Different modes of expression of AMPA and NMDA receptors in hippocampal synapses

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1 articles Different modes of expression of AMPA and NMDA receptors in hippocampal synapses Yutaka Takumi 1,2, Vania Ramírez-León 1,3, Petter Laake 4, Eric Rinvik 1 and Ole P. Ottersen 1 1 Department of Anatomy, Institute of Basic Medical Sciences, University of Oslo, POB 1105 Blindern, 0317 Oslo, Norway 2 Department of Otorhinolaryngology, Hirosaki University School of Medicine, Hirosaki , Japan 3 Department of Neuroscience, Karolinska Institute, S Stockholm, Sweden 4 Section of Medical Statistics, University of Oslo, POB 1122 Blindern, 0317 Oslo, Norway Correspondence should be addressed to O.P.O. (o.p.ottersen@basalmed.uio.no) Postembedding immunogold labeling was used to determine the relationship between AMPA and NMDA receptor density and size of Schaffer collateral commissural (SCC) synapses of the adult rat. All SCC synapses expressed NMDA receptors. AMPA and NMDA receptors were colocalized in at least 75% of SCC synapses; the ratio of AMPA to NMDA receptors was a linear function of postsynaptic density (PSD) diameter, with AMPA receptor number dropping to zero at a PSD diameter of ~180 nm. These findings indicate that silent SCC synapses are smaller than the majority of SCC synapses at which AMPA and NMDA receptors are colocalized. Thus synapse size may determine important properties of SCC synapses. AMPA and NMDA receptors are the major classes of ionotropic receptors in central glutamatergic synapses 1 3. There is now strong evidence from high-resolution immunogold analyses that both receptors are concentrated opposite the presynaptic active zone in a membrane domain that coincides precisely with the postsynaptic density 3 9. However, it is not known what factors determine relative density of AMPA and NMDA receptors at synapses at which the two receptors are colocalized. The physiological significance of the ratio between these receptors is illustrated by the extreme cases of zero or infinite values; the first of these extremes should produce synapses that are silent at normal resting potentials 10 12, whereas the latter would be incompatible with NMDA receptor-dependent synaptic plasticity 13. Here we explore the hypothesis that synaptic size is an important factor determining the ratio of AMPA to NMDA receptors at the synapse. We focused our study on Schaffer collateral commissural synapses. These synapses show considerable size heterogeneity 14,15 and sustain NMDA receptor-dependent long-term potentiation (LTP) 13,16,17. Moreover, some SCC synapses contain few or no AMPA receptors, and the number of AMPA receptors increases with increasing synapse size 8. However, it is unknown whether the NMDA receptors show the same dependence on synapse size. Using a highly sensitive postembedding immunogold procedure 5, we show that AMPA and NMDA receptors are differentially expressed in SCC synapses and that the ratio between the two receptors increases linearly with synapse diameters above 180 nm. We also demonstrate that the subpopulation of SCC synapses devoid of detectable AMPA-receptor immunoreactivity 8,18 does contain NMDA receptors, thus conforming to properties expected for silent synapses RESULTS Using antibodies specific for glutamate, we confirmed previous observations in the stratum radiatum 19 that asymmetric synapses on spines are generally enriched in glutamate (Fig. 1). In our samples, all asymmetric synapses on spines were immunolabeled with a mixture of antibodies recognizing NR1 as well as NR2A/B (Figs. 1 and 2a c). This conclusion was based on analysis of serial sections through the same synapses. Even in single sections, over 98% of the synaptic profiles with the above ultrastructural characteristics (152 of 154 in Fig. 3a) displayed at least one gold particle within 20 nm of the inner leaflet of the postsynaptic membrane. The labeling pattern was consistent with exclusively postsynaptic localization of NMDA receptors. With few exceptions (Fig. 2a), gold particles overlying the spine plasma membrane were associated with the PSD (Fig. 2a c). In the following, PSD diameter will be used interchangeably with synapse size. In sections labeled with the NMDA-receptor antibodies, there was no significant relationship between the number of gold particles per PSD profile and PSD length (Figs. 2a c and 3a). This also holds for profiles corresponding to the PSD diameter, defined as the longest PSD profile in serial sections (Fig. 3b and c). For each of the data sets in Fig. 3a c, the confidence interval of the slope contains zero. Correlation coefficients ranged between 0.05 and 0.21, indicating that only a very small percentage of the variability (0.3 4%) can be explained by variation in size. The relationship of particle number with synapse size was also insignificant with data in Fig. 3a c combined (data not shown). In striking contrast, the number of gold particles obtained by use of a mixture of antibodies recognizing the AMPA receptor subunits GluR1, 2/3 and 4 showed a significant relationship with PSD length (Figs. 2d f and 3d f). The correlation coefficient approached r = 0.8 when analysis was restricted to profiles corresponding to the PSD diameter (Fig. 3e and f), but a positive slope was evident even in random synaptic profiles 618 nature neuroscience volume 2 no 7 july 1999

2 articles a b c Fig. 1. Double immunogold labeling. (a c) Asymmetric synapses on spines in stratum radiatum contain glutamate (large gold particles) and NMDA receptors (small gold particles). The few large gold particles in the spines (s) may reflect metabolic glutamate or postsynaptic glutamate uptake. Arrowheads indicate extent of postsynaptic densities. t, nerve terminal; scale bar, 200 nm. (Fig. 3d). The degree of correlation was independent of the general labeling intensity of the respective tissue sections (Fig. 3, compare e with f). In addition to differences in synapse size, significant sources of variation in number of gold particles per PSD diameter include differences in total receptor number independent of synapse size, asymmetric distribution of receptors around the center of the PSD ( anisotropy ) and stochastic variation in the ratio of gold particles to exposed receptors. These sources of variation explain scatter around the regression line in Fig. 3e and f. To isolate the influence of the last type of variation, defined here as measurement error, we recorded the linear gold particle densities along profiles of the same synapse, captured in two consecutive sections through or near the center of the synapse. These sections had been processed simultaneously and displayed the same general labeling intensity. Assuming no significant anisotropy (see above) in receptor distribution, any difference in the linear gold particle density between the two members of a pair of synaptic profiles (n = 54) should reflect measurement error. Because the estimated correlation coefficient was r = 0.78 (Fig. 3e and f), 39% = (1 r 2 ) 100% of the variability in number of gold particles remained unexplained by synapse size (PSD diameter). Out of an unexplained variability of 2.56, 1.36 (21% of the total variability) could be attributed to measurement error and 18% of the total variability must then be due to sizeindependent variations in receptor number (see above). A significant proportion of the synapses labeled with the NMDA-receptor antibodies was immunonegative for AMPA receptors (Figs. 2g i, 3d f and 4). This conclusion was based on analysis of double-labeled sections (Fig. 2g i) as well as consecutive sections single-labeled for either NMDA or AMPA receptors. In the sample of serially sectioned synapses represented in Fig. 4b (n = 200), the proportion of AMPA-negative synapses was 25%. This value was not significantly altered by inadvertent reductions in the general labeling intensity (Fig. 4a, same material as in Fig. 3b and e). It should be noted that a synapse was considered immunonegative only if it could be traced through three or more sections without displaying any gold particles. Inclusion of the third section only marginally affected the estimated proportion of negative synapses (Fig. 5a), thus attesting to the robustness of our criterion. AMPA immunonegative synapses were small (Figs. 2 and 3). The smallest synapses represented in Fig. 3f (for which PSD length was recorded in 20-nm steps) were analyzed in more detail in Fig. 5b to identify the lower size limit for immunopositive synapses. All synapses less than 160 nm in diameter were AMPA immunonegative, as were 17 of 22 synapses less than 180 nm in diameter. The average diameter of immunonegative synapses (± s.d.) was 189 ± 25 nm (n = 50), compared with 260 ± 58 nm (n = 150) for the immunopositive ones. AMPA immunonegative synapses were not only devoid of gold particles overlying the postsynaptic density but also lacked significant labeling in extrasynaptic spine membranes and in the interior of the spine (Fig. 2d and g). Scattered particles were observed at these sites at large immunopositive synapses (Fig. 2f and i). Only a few particles on the presynaptic side were situated farther than 20 nm from the postsynaptic membrane (Fig. 2e and h). In other words, there was no evidence of a presynaptic pool of this receptor. The pattern of immunolabeling of the SCC synapses was compared with that of mossy fiber synapses. In contrast to the former synapses, the latter were all AMPA immunopositive (Fig. 6a and b), even when judged from analysis of single, random a b c d e f Fig. 2. AMPA and NMDA receptor immunogold lableling. Asymmetric synapses labeled with antibodies recognizing NMDA receptors (a c) or AMPA receptors (d f) or with antibodies to AMPA receptors (10-nm particles) followed by antibodies to NMDA receptors (g i; 20-nm particles). Whereas large (c, f, i) and medium-sized (b, e, h) synapses contain both types of receptor, a subpopulation of the small synapses displays only NMDA receptors (a, d, g). A few gold particles are associated with the extrasynaptic spine membrane (a, e) or with the spine interior (particularly of large synapses; c, f, i). Scattered particles overlying synaptic vesicles (c, i) remained after preadsorption and are likely to reflect nonspecific binding. The few particles over the presynaptic membrane are located within 20 nm of the postsynaptic specialization and can thus be explained by epitopes at the latter site (see Results). Arrowheads indicate extent of postsynaptic density. Each section corresponds to the PSD diameter, as identified in serial sections. Mitochondrion designated by m ; other abbreviations as in Fig. 1. Scale bar, 200 nm. g h i nature neuroscience volume 2 no 7 july

3 to density per unit area. In contrast, the AMPA-receptor immunolabeling along the synapse diameter is a linear function of synapse size that regresses to zero at a PSD diameter of ~180 nm. The most parsimonious interpretation of this finding (see Appendix) is that the total number of AMPA receptors (AMPA tot ) in a synapse is proportional to the available PSD area (the fraction of PSD area unoccupied by NMDA receptors). Combining equations 2 and 5 in the Appendix, one finds that the ratio between the two receptors (AMPA tot :NMDA tot ) must increase linearly with PSD diameter above a certain threshold. This threshold (~180 nm) is defined by the x-intercept in Fig. 3e and f. Several lines of evidence indicate that induction of LTP in the SCC fiber system is NMDA-receptor dependent and leads to strengthening of synaptic transmission through AMPA receptors 16, A study based on non-stationary fluctuation analysis and recording from apical dendrites of CA1 neurons concluded that much of this strengthening could be attributed to an increase in the AMPA-receptor single-channel conducarticles a b c NMDA b = p = Cl = ( 0.003, 0.11) r = 0.09 n = 154 (animal 1) Length of PSD (nm) b = p = Cl = ( 0.014, 0.10) r = 0.05 n = 34 (animal 1) b = p = Cl = ( 0.008, 0.027) r = 0.21 n = 28 (animal 2) profiles (Fig. 6c). Analysis of serial sections showed that the average number of gold particles along the PSD diameter of mossy-fiber contacts was more than twice that found in SCC synapses (Table 1). Furthermore, the linear density of gold particles was higher. A statistically significant, positive correlation was found between gold particle number and PSD diameter, but the correlation coefficient was smaller than for the synapses in stratum radiatum (Table 1). All mossy-fiber synapses were immunopositive for NMDA receptors. However, notable differences were found in intensity of NMDA-receptor labeling a between the two types of synapse (Table 1). A lack of correlation between the number of gold particles along the synapse diameter and synapse size was common to the two synapse types. DISCUSSION The present data indicate that NMDA and AMPA receptors are colocalized at about 75% of the SCC synapses 18,20. The most interesting finding, however, is that the two receptor types are expressed according to different principles. In the case of NMDA receptors, the number of gold particles along a section running through or near the center of the synapse was independent of synapse size, indicating that total NMDA receptor number (NMDA tot ) in a synapse is proportional to the diameter of the PSD (see Appendix). This may seem contradictory at first glance, but is a simple consequence of converting linear density d e f b = p < Cl = (0.020, 0.025) r = 0.72 n = 278 (animal 1) b = p < Cl = (0.024, 0.033) r = 0.78 n = 107 (animal 1) b = p < Cl = (0.048, 0.060) r = 0.78 n = 200 (animal 2) AMPA Length of PSD (nm) Percentage of synapses Fig. 3. Regression analysis of serially sectioned asymmetric synapses on spines in stratum radiatum. The number of gold particles per PSD profile shows a positive relationship with PSD length in sections incubated with AMPA receptor antibodies (d f), whereas no such relationship is seen after immunogold labeling of NMDA receptors (a c). The diagrams in (a) and (d) are based on random profiles, those in (b, c, e and f) on the longest PSD profiles of the individual synapses as determined in serial sections. One of the sections in the series used for AMPA receptor analysis was incubated with NMDA receptor antibodies; thus all of the synapses represented in (d f) could be confirmed as immunopositive for NMDA receptors. The data were obtained from two different animals, as indicated. The slope (b) is shown with its p value and 95% confidence interval (CI), together with the correlation coefficient (r). The x-intercepts in (e) and (f) were 184 nm and 171 nm with CIs of (167, 201) and (161, 182), respectively. Note that data from several synapses may coalesce into the same data point (PSD length was recorded in 20-nm steps). Frame in (f) indicates region analyzed at higher resolution in Fig. 5b. Fig. 4. Distribution of PSD profiles according to labeling intensity for AMPA receptors (bin width corresponds to one gold particle). Synapses represented by the first column (~25% of total) failed to display any gold particles in each of three consecutive sections including the section passing through the center of the synapse. The histograms are from two animals represented in Fig. 3e and f. b Percentage of synapses 620 nature neuroscience volume 2 no 7 july 1999

4 articles a Proportion of AMPAnegative profiles (%) Number of section tance 17. However, this mechanism could not explain the expression of LTP in all cells. An additional mechanism proposed by several groups 10 12,23 25 and of particular relevance for latephase LTP 25 is enhancement of transmission by insertion of new AMPA receptors in the synapse. This could occur even in synapses lacking AMPA receptors, thus converting silent synapses (see below) into active ones Based on the present data, one would predict that insertion of new AMPA receptors would be associated with a growth of the PSD. There is solid evidence from analyses of intact animals 26,27 that growth processes may take part in the expression of LTP. However, few studies 28 have focused specifically on PSD size, and it remains to be shown whether the PSD is enlarged in potentiated SCC synapses. A notable finding in the present study was that about 25% of the SCC synapses were devoid of AMPA-receptor immunolabeling. Analysis of serial sections rules out the possibility that the AMPAimmunonegative profiles represent margins of larger synapses. Further, the finding of immunonegative synapses cannot merely reflect suboptimal sensitivity, as the smallest synapses were uniformly negative (Fig. 5b). It should also be recalled that, as shown previously 8, mossyfiber synapses were consistently immunopositive for AMPA receptors. We thus conclude that the synapses we defined as immunonegative contained a very low number of AMPA receptors, and possibly, none. Of course, becuase a large fraction of the receptors were hidden b Number of gold particles (accumulated) Fig. 5. Proportion and sizes of AMPA-immunonegative synapses. (a) Robustness of procedure for determining the proportion of AMPAimmunonegative synapses (data in Fig. 3e). About 50% of the synapses are negative (no associated gold particles), when judged by a single profile. When a second, consecutive profile through these synapses is examined, the proportion of negative synapses drops to about 30%. Only a marginal change is seen after inclusion of a third section. For each synapse, one of the three sections runs through the center of the PSD. (b) Detailed analysis of the smallest synapses represented in Fig. 3f (frame). This analysis was performed to identify the size threshold below which no positive synapses occur. The values along the ordinate indicate accumulated number of gold particles; the values along the abscissa indicate the diameter of the PSD as judged by serial sections. All synapses with a PSD diameter <160 nm are immunonegative by the same criterion given for (a). inside each >50-nm-thick Lowicryl section and unavailable for immunolabeling 29, the total number of gold particles in a serially sectioned synapse will necessarily be lower than the number of functional AMPA receptors. The ratio between these numbers was previously estimated at ~1:2.3 in similarly processed tissue 8. This estimate was based on an immunogold labeling of mossy-fiber synapses of 17-day-old rats for which the number of functional AMPA receptors has been determined by patch-clamp analyses 30. Extrapolating to SCC synapses in adult rats, Nusser et al. concluded that ~15% of these synapses contained fewer than 3 AMPA receptors 8. It should be noted that the labeling efficiency in Nusser s material seems comparable to that obtained here, with a maximum of particles per SCC profile. Additionally, there is evidence that the number of AMPA-immunonegative CA1 asymmetric synapses decreases between P2 and 5 weeks postnatally 31, and that the number of silent synapses may be regulated during development by changes in synaptic activity 32. The AMPA-immunonegative/NMDA-immunopositive fraction of SCC synapses could correspond to synapses that are electrophysiologically silent at normal resting potentials 10 12, Such synapses are predicted to contain NMDA receptors but no (or very few) AMPA receptors. Our findings and those of Nusser et al. 8 thus indicate that some synapses are silent because they lack AMPA receptors and not because existing receptors are inactive. A study of autapses in single neuron cultures 33 seems to rule out the possibility that lack of AMPA receptor response can be explained simply by spillover of glutamate to adjacent synapses 34. We can conclude at this point that the number of AMPA receptors in SCC synapses varies over a wide range and that the pronounced heterogeneity in synapse size can be viewed as a morphological correlate of this. The physiological correlate is a large variability in synaptic strength. In contrast, NMDA receptors show a lower degree of size-dependent variability, being present in all synapses and increasing only modestly with synapse size. This is consistent with the idea that the function of NMDA receptors as a coincidence detector requires a minimum of NMDA receptors at the synapse, and that a large increase beyond this minimum is unnecessary and possibly harmful (because of toxic effects of excessive Ca 2+ influx). Importantly, the present findings indicate that all SCC synapses are potential loci for NMDA-receptor-dependent plasticity. The pattern of AMPA receptor distribution in SCC synapses a b c Particles Fig. 6. Mossy fiber synapses (mf) labeled with antibodies to AMPA receptors. Note that all synaptic contacts are positive. This is shown graphically in (c); values along abscissa represent number of gold particles per profile; single section analysis. Postsynaptic thorn, th. Arrowheads indicate extent of PSD. Scale bars, 500 nm (a); 200 nm (b). Percentage of synapses n = 95 nature neuroscience volume 2 no 7 july

5 articles differed substantially from that in the mossyfiber synapses. In addition to being more strongly and uniformly labeled for AMPA receptors as shown previously 8, mossy-fiber synapses were less immunoreactive for NMDA receptors than SCC synapses 35,36. It is tempting to relate these differences in the receptor profile to the finding that mossyfiber synapses do not show an NMDA-receptor-dependent LTP 8,37. Interestingly, the sum of the linear densities of the AMPA and NMDA receptor immunolabeling was smaller for the mossy fiber synapses than for the SCC synapses (Table 1). If the labeling efficiency is the same for both antigens (which remains to be shown), our findings suggest that AMPA and NMDA receptors occupy a smaller fraction of the PSD in mossy fiber synapses than in SCC synapses. Kainate receptors may populate part of the remaining space 38,39. In conclusion, the present data on SCC synapses suggest that the ratio between AMPA and NMDA receptors depends critically on PSD diameter 40. In other words, the receptors are expressed not according to a fixed stoichiometry, but rather, as distinct functions of synapse size. It will be interesting to resolve whether similar principles for receptor expression explain why neonatal hippocampal CA1 synapses have NMDA receptors but no functional AMPA receptors 41, that is, whether the size threshold obvious in mature synapses also applies during the initial development and growth of synaptic contacts. METHODS Tissue preparation. Four adult male Wistar rats ( g, Möllegaard Laboratories, Ejby, Denmark) were deeply anesthetized by an intraperitoneal injection of a mixture of midazolam, fentanyl citrate and fluanisone (3.8, 0.24 and 7.5 mg per kg body weight, respectively). The animals were transcardially perfused with a mixture of 4% formaldehyde and 0.1% glutaraldehyde as described 42. Small tissue blocks from the CA1 region of the hippocampus were subjected to freeze-substitution and low-temperature embedding in Lowicryl HM20 (refs. 5, 43). All experiments were performed in accordance with the guidelines of the Norwegian Committee on Animal Experimentation. Postembedding immunocytochemistry. Serial ultrathin sections (50 70 nm) were mounted on formvar-coated grids and processed for immunogold cytochemistry 5. In brief, sections were immersed in a saturated solution of NaOH in absolute ethanol for 2 3 s and incubated at room temperature first for 10 min in 0.1% sodium borohydride and 50 mm glycine in 5 mm Tris buffer containing 0.3% NaCl and 0.1% Triton X-100 (TBNT), followed by incubation in 2% human serum albumin (HSA) in TBNT, then for h in mixtures of rabbit antibodies to GluR1, GluR2/3 and GluR4 (final concentrations, 2.0 mg per ml each) or to NMDAR1 and NMDAR2A/B (final concentrations, 2.3 and 5.0 mg per ml, respectively) in TBNT containing 2% HSA. Next, sections were placed in 2% HSA in TBNT for 10 min and, finally, in goat anti-rabbit Fab fragments coupled to 10-nm gold particles (GFAR10; British BioCell International, Cardiff, UK) diluted 1:20 in TBNT containing 2% HSA and polyethylene glycol (0.5 mg per ml) for 2 hours. Preabsorption of the antibody solutions with excess immunizing peptide removed all labeling. All antibodies have been extensively characterized Postembedding immunogold double labeling. Double labeling of NMDA and AMPA receptors or of NMDA receptors and glutamate was carried out as described 47. NMDA receptor immunolabeling with 10-nm gold particles was followed by AMPA receptor immunolabeling with 20-nm gold particles (GAR20; British BioCell International, Table 1. Immunogold labeling of AMPA and NMDA receptors: comparison between Schaffer collateral/commissural-fiber (SCC) synapses and mossy-fiber synapses. Synapses SCC Mossy fiber AMPA receptors Average number of gold particles along synapse diameter 2.3 ± ± 0.3 (n = 107) (n = 95) Correlation between synapse size and number of gold particles along synapse diameter r = 0.78 r = 0.42 p < p < Linear density (particles per 100 nm PSD) NMDA receptors Average number of gold particles along synapse diameter 6.0 ± ± 0.2 (n = 34) (n = 47) Correlation between synapse size and number of gold particles along synapse diameter n.s. (p > 0.05) n.s. (p > 0.05) Linear density (particles per 100 nm PSD) The first set of values for each receptor type is given in number of gold particles (mean ± s.e.) recorded along the longest PSD profile of each synapse identified in serial sections (perforated synapses were excluded; see Methods). The longest profile is taken to represent the synapse diameter. (Average diameters ± s.d. were ± 70.1 and ± nm for SCC and mossy fiber synapses, respectively.) Comparisons are made within the same sections to ensure identical incubation conditions. The data presented were obtained from animal 1 (Fig. 3b and e; Fig. 6). The same pattern was observed in two additional animals. Cardiff, UK). The glutamate antibody (#607; ref. 5) was diluted 1:2000 and visualized with 15-nm gold particles (GAR15; Auroprobes, Amersham, UK). Sampling and analysis of the data. All direct comparisons between synapses (for instance, in Table 1) were made within the same series of sections incubated simultaneously. Electron micrographs were obtained at random from stratum radiatum of CA1b of the dorsal hippocampus ( 3.0 mm, approximate AP level 48 ), from a zone within 50 mm of the pyramidal cell bodies and from a zone ~200 mm distal. The two samples of synapses showed the same labeling characteristics and were therefore pooled for quantitative analysis. All asymmetric axospinous synapses with a distinct postsynaptic density were included, whereas asymmetric synapses on dendritic shafts were excluded. Perforated synapses were also excluded, as it is still unclear how to record their sizes in a biologically meaningful context. A serial section analysis (6 8 sections per series) was performed in 3 animals. An average of four to five consecutive sections sufficed to cover the entire synapse. Gold particles were counted in each synaptic profile and the length of the PSD recorded. Gold particles were included only if their centers were projected within 20 nm of the inner leaflet of the postsynaptic membrane 5 and within 20 nm of the lateral edge of the PSD. Mossy-fiber synapses were sampled according to the same principles. Only continuous PSDs were recorded. Quantitative analysis was carried out on single-labeled sections, as double labeling slightly reduced labeling intensity for the second antigen. All analyses were done in parallel and confirmed by two independent observers. The relationship between the PSD diameter (determined as the maximum PSD length in serial sections) and the number of gold particles along a section corresponding to the diameter is represented as a straight line regressing the number of gold particles on PSD length maxima. This approach should rule out the confounding effects of any heterogeneities in receptor distribution along the radial axis of the PSD. ACKNOWLEDGEMENTS This work was supported by the Norwegian Research Council, Professor Letten F. Saugstad s Fund and EU Biomed grant PL A travel grant from Hjärnfonden, Erik & Edith Fernström s Fund and the Swedish Medical Research Council (to V.R.-L.) is gratefully acknowledged. Antibodies were provided by R. J. Wenthold. We thank R. J. Wenthold, R. Nicoll, Y. Ben-Ari, Johannes Helm and Ø. Hvalby for reading the manuscript. 622 nature neuroscience volume 2 no 7 july 1999

6 articles APPENDIX Assuming a circular PSD, the receptors with diameter D rec that are hit by a section plane along the PSD diameter are those whose centers are located less than D rec /2 away from the section plane. All of the receptors that are hit by the plane of section (the number of which is defined as n d ) are therefore located within a sector S with area D rec D, where D is the diameter of the PSD. We assume here that D rec << D. The ratio between n d and the total number of receptors in the PSD (n tot ) must be equal to the ratio between the area of the sector S and the area of the entire PSD. Thus n tot = n d p(d/2) 2 / (D rec D) (1) If n d is constant or shows only a moderate size-independent variability, which we assume is the case for the NMDA receptors (Fig. 3), then we see from eq. 1 that the total number of NMDA receptors (NMDA tot ) in the PSD will be proportional to the PSD diameter. Thus, NMDA tot = k 1 D (2) where k 1 is n d p/4 1/D rec. The NMDA receptors will occupy an area A NMDA, which is given by the following equation A NMDA = NMDA tot p(d receff /2) 2 (3) where D receff is the effective diameter of the NMDA receptors in a situation of maximum packing density (The term D receff > D rec is introduced to allow for some obligatory space between the receptors.). Combining equations 2 and 3, and letting n d represent NMDA receptors, the size of the remaining fraction (DA) of the PSD can be expressed as follows: DA = A A NMDA = A k 2 D (4) where k 2 is k 1 p D 2 receff /4. If we assume that the total number of AMPA receptors in the PSD (AMPA tot ) is proportional to the available area DA (that is, the area not occupied by NMDA receptors) then AMPA tot = k 3 (A k 2 D) (5) where k 3 is a constant with the dimension m 2. RECEIVED 19 MARCH; ACCEPTED 24 MAY Seeburg, P. H. The TIPS/TINS lecture: the molecular biology of mammalian glutamate receptor channels. Trends Pharmacol. Sci. 14, (1993). 2. Hollmann, M. & Heinemann, S. 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