Unified quantitative model of AMPA receptortrafficking at synapsesKatalin Czöndöra,b,1, Magali Mondina,b,1, Mikael Garciaa,b,1, Martin Heinec, Renato Frischknechtc, Daniel Choqueta,b,Jean-Baptiste Sibaritaa,b, and Olivier R. Thouminea,b,2

aInterdisciplinary Institute for Neuroscience, University of Bordeaux, F-33000 Bordeaux, France; bInterdisciplinary Institute for Neuroscience, Centre Nationalde la Recherche Scientifique, F-33000 Bordeaux, France; and cLeibniz Institute of Neurobiology, 39118 Magdeburg, Germany

Edited* by Richard L. Huganir, Johns Hopkins University School of Medicine, Baltimore, MD, and approved January 19, 2012 (received for review June20, 2011)

Trafficking of AMPA receptors (AMPARs) plays a key role in syn-aptic transmission. However, a general framework integratingthe two major mechanisms regulating AMPAR delivery at post-synapses (i.e., surface diffusion and internal recycling) is lacking.To this aim, we built a model based on numerical trajectories ofindividual AMPARs, including free diffusion in the extrasynapticspace, confinement in the synapse, and trapping at the post-synaptic density (PSD) through reversible interactions with scaf-fold proteins. The AMPAR/scaffold kinetic rates were adjusted bycomparing computer simulations to single-particle tracking andfluorescence recovery after photobleaching experiments in pri-mary neurons, in different conditions of synapse density and mat-uration. The model predicts that the steady-state AMPAR numberat synapses is bidirectionally controlled by AMPAR/scaffold bind-ing affinity and PSD size. To reveal the impact of recycling pro-cesses in basal conditions and upon synaptic potentiation or de-pression, spatially and temporally defined exocytic and endocyticevents were introduced. The model predicts that local recyclingof AMPARs close to the PSD, coupled to short-range surface dif-fusion, provides rapid control of AMPAR number at synapses. Incontrast, because of long-range diffusion limitations, extrasynap-tic recycling is intrinsically slower and less synapse-specific. Thus,by discriminating the relative contributions of AMPAR diffusion,trapping, and recycling events on spatial and temporal bases, thismodel provides unique insights on the dynamic regulation ofsynaptic strength.

glutamate receptor | scaffold molecules | synaptic plasticity |theoretical model | diffusion/trapping

Controlling the number of AMPA-type glutamate receptors(AMPARs) at excitatory synapses is of fundamental impor-

tance in synaptic transmission (1). AMPARs are anchored at thepostsynaptic density (PSD) via specific interactions with scaffoldmolecules, but can dynamically exchange between intracellularand extrasynaptic membrane compartments. This turnover in-volves two major mechanisms: endo/exocytic recycling and sur-face diffusion (2).A number of studies have demonstrated the importance of

AMPAR recycling in synaptic plasticity. Synaptic potentiationinduces AMPAR exocytosis, whereas disrupting basal exocytosisleads to a run-down of AMPAR-dependent synaptic transmissionand reduces long-term potentiation (LTP) (3–8). Inversely, in-hibition of basal endocytosis gradually increases AMPAR ex-citatory postsynaptic currents (EPSCs), and occludes long-termdepression (LTD) (1, 9). Furthermore, an endocytic zone (EZ)located near the PSD and responsible for local AMPAR recyclingis essential for regulating synaptic transmission (10–12). Despitethese advances, the exact locations and kinetics of AMPAR exo-cytosis and endocytosis, both in basal conditions and in responseto LTP and LTD stimuli, respectively, are still unclear (13).The other mechanism controlling AMPAR trafficking at synap-

ses is surface diffusion (14). Fluorescence recovery after photo-bleaching (FRAP) and single-particle tracking (SPT) experiments

have shown that AMPARs diffuse freely in the extrasynaptic spaceand are confined at the synapse (5, 15–17). Surface-diffusingAMPARs are captured at PSDs via PDZ domain scaffold proteins,including postsynaptic density protein 95 (PSD-95), which interactswith AMPAR auxiliary subunits (i.e., transmembrane AMPARregulatory proteins, or TARPs), or synapse-associated protein 97(SAP-97) and protein interacting with protein kinase C (PICK)/glutamate receptor interacting protein (GRIP), which recognizeGluA1 and GluA2 AMPAR subunits, respectively (1, 18–20). Im-portantly, AMPAR diffusion and trapping at the synapse are bi-directionally regulated by synaptic activity (19, 21). However, therelative importance of diffusion and binding in regulating AMPARdynamics is difficult to assess, because the kinetic rates character-izing AMPAR/scaffold interactions are unknown.Despite a crucial role of AMPAR trafficking in synaptic func-

tion, a general model describing the kinetic interplay betweenAMPAR diffusion and vesicular recycling is still lacking. Previoustheoretical papers described AMPAR diffusion in synapses (22–25), but those contained many unknown parameters and re-mained far from actual experimental paradigms. We built herea unified quantitative framework integrating exo/endocytic eventsand diffusion/trapping at postsynaptic sites, with only two adjust-able parameters: the AMPAR/scaffold binding and unbindingrates. Our model closely sticks to SPT, FRAP, and electrophysi-ology data, and allows predictions of AMPAR dynamics at syn-apses in various biological conditions.

ResultsThe model integrates the three major components of AMPARtrafficking: surface diffusion, trapping at postsynapses, and recy-cling (Fig. 1A). The outputs of the computer program (Fig. S1)were simulated 2D trajectories of membrane-diffusing AMPARs,transiting between three distinct compartments: extrasynapticspace, synapse, and PSD (Fig. 1B and Movie S1), and directlycomparable to SPT data (Fig. 1C). Model hypotheses and pa-rameter values are given in SI Materials and Methods and Table S1.

Fitting the Model to SPT Experiments. We first compared modelpredictions to SPT experiments performed in primary hippo-campal neurons at different ages [days in vitro (DIV) 4–15] andtransfected with Homer1c:GFP to identify postsynapses (Fig. 1 C–E). Endogenous AMPARs were labeled with anti-GluA2 conju-gated Quantum dots (Qdots), and individual Qdot trajectorieswere recorded by fluorescence imaging. Simulations mimicked

Author contributions: D.C., J.-B.S., and O.R.T. designed research; K.C., M.M., M.G., M.H.,R.F., and O.R.T. performed research; J.-B.S. contributed new reagents/analytic tools; K.C.,M.M., M.G., M.H., R.F., and O.R.T. analyzed data; and K.C. and O.R.T. wrote the paper.

The authors declare no conflict of interest.

*This Direct Submission article had a prearranged editor.1K.C., M.M., and M.G. contributed equally to this work.2To whom correspondence should be addressed. E-mail: othoumin@u-bordeaux2.fr.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1109818109/-/DCSupplemental.

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qualitatively well extrasynaptic diffusion and synaptic confinementof AMPARs observed in SPT experiments, with slight discrep-ancies attributed to limitations of the Qdot technique (Fig. 1 Band C and Fig. S2). The mean square displacement (MSD) wasfitted by linear regression to yield a global diffusion coefficient(Fig. S3 A and B). The experimental distribution of diffusioncoefficients was shifted to the left as neurons grew older (Fig.S3C), and matched by increasing obstacle density in the model(Fig. S3D). Overall, the median AMPAR diffusion coefficientdecreased as synapse density was increased, in agreement with themodel (Fig. 1E). Increasing kon to enhance AMPAR trapping atpostsynapses reduced global AMPAR mobility (Fig. 1E), whereasincreasing koff had the opposite effect (Fig. S4C), thus leading toseveral combinations of kon and koff that could equally fit SPT data(Fig. S4D). To experimentally alter AMPAR diffusion withoutaffecting developmental age, we overexpressed either the adhe-sion protein neuroligin-1 to increase synapse density (26), or the

scaffold protein PSD-95 to induce synapse maturation (27, 28)(Fig. 1D). Both conditions greatly diminished global AMPARdiffusion (Fig. 1F). These effects were reproduced in the model,the former by doubling obstacle density and the latter by increasingsimultaneously PSD size and kon. Overall, the model could in-terpret SPT experiments in a wide range of biological conditions.

AMPAR Dynamics at Synapses Compared with FRAP and PeptideCompetition Data. To refine the estimation of kinetic parameters,we challenged the model against FRAP experiments performedon primary neurons expressing recombinant pHluorin-taggedGluA1 or GluA2 subunits (16). We superimposed 500 individualtrajectories to build AMPAR maps resembling fluorescenceimages, over time. After a 10-s baseline, photobleaching wasmodeled by setting an intensity parameter irreversibly to zerowhen AMPARs reached one particular synapse (Fig. 2A andMovie S2). The simulated FRAP curves using the parameter setkon = 1.5 s−1 and koff = 0.1 s−1 matched very well experimentaldata at DIV 10 (Fig. 2B). However, FRAP curves in olderneurons (DIV 24) showed a lower recovery than at DIV 10. Tofit those data, we had to decrease koff = 0.02 s−1 for the wholeAMPAR population, or to introduce a 30% AMPAR fractionwith a zero koff, this second option better accounting for the fast

Fig. 1. Model definition and comparison with SPT experiments. (A) Schematicdiagram of themodel. Kinetic parameters include Dout (extrasynaptic diffusion),Din (synaptic diffusion), DPSD (diffusion coefficient of the PSD), kon (AMPAR/scaffold binding rate), koff (AMPAR/scaffold dissociation rate), and kendo (en-docytosis rate). (B) Simulated trajectory (50 s). The synapse is in green, the PSDin red, and dendrite borders in gray. Geometric parameters are: a (synapsespacing), b (synapse width), c (PSD width), w (dendrite width). (C) High-mag-nification 30-s trajectory of an AMPAR-bound Qdot on the surface of a DIV 9neuron, Homer1c:GFP puncta being outlined in green. (D) AMPAR trajectories(red traces) are shown for DIV 7 and DIV 15 neurons expressing Homer1c:GFP(white), and for DIV 9 neurons coexpressing Homer1c:GFP (white) and neuro-ligin-1, or expressing PSD-95:GFP (white). (E) Experimental (○) and simulated(plain curves) AMPAR median diffusion coefficients obtained at differentneuronal ages (DIV 4–15) or varying synaptic spacing (0.75–30 μm), respectively,were plotted against synapse density. The simulated curves were computed fordifferent kon values, keeping koff = 0.1 s−1. (F) Interquartile distributions ofAMPAR diffusion coefficients from experiments (black) and simulations (green).Neuroligin-1 expression, which doubled the number of Homer1c-positivepuncta, was mimicked by a decrease in synapse spacing (a = 1 μm). Over-expressing PSD-95 was modeled by enhancing kon (2.5 s−1) to mimic an increasein PSD binding sites, plus an increase in PSD size (c = 0.4 μm).

Fig. 2. Comparison of the model with FRAP and peptide competitionexperiments. (A) Time-lapse images of simulated FRAP experiments. AMPARswere treated as light point sources represented by Gaussian intensity pro-files. The synapse on the left was photobleached at t = 10 s (arrow), andfluorescence recovery was monitored for 75 s. AMPAR levels at controlsynapses (Right) slightly decrease due to redistribution of bleached AMPARs.(B) Simulated recovery curves generated using several (kon, koff) pairs (grayscale) plotted against experimental FRAP data obtained for DIV 10 and DIV24 neurons expressing pHluorin-tagged GluA1 or GluA2 (red and greencircles, respectively). The black curve represents 70% mobile AMPARs (kon =1.5 s−1 and koff =0.1 s−1) plus 30% immobile AMPARs (kon = 1.5 s−1 and koff =0 s−1). (C and D) To mimic disruption of AMPAR/scaffold interactions by in-tracellular peptides, kon was set to zero at t = 10 s, resulting in rapid AMPARloss from the synapse. All AMPARs were considered either mobile (koff =0.1 s−1; red) or 60% mobile and 40% immobile (koff = 0 s−1; green). AMPARlevels at control synapses (gray) slightly increase because AMPARs displacedby peptide competition redistribute among neighboring synapses.

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and saturatable experimental data. Similarly, we also had toconsider immobile AMPARs to fit the slow decay at synapsesobserved in fluorescence loss in photobleaching experiments (12,15) (Fig. S5). This reduction in koff observed upon neuronalmaturation with ensemble measurements of AMPAR dynamicscould not be well detected in SPT experiments, which tend tounderestimate long synaptic dwell times due to short trajectoriesand difficulty of Qdots to access the core of the PSD (Fig. S2B).Interestingly, such a stable AMPAR population was also ap-

parent in patch-clamp recordings, where a quick and persistent50% drop in AMPA-mediated EPSCs was observed upon ap-plication of peptides that acutely disrupt the stargazin/PSD-95interaction (20). To mimic these experiments, we set kon to zeroat a given time. If AMPARs were all considered mobile,AMPAR level at the postsynapse dropped to almost zero (Fig. 2C and D and Movie S3). To reach a 50% reduction in synapticAMPAR level as observed in experiments, we introduced a 40%immobile AMPAR fraction compatible with FRAP data. Thecharacteristic time of decrease in AMPAR level (10 s) was roughlythe inverse of koff, corresponding to AMPAR detachment fromthe PSD. Fitting the model with those different experiments thusallowed a fine-tuning of the kinetic parameters, which were usedfor further predictions.

Mapping AMPAR Distribution and Fluctuations at Synapses. We firstexamined AMPAR distribution in extrasynaptic and synapticcompartments. AMPARs starting from initial random locationsprogressively accumulated at PSDs in a diffusion-limited manner(Fig. S6 and Movie S4). The steady-state AMPAR number atsynapses was linearly related to the PSD area (Fig. 3 A and C), inquantitative agreement with EM data (29). Furthermore, thesynaptic AMPAR enrichment (AMPARs bound to scaffold vs.free AMPARs) at equilibrium was strictly proportional to kon/koff (Fig. 3 B and D), which characterizes the binding affinity.Under basal conditions, the AMPAR density in the PSD wasabout 100-fold higher than in the extrasynaptic membrane,consistent with experimental estimates (30). To map the occu-pancy of PSD scaffolds, the 300 × 300-nm area correspondingto a single PSD was further decomposed into a grid of 20 ×20 pixels of 15 nm each, representing an array of 400 scaffoldmolecules. On average, 88% of the pixels were occupied by zeroAMPAR, 11% by one AMPAR, and only 1% by two AMPARs(Fig. 3E), consistent with our hypothesis that scaffolds were notsaturated by AMPARs.We also looked at the fluctuations of AMPAR numbers at

synapses per unit of time, due to continuous diffusional ex-change. First, we varied the density of receptors in the simu-lations (10–125 μm−2) and predicted that the coefficient ofvariation (CV) decreased inversely to the square root of thesynaptic AMPAR number (Fig. 3G). Assuming that AMPAEPSCs are proportional to AMPAR number at PSDs, this resultis consistent with glutamate iontophoresis experiments, wherehigher scatter was seen for weaker synapses (Fig. 3 F and G).Second, to mimic the reduction in the fluctuations of synapticAMPA currents induced by antibody cross-link of surfaceAMPARs (21), we decreased Dout and Din according to experi-mental values (0.0002 μm2/s) (26, 31) and simultaneously low-ered koff by fivefold (0.02 s−1) to take into account the fact thatapparent bond lifetimes increase upon multimerization (32).Under these conditions, the average AMPAR number was un-changed, but the CV dropped from 7.0 ± 0.4% to only 1.2 ±0.2% (mean ± SEM of five PSDs, P < 0.0001 by paired Studentt test; Fig. 3H and Movie S5). This difference corresponds closelyto the drop in the CV of AMPA EPSCs, without a change inamplitude, as observed upon cross-linking (21). Taken together,these data suggest that a significant fraction of the scatter inAMPAR synaptic transmission can be attributed to fluctuationsin the number of surface-diffusing AMPARs. Other sources of

fluctuations might include postsynaptic changes in channel con-ductance and open probability, as well as presynaptic variationsin vesicle size and glutamate content (33).

Effects of Exocytosis and Enhanced Trapping on Synaptic AMPARLevel. To reveal the impact of vesicular recycling on AMPARdynamics both in basal conditions and in response to synapticstimulation, we introduced discrete exo/endocytic events into thesimulations. To describe synaptic potentiation, we took into ac-count increases in AMPAR exocytosis and AMPAR binding toscaffold proteins, both linked to the phosphorylation of GluA1and stargazin C-terminal domains, as well as increases in synapsesize (1, 34).

Fig. 3. Mean and fluctuations of AMPAR number at synapses. (A and B) Heatmaps of AMPAR distribution in the plasma membrane, calculated for differ-ent PSD sizes and kon values, respectively. The intensity corresponds to thenumber of times each pixel was visited by an AMPAR during a 100-s period.(C) AMPAR number per synapse as a function of PSD area (mean ± SEM, 10PSDs). For larger PSDs, there is an inflection in the curve because of limitednumbers of available AMPARs to populate synapses in the simulations. (D)Ratio between AMPAR density at the PSD vs. extrasynaptic space as a functionof kon/koff (mean ± SEM, 10 PSDs). The arrow points to the AMPAR enrich-ment corresponding to kon = 1.5 s−1 and koff = 0.1 s−1. (E) Fluctuations ofAMPAR number at a single PSD over time. The number of AMPARs per pixel iscolor coded. (F) AMPAR-mediated EPSCs upon ionotophoretic application ofglutamate at synapses. Several recordings are superimposed. Note a largerscatter for the synapse showing the smaller average AMPAR current. (G) Themean and variance in AMPAR number at synapses were calculated for dif-ferent AMPAR densities in the simulations (25–125 AMPAR/μm2). CV plottedvs. the mean synaptic AMPAR number (black circles). The red curve representsa fit with the equation √P(1 − P)/n, expected from a binomial distribution,where n is the average synaptic AMPAR number and P is the probability foran AMPAR to be in a synapse (P = 0.65, taken as the ratio between synapticand total AMPAR numbers). Green circles represent electrophysiology data.(H) Reduction in the fluctuations of AMPAR number at PSDs upon mimickingcross-linking by lowering koff (0.02 s−1) and Dout (0.0002 μm2/s) simultaneously(at t = 25 s). Three representative curves are shown.

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To simulate enhanced exocytosis, a bolus of 50 AMPARs,which lies in the range of experimental estimates (4, 7), wassuperimposed at a given time to an already populated 2D spacecontaining five synapses. When AMPARs were inserted at ex-trasynaptic locations (0.5–5 μm from synapses), they instantlydiffused throughout the membrane, and showed slight accumu-lation at nearby synapses in a distance-dependent manner (Fig. 4A and B and Movie S6). These predictions are in agreement withsmall increases in GluA1-pHluorin signal (10–20%) at synapseslocated near the exocytic spot (4, 6). In contrast, when the sameAMPAR bolus was inserted within the synapse, AMPAR densityat the PSD was immediately much higher, and persisted fora fairly long time (Fig. 4 C and D and Movie S7). If bindingparameters were kept constant, the signal eventually went backto baseline, corresponding to detachment of AMPARs from thePSD. Overall, the relative increase in synaptic AMPAR levelcontributed by exocytosis decreased exponentially with respect tothe distance between the exocytic locus and the PSD (Fig. 4E).To mimic enhanced AMPAR/scaffold binding, we increased

kon (Fig. 4 C and D and Movie S8) or decreased koff (Fig. S7 Aand B), resulting in a higher steady-state AMPAR enrichment atthe PSD within a longer time course than the one obtained withexocytosis alone. Importantly, a rapid and stable increase inAMPAR content at the PSD was obtained only if exocytosis wastriggered at the synapse and kon was simultaneously increased(Movie S9). Thus, the model suggests that the rapid phase ofsynaptic potentiation is accounted for by transient exocytosis

within or very close to the synapse, whereas the plateau is dic-tated by a persistent increase in trapping strength. Alternatively,long-term synaptic potentiation could also be simulated by in-creasing the size of the PSD (Fig. S7 C and D) to mimic an in-crease in the number of AMPAR binding slots (1).

Effects of Basal Endocytosis on AMPAR Distribution. To address therole of AMPAR endocytosis in basal conditions and upon syn-aptic depression, we introduced regularly spaced EZs of dimen-sions 150 × 150 nm, one adjacent to the PSD and one betweentwo synapses (10, 11) (Fig. 5 A and B and Fig. S8A). Endocytosiswas considered as a sink governed by the rate constant kendo(s−1). AMPAR density at the cell surface decreased linearly overtime, at a speed dictated by kendo (Fig. S8 B and C). The curveobtained with kendo = 0.1 s−1 closely corresponded to AMPARinternalization rates measured by antibody-feeding experiments(i.e., 10–20% in 5 min) (10, 11, 35, 36). Strikingly, AMPAR lossfrom the cell surface was about fivefold more rapid when endo-cytosis was induced within synapses than extrasynaptically (Fig. 5A and B and Fig. S8 B and C), consistent with long-rangeAMPAR diffusion being rate limiting. To assess the importanceof the localization of AMPAR recycling events, we compensatedconstitutive AMPAR endocytosis by periodic exocytosis witha frequency adjusted to experimental values (4, 6), thus restoringsteady-state AMPAR density (Fig. 5 A and B). For synaptic en-docytosis, which caused a rapid loss in surface AMPARs, thebolus was adjusted to 33 AMPARs, whereas for extrasynapticendocytosis, which induced a slower decrease in AMPARs, thebolus contained only 10 AMPARs. Synaptic recycling resulted in

Fig. 4. Effect of exocytosis and trapping on AMPAR accumulation at thePSD. (A) Time-lapse images of extrasynaptic exocytosis, where a bolus of 50AMPARs was delivered 1 μm from a synapse (arrow). (B) The distance be-tween the locus of exocytosis and synapses was varied between 1 and 5 μm,and AMPAR level was measured in synapses (color) or at the exocytosis lo-cation (gray), both normalized by the basal synaptic AMPAR level. (C) Time-lapse images of simulated experiments, where the AMPAR bolus was de-livered in the synapse 0.2 μm from the PSD (arrow), kon was doubled (plussign), or both modifications were applied simultaneously. (D) Normalizedsynaptic AMPAR level over time, for the three conditions indicated in C. (E)Initial increase in synaptic AMPAR level as a function of the distance be-tween the exocytic zone and the PSD (mean ± SD, 16 simulations). The redcurve is an exponential decay fitting the data.

Fig. 5. Effect of endocytosis and trapping on AMPAR distribution at thePSD. (A and B) AMPAR endocytosis at EZs (red squares) was counterbalancedby periodic exocytic events (arrows). Images show the AMPAR distributionfor extrasynaptic (A) or synaptic recycling (B). Note AMPAR enrichment atthe PSD in the latter case. The graphs show the overall decrease of AMPARsurface density by endocytosis alone (green), and the steady-state AMPARlevel (red) restored by periodic exocytosis (gray peaks). (C) Images illustrat-ing changes in AMPAR level in four different conditions, imposed at t = 10 s:kendo was increased 10-fold above baseline either at extrasynaptic (gray) orsynaptic (blue) EZs; kon was decreased twofold (minus sign, green); or bothkendo was increased and kon decreased simultaneously (red). (D) SynapticAMPAR level vs. time for the four conditions illustrated in C.

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a 24 ± 1% greater AMPAR enrichment (n = 6) compared withnonrecycling synapses, suggesting that local synaptic recycling isimportant for AMPAR accumulation at PSDs.

Effect of Acute Endocytosis and Reduced Trapping on SynapticAMPAR Level. To describe synaptic depression, one has to con-sider increases in AMPAR endocytosis triggered by phosphatasesignaling and decreases in AMPAR binding to AMPA receptorbinding protein (ABP)/GRIP and PSD-95—induced by phos-phorylation of GluA2 and stargazin, respectively—as well as re-ductions in synapse size (1, 34). To simulate enhanced AMPARendocytosis, we raised kendo by 10-fold above the basal rate (37).When endocytosis was induced extrasynaptically, the decreasein AMPAR level at the PSD was fairly slow (Fig. 5 C and D), asobserved for basal endocytosis. Strikingly, the loss in AMPARlevel was more pronounced and synapse specific when endocy-tosis was induced within the synapse. To mimic a sudden reduc-tion in AMPAR/scaffold binding affinity, kon was decreased(Fig. 5 C and D) or koff was increased (Fig. S7 A and B), resultingin a drop of AMPAR level within seconds, to a plateau belowbaseline. This effect was due to the fact that AMPARs detachingfrom the PSD can escape the synapse by diffusion. Interestingly,an increase in the diffusion of synaptic AMPARs has been ob-served by SPT upon induction of chemical LTD (17), possiblyreflecting AMPAR/scaffold detachment. When synaptic endocy-tosis was combined with a decrease in kon, the effects added toeach other and resulted in both rapid and sustained decrease inAMPAR level, to about 50% below baseline (Fig. 5 C and D andMovie S10). Thus, the model predicts that the rapid loss ofAMPAR from synapses is due to a decrease in trapping force,whereas the persistent decrease in AMPARs is due to endocy-tosis. Alternatively, synaptic depression could also be simulatedby reducing the size of the PSD (Fig. S7 C and D) to mimic adecrease in the number of AMPAR binding slots.

DiscussionThis framework allows spatial and temporal discrimination ofthe roles of AMPAR diffusion, trapping, and exo/endocytosis inregulating AMPAR dynamics at synapses. The model shows thatAMPAR surface diffusion is an obligatory link between internalrecycling and trapping at the PSD, and clarifies the impact ofrecycling events compared with changes in AMPAR/scaffoldaffinity or PSD size in synaptic plasticity. The main prediction isthat synapses endowed with internal endocytic and exocytic re-cycling mechanisms are privileged over other synapses, becausethey can efficiently regulate their AMPAR level in response topotentiation or depression stimuli.

Intrinsic AMPAR Dynamics at Synapses. This model allowed a cleardistinction of diffusion and binding events, which are generallyhidden in FRAP curves (23). By fitting simulations to both SPTand FRAP data, we estimated the AMPAR/scaffold reaction rates.The overall AMPAR/scaffold dissociation rate (koff = 0.1 s−1) isabout 10-fold lower than the value measured by surface plasmonresonance between single PDZ domains and PDZ binding motifs(38). This longer lifetime measured in live neurons is likely toreflect an increased avidity coming from the simultaneous bindingof AMPARs or TARPs to multiple PDZ domains (20, 32).The model predicted that in young neurons a majority of

AMPARs exchanged within tens of seconds between synaptic andextrasynaptic compartments. In contrast, older neurons werecharacterized by a lower koff (0.02 s−1), or the appearance of astable AMPAR population. Because stargazin peptides that spe-cifically compete with class I PDZ scaffold proteins, includingPSD-95 and SAP-97, did not completely abolish AMPA EPSCs(20), stable AMPAR anchoring might involve higher valencies orother molecules, e.g., class II PDZ scaffold proteins such as ABP/GRIP or PICK1 (18), the actin-binding protein 4.1N (6), or the

adhesion protein N-cadherin involved in synaptic maturation (39).Stable AMPARs may also bear specific subunit composition:GluA1 and GluA2 subunits exhibited similar recovery curves, butit is possible that GluA3- or GluA4-containing AMPARs haveslower kinetics. The appearance of a stable fraction may also belinked to geometrical effects of dendritic spine maturation, inwhich the neck acts as a diffusion barrier (15, 23).Our model also predicts that under basal conditions, AMPARs

are about 100-fold enriched at PSDs compared with the extra-synaptic space. This result is consistent with glutamate ionto-phoresis experiments (21, 40) and with immunogold labeling ofsurface AMPARs after freeze fracture electron microscopy (30).However, these values are higher than other estimates usingimmunolabeling (7) or overexpression of fluorescently taggedAMPAR subunits (15, 16). Most likely, those techniques are un-derestimating synaptic AMPAR enrichment, the former because ofthe difficulty for antibodies to access the crowded synaptic space,and the latter because it biases the stoichiometry of AMPARs toscaffold molecules. An alternative explanation would be the ex-istence of AMPAR nanoclusters at the synapse (2). In addition,the model predicts that fluctuations in synaptic AMPAR numbersdue to diffusional exchange are smaller for synapses containingmore AMPARs, reflecting more reliable synaptic transmission.

AMPAR Exocytosis and Trapping in Synaptic Potentiation. The issueof where AMPAR exocytosis takes place is controversial. Somestudies reported essentially extrasynaptic AMPAR exocytosis (4–7), whereas others described AMPAR exocytosis intrasynapti-cally or near the synapse (8, 41, 42). In this debated context, ourmodel shows that extrasynaptic exocytosis is relatively inefficientand unspecific in delivering AMPARs to synapses compared withsynaptic exocytosis, because AMPARs rapidly dilute in the ex-trasynaptic membrane. In contrast, if AMPAR exocytosis occurswithin or close to the synapse (<1 μm), trapping is efficient andfast (within seconds). Moreover, AMPAR accumulation persistsfor a relatively long time (1 min) because of slow AMPAR dif-fusion in the synapse, such that newly exocytosed AMPARs stayavailable for trapping. If, in addition to exocytosis, the AMPAR/scaffold affinity is increased, then the initial burst persists forminutes. Both types of kinetics were reported by observingGluA1-pHluorin accumulation at synapses upon chemical LTP(8, 42). The synaptic response could involve a selective exocytosisof GluA1-containing AMPARs providing the rapid enhancementin synaptic strength (4, 6), followed by a long-term trapping ofGluA2-containing subunits through enhanced scaffold interac-tions (43). The model thus predicts a repertoire of LTP responsesdictated by the relative contributions of AMPAR exocytosis,trapping, and changes in PSD size.

AMPAR Endocytosis and Trapping in Synaptic Depression. AMPARinternalization was predicted to be threefold more efficient withinthe synapse than in the extrasynaptic space, consistent with theexpression of dominant-negative dynamin-3, which displaces EZsaway from synapses (10). In addition, constitutive recycling ofAMPARs within the synapse resulted in stronger AMPAR en-richment compared with synapses with no recycling, matching theloss in synaptic AMPARs in neurons expressing the dynamin-3mutant (10) or treated with endocytosis inhibitors (12). Whenextrasynaptic endocytosis was acutely triggered, it was again rela-tively inefficient in removing AMPARs from nearby synapses. Thisresult matched the progressive decline of GluA1-pHluorin signalat synapses, following AMPAR endocytosis in the shaft uponNMDA treatment (44). Thus, an intrinsic limitation of NMDAR-dependent LTD may be a saturation of the endocytic capability,unable to capture fast-diffusing extrasynaptic AMPARs. In con-trast, synaptic endocytosis resulted in a more-pronounced lossof AMPARs from synapses, in agreement with NMDAR-de-pendent LTD induced by electrical stimulation (36). Finally,

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when AMPAR/scaffold affinity was simultaneously reduced, thedecrease was more rapid and reached a lower steady state thanwith endocytosis alone. This behavior is close to the drop inAMPA EPSCs observed within 1 min upon mGluR-dependentLTD (35). Together with changes in PSD size, the fine-tuningbetween these processes potentially gives rise to a panel of syn-aptic responses, according to the LTD stimulation protocol.

Materials and MethodsExperiments and model are described in SI Materials and Methods. Briefly,SPT, FRAP, and patch-clamp methods were described previously (16, 26, 31).Computer simulations of individual AMPAR movement, including diffusion,

trapping at the PSD, and exo/endocytic events, were programmed usingMathematica software. Superimposition of trajectories to visualize AMPARdistribution over time was made using a custom program written inMetamorph.

ACKNOWLEDGMENTS. We thank P. Scheiffele, S. Okabe, and K. Keinänenfor plasmids; B. Tessier for molecular biology; J. Delgado, G. Giannone,Y. Humeau, D. Jullié, D. Perrais, and M. Sainlos for discussions; and C. Breillat,D; Bouchet, A. Frouin, and N. Retailleau for primary neurons. Funding forthis study was provided by European Union Seventh Framework ProgramGrant 232942 Nano-Dyn-Syn, the Centre National de la Recherche Scientifi-que, Agence Nationale de la Recherche Projects Neuroligation and Synapse-2Dt, Conseil Régional Aquitaine, Fondation pour la Recherche Médicale, andERA-Net NEURON (Moddifsyn).

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