Choquet Model

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Czöndör, Mondin, Garcia, Heine, Frischknecht, Choquet, Sibarita, Thoumine • 2012 • PNAS - PDF

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Trafficking of AMPA receptors (AMPARs) plays a key role in synaptic transmission. However, a general framework integrating the two major mechanisms regulating AMPAR delivery at postsynapses (i.e., surface diffusion and internal recycling) is lacking. To this aim, we built a model based on numerical trajectories of individual AMPARs, including free diffusion in the extrasynaptic space, confinement in the synapse, and trapping at the postsynaptic density (PSD) through reversible interactions with scaffold proteins. The AMPAR/scaffold kinetic rates were adjusted by comparing computer simulations to single-particle tracking and fluorescence recovery after photobleaching experiments in primary neurons, in different conditions of synapse density and maturation. The model predicts that the steady-state AMPAR number at synapses is bidirectionally controlled by AMPAR/scaffold binding affinity and PSD size. To reveal the impact of recycling processes in basal conditions and upon synaptic potentiation or depression, spatially and temporally defined exocytic and endocytic events were introduced. The model predicts that local recycling of AMPARs close to the PSD, coupled to short-range surface diffusion, provides rapid control of AMPAR number at synapses. In contrast, because of long-range diffusion limitations, extrasynaptic 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, this model provides unique insights on the dynamic regulation of synaptic strength.


Controlling the number of AMPA-type glutamate receptors (AMPARs) at excitatory synapses is of fundamental importance in synaptic transmission (1). AMPARs are anchored at the postsynaptic density (PSD) via specific interactions with scaffold molecules, but can dynamically exchange between intracellular and extrasynaptic membrane compartments. This turnover involves two major mechanisms: endo/exocytic recycling and surface diffusion (2).

A number of studies have demonstrated the importance of AMPAR recycling in synaptic plasticity. Synaptic potentiation induces AMPAR exocytosis, whereas disrupting basal exocytosis leads to a run-down of AMPAR-dependent synaptic transmission and reduces long-term potentiation (LTP) (3–8). Inversely, inhibition of basal endocytosis gradually increases AMPAR excitatory postsynaptic currents (EPSCs), and occludes long-term depression (LTD) (1, 9). Furthermore, an endocytic zone (EZ) located near the PSD and responsible for local AMPAR recycling is essential for regulating synaptic transmission (10–12). Despite these advances, the exact locations and kinetics of AMPAR exocytosis and endocytosis, both in basal conditions and in response to LTP and LTD stimuli, respectively, are still unclear (13). The other mechanism controlling AMPAR trafficking at synapses is surface diffusion (14). Fluorescence recovery after photobleaching (FRAP) and single-particle tracking (SPT) experiments have shown that AMPARs diffuse freely in the extrasynaptic space and are confined at the synapse (5, 15–17). Surface-diffusing AMPARs are captured at PSDs via PDZ domain scaffold proteins, including postsynaptic density protein 95 (PSD-95), which interacts with AMPAR auxiliary subunits (i.e., transmembrane AMPAR regulatory proteins, or TARPs), or synapse-associated protein 97 (SAP-97) and protein interacting with protein kinase C (PICK)/ glutamate receptor interacting protein (GRIP), which recognize GluA1 and GluA2 AMPAR subunits, respectively (1, 18–20). Importantly, AMPAR diffusion and trapping at the synapse are bidirectionally regulated by synaptic activity (19, 21). However, the relative importance of diffusion and binding in regulating AMPAR dynamics is difficult to assess, because the kinetic rates characterizing AMPAR/scaffold interactions are unknown.

Despite a crucial role of AMPAR trafficking in synaptic function, a general model describing the kinetic interplay between AMPAR diffusion and vesicular recycling is still lacking. Previous theoretical papers described AMPAR diffusion in synapses (22– 25), but those contained many unknown parameters and remained far from actual experimental paradigms. We built here a unified quantitative framework integrating exo/endocytic events and diffusion/trapping at postsynaptic sites, with only two adjustable parameters: the AMPAR/scaffold binding and unbinding rates. Our model closely sticks to SPT, FRAP, and electrophysiology data, and allows predictions of AMPAR dynamics at synapses in various biological conditions.



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The model integrates the three major components of AMPAR trafficking: surface diffusion, trapping at postsynapses, and recycling (Fig. 1A). The outputs of the computer program (Fig. S1) were simulated 2D trajectories of membrane-diffusing AMPARs, transiting between three distinct compartments: extrasynaptic space, synapse, and PSD (Fig. 1B and Movie S1), and directly comparable to SPT data (Fig. 1C). Model hypotheses and parameter values are given in SIMaterials and Methods and Table S1.

Fitting the Model to SPT Experiments.

We first compared model predictions to SPT experiments performed in primary hippocampal neurons at different ages [days in vitro (DIV) 4–15] and transfected with Homer1c:GFP to identify postsynapses (Fig. 1 C– E). Endogenous AMPARs were labeled with anti-GluA2 conjugated Quantum dots (Qdots), and individual Qdot trajectories were recorded by fluorescence imaging. Simulations mimicked qualitatively well extrasynaptic diffusion and synaptic confinement of AMPARs observed in SPT experiments, with slight discrepancies attributed to limitations of the Qdot technique (Fig. 1 B and C and Fig. S2). The mean square displacement (MSD) was fitted by linear regression to yield a global diffusion coefficient (Fig. S3 A and B). The experimental distribution of diffusion coefficients 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 coefficient decreased as synapse density was increased, in agreement with the model (Fig. 1E). Increasing kon to enhance AMPAR trapping at postsynapses reduced global AMPAR mobility (Fig. 1E), whereas increasing koff had the opposite effect (Fig. S4C), thus leading to several combinations of kon and koff that could equally fit SPT data (Fig. S4D). To experimentally alter AMPAR diffusion without affecting developmental age, we overexpressed either the adhesion 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 AMPAR diffusion (Fig. 1F). These effects were reproduced in the model, the former by doubling obstacle density and the latter by increasing simultaneously PSD size and kon. Overall, the model could interpret SPT experiments in a wide range of biological conditions.