tip. Although on the time scale of recording (1-2 s), the pulse represented a quasi-instantaneous event, the non-instantaneous ejection event could expand the effective diffusion source size beyond the 1 μm wide pipette tip (33). Indeed, 10-15 ms after the pulse onset, the fluorescence profile of Alexa near the tip appeared 4-5 μm wide (Fig. 1, B). To test if this could distort the point-source approximation, we compared the classical point-source solution (see below) with a solution for a 5 μm wide spherical source (the conservative-case scenario). Calculations showed that 200-300 ms post-pulse, the difference in the concentration profiles between these two cases was <3%, thus confirming the validity of the point-source approach in our conditions. In separate experiments, we also applied pressure pulses in a rapidly moving bath medium (mimicking quasi-instantaneous diffusion) confirming that the fluorescent ejection flux ceases completely in several milliseconds post-pulse.
The fluorescence profiles were therefore fitted as described earlier (24) using the classical point-source solution
where C(r,t) is the space-time concentration profile, Q is the total amount of ejected diffusing substance (a scaling factor) and D is the diffusion coefficient. In each experimental phase, ten to twenty line-scan sweeps, 30-60 s apart, were recorded and stored as a stack of 8-bit images preserving the original brightness values. An important advantage of the instantaneous point-source approach is that individual pulses are too short to have any lasting effect on the residual fluorescence in the region of interest (which might occur due to non-specific residual binding of a proportion of the indicator molecules to cell membranes). To ensure that the residual fluorescence accumulated during multiple pulses does not affect our estimates, we also routinely subtracted the pre-pulse fluorescence profile from the recorded diffusion profiles.
The parameter Diti (equation above, index denotes an individual sampled profile) was obtained by non-linear least square fitting of the Gaussian fluorescence profile I(r,ti), which is proportional to the concentration profile C(r,ti), at every time point ti (line scans at 2 ms intervals). The classical test for linear diffusion (D = const) is that the Dti value should increase linearly with ti. We observed that this linearity generally holds at >100 ms (after an initial slight deviation resulting from the pressure pulse) until ~500 ms; at >500 ms post-pulse, the signal-to-noise ratio became too low. We therefore normally sampled all fluorescence profiles between 100-500 ms, to obtain an estimate of D. Fitting procedures were custom written in MATLAB7.
Three-dimensional structure of Schaffer collaterals - CA1 pyramidal cell synapses has been documented in detail (15,34,35), and the fate of glutamate released at these synapses has been explored in several Monte Carlo models (9,36-39). The present study improves the accuracy of such models by adjusting extracellular diffusivity, synaptic environment architecture, and the uneven occurrence of local glutamate transporters, in accordance with the available experimental data.
First, to verify that random-walk simulations faithfully reproduce microscopic interactions between glutamate molecules and receptors, we simulated responses of 20 AMPARs to instantaneous injection of glutamate in a cylindrical volume (Fig. 2 A), with receptor kinetics set in accordance with (40). We thus simulated the experimental arrangement of outside-out patches, excised from CA1 or CA3 pyramidal cells, where glutamate is applied using a rapid concentration switch (41,42). The simulated AMPAR currents at different glutamate concentrations were consistent with the experimental data (Fig. 2, B and C).
In the synaptic environment model, the presynaptic part (en-passant boutons) and the postsynaptic part (dendritic spine heads) were represented by truncated hemispheres separated by a 300 nm wide 20 nm high apposition zone including a 200 nm wide synaptic cleft (Fig. 2 D), consistent with the characteristic three-dimensional ultrastructure reported for these synapses (14,15,35,43). The synapse was surrounded by a system of three-dimensional 20-30 nm wide extracellular gaps giving an extracellular space fraction α ~ 0.15 (22,23,44). The extracellular diffusion coefficient for glutamate (excluding space tortuosity due to cellular obstacles) was routinely set at 0.4 μm2/ms, between the intra-cleft value of ~0.33 μm2/ms estimated in electrophysiological experiments (45) and an average extracellular value of ~0.45 μm2/ms estimated here (see Results). In baseline conditions, 80 AMPARs and 20 NMDA receptors (NMDARs) were scattered randomly within the synaptic active zone (46,47), and their kinetics were set in accordance with (40) and (48), respectively. Glutamate glial transporters (EAAT1-2 type) were distributed within a spatial segment of the extrasynaptic membranes (Fig. 2 D), to match their average extracellular density of ~0.2 mM, a membrane surface density of 5-10·103 μm−2 (10), and to reflect the uneven pattern of glia surrounding these synapses (14,15).
We verified that the Monte Carlo approach simulations agreed with analytical solutions and multi-compartmental algorithms operating in simpler geometries (14,39). Indeed, releasing 2000-3000 glutamate molecules in the cleft center produced synaptic currents consistent with those recorded in CA1 pyramidal cells (Fig. 2, E and F) and with the currents predicted by previous models (see above). Simulations were carried out using a dedicated 14-node PC cluster running under Linux.
In order to evaluate the dynamics of extracellular glutamate on the scale of synaptic populations, we also simulated synaptic network activity in a 40 μm wide cube of neuropil. Although Monte Carlo modeling of free extracellular diffusion on this scale is in principle possible (49,50), the addition to the system of multiple reactions with unevenly distributed receptors would be computationally demanding (beyond a feasible scale). Furthermore, the aim of such modeling was to understand the landscape of extracellular glutamate with resolution sufficient to discern effects of individual synapses (the average nearest-neighbor distance between synapses in this area is 0.5 μm (51)) rather than tracing the fate of individual glutamate molecules. We therefore modeled the neuropil on this scale as a three-dimensional porous medium (52), again with α = 0.15 and the apparent (macroscopic) glutamate diffusion coefficient D set in accordance with the in situ measurements (see Results). Synaptic release sites for glutamate were scattered randomly, in accordance with the volume density of synapses in area CA1, NV = 2.0 μm−3 (51). Individual sites released 3000 molecules of glutamate (see below) at an arbitrarily chosen time point.
In this macroscopic model, the space was divided into 0.25 μm-wide cubic compartments. While this spatial resolution is sufficient to discern individual synapses (see above), averaging across individual space compartments might in principle distort the time course of extracellular glutamate in the proximity of release sites. To eliminate this source of uncertainty, we first used the Monte Carlo model (Fig. 2) to calculate the average glutamate concentration time course within virtual 0.25 μm-wide cubes that make up the simulated environment (Fig. 6 A, inset). Next, we compared the resulting glutamate profiles with those generated by the macroscopic compartmental model in which release events were represented by a volume-average glutamate concentration jump in the synapse-containing 0.25 μm compartment. We found that the concentration time course predicted by the two models produced a reasonable match (Fig. 6 A). This ensured that the macroscopic compartmental model was consistent with the microscopic events occurring in the immediate synaptic vicinity.
To evaluate extracellular diffusivity, we imaged point-source diffusion of the small cell-impermeable indicator Alexa Fluor 350 (MW 349) excited in two-photon mode in a free medium (Fig. 1, A and B) and in stratum radiatum (Fig. 1 C and D) at 33-35°C. The focal-plane emission profiles were fitted, at multiple time points post-ejection, by the simple theoretical curve using a single-parameter optimization (Fig. 1, E and F; Materials and Methods; in individual scans, residual fluorescence increments due to possible non-specific binding of the indicator were undetectable). These experiments yielded the indicator diffusion coefficients in the extracellular space and in a free medium, respectively, De = 0.23 ± 0.01 μm2/ms (n = 37) and Df = 0.48 ± 0.03 μm2/ms (n = 22; Fig. 1 G). The average free-to-neuropil diffusion retardation factor, calculated by averaging Df/De among individual slice experiments, was R = Df/De = 2.66 ± 0.43 (n = 19). This corresponds to the tortuosity λ = (Df/De)0.5 = 1.59. Diffusion retardation R generally incorporates a geometric hindrance factor Rg (due to extracellular space tortuosity) and an extracellular medium viscosity factor Rv, such that R = RgRv (53). Detailed Monte Carlo simulations of the three-dimensional neuropil represented by densely packed particles propose that Rg = 1.4 for the extracellular volume fraction values α of up to ~0.3 (49,50). This, together with our measurements, gives the viscosity factor Rv = R/ Rg =1.9.
The Alexa Fluor 350 molecules used in our measurements are only twice as heavy as glutamate molecules (MW 349 and 175, respectively), which corresponds to only a ~26% difference in their spherical hydration radii. Both species are more than an order of magnitude smaller than any inter-cellular gaps. Furthermore, diffusion of both Alexa Fluor 350 and a much heavier indicator Alexa Fluor 594 (MW 759) is retarded to the same relative degree by dextran solutions that mimic the extracellular medium viscosity (24). Taken together, these observations indicate that diffusion retardation of Alexa Fluor 350 in the neuropil, relative to its diffusion in a free medium, should be representative of that for glutamate.
The diffusion coefficient of glutamate (based on glutamine measurements) at 25°C in water is 0.76 μm2/ms (54). The viscosity of a standard physiological solution measured at 22-24°C using a falling ball viscometer is 1.05 mPa·s (53) whereas standard water viscosity in these conditions is ~10% lower, 0.93-0.95 mPa·s (55). This indicates that the glutamate diffusion coefficient at 22-24°C in the bath medium is ~0.68 μm2/ms. However, NMR-based measurements of water self-diffusion show a ~26% increase between 25°C at 35°C (56). This predicts the glutamate diffusivity value at near-physiological temperature of Df = 0.68 × 1.26 = 0.86 μ2/ms. Our measurements (Fig. 1) suggest therefore that the average macroscopic extracellular diffusivity of glutamate in the stratum radiatum neuropil is Df / R = 0.32 μm2/ms whereas its average diffusivity in the interstitial space unhindered by cell obstacles will depend on the viscosity factor Rv only, thus yielding Df / Rv = 0.45 μm2/ms.
In the hippocampal neuropil, glial glutamate transporters are thought to provide >95% of glutamate uptake (11). With an average equivalent extracellular concentration T = 0.2 mM (10) and an upper limit cycling rate kc ~ 0.05 ms−1 (8,57), these transporters should sustain steady-state glutamate uptake at a rate of up to kcT = 10 μM·ms−11. How does this compare with glutamate release in the course of synaptic activity? In area CA1, excitatory synapses occur at a density of NV ≈ 2 μm−3 (51,58). Classically, an action potential arriving at one of such synapses releases one, or occasionally more than one (59), synaptic vesicle with probability Pr = 0.2-0.5. Each release event frees ng = 2000-3000 glutamate molecules (60-62) (although see (34)). The extracellular volume fraction α in the CA1 area is 0.13-0.20 (22,23) and the time-average axonal firing rate f of Schaffer collaterals is unlikely to exceed 100 Hz. These data suggest that the upper limit glutamate release rate, with all axons firing continuously, is in the region of NV·Pr·ng·α−1·f· NA−1 ≈ 2-5 μM·ms−1 (NA is Avogadro's number).
However, it is unlikely that all synapses discharge glutamate at this rate. In fact, experiments in acute slices suggest that synchronous activation of only 0.5-1% of all excitatory synapses is sufficient to excite a CA1 principal neuron in the absence of inhibition (16,18). Because synaptic activity is unlikely to occur homogenously in space (and therefore clusters of higher-than-average synaptic activity are likely), we consider a conservative assumption that 10% of local synapses can be active at a time. This corresponds to a time-average glutamate release rate of 0.2-0.5 μM·ms−1. When compared to the steady-state glutamate uptake rate of 10 μM·ms−1 (see above), this figure suggests that synaptic activity in area CA1 occurs with a glutamate uptake safety factor of 20-50. This is consistent with experimental observations that suggest that synaptic glutamate release does not overwhelm transporters (13,63). Such space-and-time average estimates, however, may conceal the diversity of microscopic events occurring at a sub-synaptic scale where the local transporter distribution is not homogenous.
Do glutamate transporters occurring immediately outside the synaptic cleft affect receptor activation inside the cleft? Here we focused on AMPARs, which are expressed predominantly within the postsynaptic density (46,64) and mediate the bulk of excitatory response at the synapses in question. We used the detailed Monte Carlo model (Fig. 2; Materials and Methods) to ask whether varying the number of EAAT1-2 type glial transporters (10) outside the synaptic cleft influences synaptic AMPAR responses. Because such influences might in principle depend on the intra-cleft diffusion coefficient of glutamate (45), we explored this parameter around its predicted average value of ~0.45 μm2/ms (see above). The results show that extrasynaptic transporters have little influence on AMPAR responses: varying the number of transporters scattered over the designated extrasynaptic segment from none to 1500 (Fig. 2 D; corresponds to an average local extracellular concentration of ~0.2 mM) results in only a <10% variation in receptor activation, irrespective of local glutamate diffusivity (Fig. 3 A).
Next, we tested the effect of glutamate transporters co-occurring with AMPARs inside the synaptic cleft. The existence of intra-synaptic glutamate uptake is debated, and the main candidate at hippocampal synapses is the neuronal transporter EAAT3 (9,11,65-67). Our simulations suggested that, unlike extra-synaptic transporters, only a few dozen intra-synaptic transporter molecules could reduce the activation of AMPARs that occur nearby (Fig. 3 B; the effect was somewhat counter-intuitive because the number of released glutamate molecules much exceeded the number of transporters; one possible explanation is that at the peak of AMPAR activation - several hundred microseconds post-release - only a small proportion of released glutamate remains in the cleft). This result leads to a prediction that glutamate uptake blockade should facilitate AMPAR-mediated responses when more than several dozens of transporters occur inside the cleft.
To test whether such facilitation indeed occurs in our conditions, we recorded AMPAR-mediated EPSCs in CA1 pyramidal cells either during miniature synaptic events (in 1 μM TTX) or in response to minimal stimulation which activates only one or very few synapses on the recorded cell (29). In both cases, the low density of active synapses should exclude any inter-synaptic influence of escaping glutamate, with or without intact glutamate uptake (16,18), reflecting the conditions of the single-synapse model. Blocking glutamate uptake with 50 μM TBOA had no detectable effect in either case (Fig. 3, C and D), consistent with earlier observations made using other pharmacological tools (19,20). While arguing that the number of intra-cleft transporters is not greater than 20-30, such results however do not rule out the presence of glutamate transport in the cleft in principle.
In addition to the AMPARs occurring inside the synaptic cleft, there are a number of perisynaptic receptors, in particular those diffusing laterally outside the synapse (68). Do local transporters affect activation of such receptors by glutamate? Our simulations showed that activation of the low-affinity AMPARs declines steeply with distance from the release site, consistent with previous reports (14,38,69), with or without transporter action (Fig. 4, A-C). Similarly, extrasynaptic transporters have little effect on the activation of synaptic AMPARs in response to repetitive releases, when the proportion of receptors in a desensitized state gradually increases (Fig. 4, D-E).
One of the most plausible targets for the actions of escaped glutamate are high-affinity extrasynaptic NMDARs, in particularly those containing the NR2B subunit (70-72). To determine whether spatial juxtaposition with respect to transporters, on the 10-100 nm scale, plays a part in the activation of such receptors, we placed a cluster of 20 NMDARs at different distances from the release site, exploring areas either enriched or devoid of transporters (Fig. 5 A; in these simulations, we assumed that the neuronal membranes were sufficiently depolarized to relieve the Mg2+ block of the NMDARs). Because of the unreasonably long computing time (weeks) required to simulate microscopic events for 200 ms post-release in each set of conditions, we documented the NMDAR charge transfer between 0-20 ms post-release. This parameter should faithfully represent the degree of receptor activation because the amount of glutamate remaining in the system by that time point is negligible. The results indicate that the activation of intra-synaptic NMDARs is largely insensitive to transporter actions whereas activation of extra-synaptic NMDARs is clearly reduced when these receptors occur in the vicinity of transporters (Fig. 5, B to D). In general, however, the NMDAR activation level at distances of up to 600 nm from the release site remained above 10% of that inside the cleft (Fig. 5 C). This is somewhat higher than earlier theoretical estimates based on compartmental models, in which both glutamate and transporters were represented by the continuously distributed concentrations (14,18,37) (see Discussion).
We next asked to what degree local glutamate transporters affect activation of perisynaptic metabotropic glutamate receptors (mGluRs). While a facilitatory effect of transporter blockade on mGluR activation has been demonstrated in electrophysiological experiments (73,74), it is not fully understood whether this reflects events on a sub-micron, as opposed to macroscopic, scale. Because the exact kinetics of physiological actions exerted by mGluRs is not known, we considered the proportion of mGluRs singly-bound by glutamate post-release (75,76), as implemented in the GENESIS computational medium (77). In our model, mGluRs were distributed either at the synaptic perimeter, in accordance with experimental observations (78,79), or further away maintaining the shape of a concentric ring segment (Fig. 5, D). Simulations indicated that the net effect of perisynaptic transporters on the activation of local mGluRs is modest (5-20%) but in relative terms increases rapidly with distance from the release site (Fig. 5, D-F). Because electrophysiological experiments showed substantially greater effects of the transporter blockade (73), our results suggest that either the recorded physiological actions of mGluRs are highly supra-linear with respect to receptor binding to glutamate or these receptors occur, on average, at a significant distance from glutamate release sites.
To evaluate extrasynaptic and long-range actions of glutamate, we simulated a (40 μm)3 neuropil region divided into 0.25 μm space compartments. On a local scale, we confirmed the compartmental approach faithfully represents the microscopic events occurring in the synaptic vicinity, by comparing the volume-average glutamate concentration time course obtained using the Monte Carlo model with that obtained with the compartmental model (Fig. 6 A; Materials and Methods). On the scale of neuropil, we distributed glutamate release sites representing individual synapses as a hard-core spatial Poisson process (uniformly random process of rigid spheres with a density of 2.0 μm−3 and a core radius of 300 nm), to reflect the pattern of excitatory synapses in the CA1 area (15,51,58). The model allowed us to activate arbitrarily selected synapses at arbitrary time points.
To examine the landscape of extracellular glutamate during the unevenly distributed synaptic activity, we initiated release from multiple sites within two separate active ‘pools’ of synapses (spherical regions, 5 and 15 μm wide, 10 μm apart; Fig. 6 B). Within each pool, synaptic discharges followed a stochastic Poisson process, so that ~2% of synapses discharged randomly over a 10 ms time widow (equivalent to an average singe-synapse discharge rate of ~2 Hz). This intensity reflects experimental estimates of the (upper limit) volume-average synaptic activity sufficient to excite CA1 pyramidal cells (16,18).
Outside the active pools, synapses released glutamate at a much lower average rate, ~0.05 Hz. At the baseline level of EAAT1-2 expression in the CA1 neuropil, 0.2 mM (10), this leads to an ambient glutamate concentration of 30-50 nM, consistent with recent measurements of extracellular glutamate in area CA1 in quiescent slices (13).
Simulation snapshots in Fig. 6, C to F, depict extracellular glutamate profiles produced at three levels of glial glutamate transporters, corresponding to 100%, 10%, 5% and 2.5% of the baseline EAAT1-2 expression in the CA1 neuropil (10). The results indicate that, when glutamate uptake is intact, synaptic activity sufficient to excite principal cells elevates the local ambient glutamate concentration only slightly, with relatively sparse ‘hotspots’ reaching ~1 μM (Fig. 6 C). This is consistent with detectable activation of extra-synaptic NMDARs (mainly those containing NR2B subunits) in CA1 pyramidal cells following synchronous excitation of multiple Schaffer collaterals (16,18,80). Outside the active synaptic pools, however, the ambient glutamate concentration remains virtually unaffected. Furthermore, synaptic releases appear to summate in a co-operative manner: the glutamate level within the smaller synaptic pool shows almost no detectable increases even though the spatial density of release sites and the release rate are similar in both pools (Fig. 6 C).
A persistent increase in the ambient glutamate level above 1 μM occurs when 90% of all available transporters are switched off (Fig. 6 D). However, even in these conditions increases in the ambient glutamate level are still largely restricted to the pools of active synapses. It is only when 95-98% of the uptake system is impaired that glutamate released within a pool of active synapses may reach concentrations exceeding 1 μM over larger neuropil areas. In the latter case, co-operative glutamate action between active pools of synapses may occur at the scale of tens of microns (Fig. 6 F).
The main findings of this study are as follows. First, we measured retardation of extracellular diffusion of small molecules in hippocampal area CA1 using a concentration readout method based on two-photon imaging. Second, we combined such measurements with a Monte Carlo model and electrophysiological experiments to conclude that little effect of glutamate transport on AMPAR responses is expected irrespective of the receptor location. This contrasts with the role of extrasynaptic transporters which reduce activation of nearby NMDARs or mGluRs. Finally, simulations of glutamate release, diffusion and uptake on the scale of synaptic populations predict that synaptic activity sufficient to excite principal neurons leads to only modest (<1-2 μM) and sparse (microns apart) rises of ambient glutamate, within the active pool of synapses, unless the uptake systems fail catastrophically.
The updated method to measure extracellular diffusion with two-photon excitation imaging of a fluorescence point-source (24) (Fig. 1) yielded an average diffusion retardation factor R = 2.66, which is in between the two estimates obtained earlier with an iontophoretic method, 2.07-2.16 (22) and 2.92 (81). The value of R assessed here corresponds to an average glutamate diffusion coefficient in the space between cell membranes (excluding tissue geometry) of ~0.45 μm2/ms. Because synaptic clefts occupy only 1-2% of the extracellular space in area CA1 (82), this estimate applies predominantly to the extra-synaptic extracellular compartment. Electrophysiological experiments in cerebellar synapses suggest a lower diffusivity value inside the synaptic cleft, ~0.33 μm2/ms (45). This disparity indicates that synaptic clefts are packed with macromolecular obstacles that exert substantial steric hindrance to the diffusing neurotransmitter molecules, consistent with recent electron microscopy evidence (83).
Detailed Monte Carlo simulations of the three-dimensional synaptic environment (Fig. 2) suggest that perisynaptic glutamate transporters have little influence on the activation of intra-synaptic AMPARs, even when their numbers are comparable with those of released glutamate molecules, (Fig. 3 A). At the same time, only a few dozen transporters distributed quasi-randomly inside the synaptic cleft should attenuate activation of co-occurring AMPARs (Fig. 3 B). Although this observation appears somewhat counterintuitive, we note that only a small proportion of 3000 released glutamate molecules are likely to remain in the cleft when AMPARs are at the peak of their doubly-bound occupancy. When the high-affinity transporters occur nearby, they may successfully compete with AMPARs for glutamate binding. Consistent with the previous observation, our experiments show that neither miniature nor minimal-stimulation induced (single-fiber) AMPAR-mediated EPSCs in CA1 pyramidal cells are affected by glutamate transporter blockade (Fig. 3, C and D). This result suggests that the number of glutamate transporters co-occurring with AMPARs within synaptic clefts is, if anything, small (< 20-30).
Outside the cleft, activation of extrasynaptic NMDARs is substantially reduced if they share their spatial domain with glutamate transporters but could be significant if no transporters are expressed in their immediate vicinity (Fig. 5, A to C). This result provides a quantitative reference for evaluating the extent of extra- and/or inter-synaptic signalling in the hippocampus, an issue remaining a subject of debates (18,37). The present simulations also predict a somewhat higher level of activation for NMDARs occurring in the transporter vicinity than reported previously in comparable conditions (14,37,51). Again, one plausible explanation is that the previous models dealt with continuous concentrations rather than with individual molecular events. In addition, glutamate transporters in the present approach are accumulated within a restricted area (a fragment of the glial membrane), in accordance with experimental observations, rather than distributed homogeneously at a lower density. These two factors might increase the probability that diffusing glutamate molecules encounter an NMDAR before being bound to a transporter molecule. Our data have also suggested that the effect of transporters on mGluR binding by glutamate increases rapidly with the distance to the release site (Fig. 5, D-F). This may relate the reported substantial effects of transporter blockade on mGluR responses in Purkinje cells (73) to a relatively large, rather than small, average distance between activated mGluRs and glutamate released sites. In summary, our observations suggest that juxtaposition of receptors and transporters has a complex effect on receptor activation, which could be masked by volume-averaging.
It has long been understood that the extracellular glutamate level on a macroscopic scale is determined by the number/ density of available transporters. The present data provide quantitative insights into the microscopic features of the glutamate landscape shaped by the activity of multiple synapses. Whilst sustained synaptic activity is likely to produce sparse, relatively small (up to 1-2 μM) local increases in the ambient glutamate level, such increases do not spread appreciably outside the pool of active synapse (Fig. 6 C). Only when >90% of glutamate transport fails, do longer-range gradients of extracellular glutamate emerge (Fig. 6, D to F). Again, this provides a quantitative reference for the observation that activation of extra-synaptic glutamate receptors is dramatically reduced in areas enriched in transporters (73). A striking demonstration of this principle can be found in the hypothalamic supraoptic nucleus where the withdrawal of transporter-enriched glial processes are associated with long-range actions of synaptically released glutamate (84).
The present results help to understand the extent of inter-synaptic cross talk via escaped glutamate. Intriguingly, individual astrocytes, which are responsible for the bulk of glutamate uptake in the hippocampus (11), occupy separate neuropil domains each filling a volume of ~9·104 μm3 while overlapping by only 3-10% with neighboring astrocytes (85,86). This suggests that failure of a single astrocyte could impair glutamate removal in the vicinity of ~1.8·105 synapses. Because an individual CA1 pyramidal cell hosts 5-10·103 synapses (87), such glial impairment may thus affect synaptic inputs to hundreds of principal cells. This prediction is significant in the light of recent findings showing that Ca2+ signaling in a single astrocyte could alter synaptic transmission properties in its vicinity (88).
This work was supported by the Wellcome Trust, Medical Research Council (UK), the European Union (PROMEMORIA 512012), and Human Frontier Science Program. The authors thank Dimitri Kullmann, Leonid Savtchenko and Kirill Volynski for valuable comments.