Choquet Model
Czöndör, Mondin, Garcia, Heine, Frischknecht, Choquet, Sibarita, Thoumine • 2012 • PNAS - PDF
Expand to view abstract
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.
Introduction
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
Media
VIDEO
{{{2}}}
MEAN SQUARED DISPLACEMENT
- Brownian Motion Mean Squared Displacement
- The goal of this calculation is to relate the simulated particle diffusion to real world values, namely velocity.
- Particle velocity will be a function of MSD x units ²⁄s which scales on space (units) and time (s) parameters.
- Space and time in the model are defined arbitrarily as Step_Size and Step where each Step a particle moves a distance randomly chosen from a normal distribution (µ=1,σ=.2)
- a step size of 1 unit/step will produce a brownian motion MSD of ~0.52 ±0.2 units ²/s
- empirical observations show that reasonable values for MSD are:
- PSD 0.01 µm ²/s
- synaptic 0.05 µm ²/s
- extrasynaptic 0.1 µm ²/s
- given an MSD of 0.52 ±0.2 units ²/s at the current parameters: 1 step = 1 unit (at µ=1,σ=.2), the model will need to be scaled such that particles move at an extrasynaptic rate of 0.1 µm ²/s.
- spines are on average 1 to 10 µm apart, if the model is comparing two spines 1 µm apart, they should be separated by 5 units of model space. This is because the current particle diffusion rate of the model is .5 µm ²/s and the empirical MSD is .1 µm ²/s
to make 0.1 units²⁄step ≈ 0.1 µm²⁄s. It was found that an XY random step-size of µ=0.4 (σ=.2) units produced an MSE ≈ 0.1 units²⁄step. Then, the arbitrary 0.5 units were given meaning (converted to 0.5 µm) by scaling the model according to real-world values (see below) by making 1 unit = 1 µm; as a convention, a subunit will be 1/10th of a unit, thus 1 subunit = 0.1 µm). The PSD areas were set to 3-subunits (.3 µm) square, 20 subunits (2 µm) apart, within a rectangular field 20 subunits (2 µm) wide and 60 subunits (6 µm) long. Given these scaled dimensions where 10 subunits ≈ 1 µm, a particle with an XY step-size of 0.5 units moving in a straight line, could theoretically go from PSD1 to PSD2 in 4 steps (obviously given the simulated particles are moving with Brownian motion, this lower-bound would be extremely rare).