Article Figures & Data
Figures
- Figure 1.
Compartmental model of AMPA receptor trafficking. A, Schematic of AMPA receptor trafficking at a dendritic spine. Receptors stored in intracellular pools are continually exchanged with surface receptors through exocytosis/endocytosis (EXO/END) and sorted for degradation (DEG). Surface receptors diffuse in the dendritic membrane and can be immobilized at the PSD through interactions with scaffolding proteins. B, Simplified two-compartment model of a dendritic spine. Free receptors (concentration P) bind to scaffolding proteins within the PSD to form bound receptors (concentration Q) at a rate α (multiplied by the concentration of free binding sites) and unbind at a rate β. Free receptors flow between the PSD and ESM at a hopping rate h and flow between the ESM and surface of the dendritic cable at a rate Ω. Free receptors (concentration R) within the ESM are internalized at a rate k. Receptors are inserted into the PSD and ESM at a rate σ. Within each compartment, there are two distinct types of receptor corresponding to GluR1/2 (type I) and GluR2/3 (type II) heteromers, respectively. The rates of binding/unbinding, hopping, and exocytosis/endocytosis depend on receptor type. Only type II receptors undergo exocytosis in the PSD (σI = 0) and only type I receptors undergo exocytosis in the ESM (σII = 0). C, LTD model. GluR2/3 receptors are assumed to exist in two distinct states corresponding to association with GRIP and PICK proteins, respectively. Under basal conditions, the transition rate μ from the GRIP-associated state to the PICK-associated state is zero so that only GRIP-associated receptors exist and the model dynamics reduces to the kinetic scheme shown in B. However, during the presentation of an LTD stimulus, μ increases so that some GRIP-associated receptors are converted to PICK-associated receptors. The latter are assumed to rapidly unbind from scaffolding proteins at a rate β*, hop from the PSD to the ESM at a rate h*, where they are endocytosed. This results in a net loss of receptors from the PSD.
- Figure 2.
Steady-state behavior of synaptic receptor number as a function of trafficking parameters. All parameters are at their basal values as listed in Table 1 unless specified otherwise. A, B, Variation of receptor number with rate of endocytosis kj, j = I, II. The solid curves show number of receptors in the PSD at the basal hopping rate between the ESM and dendrite, denoted by Ω̄j, whereas the dashed curves show corresponding receptor numbers when Ω̄j is increased by a factor of 10. Receptor number decreases with increasing endocytosis, and dependence becomes weaker with increasing hopping rate between the ESM and dendrite. C, Variation of receptor number with rate of exocytosis σI. The solid curves show number of receptors in the PSD at basal hopping rates, whereas dashed curves show corresponding receptor numbers when Ω̄I is increased by a factor of 10. Receptor number increases with increasing exocytosis, and dependence becomes weaker with increasing hopping rate between the PSD and ESM. D, Variation of receptor number with rate of exocytosis σII. The solid curves show number of receptors in the PSD at basal hopping rate between PSD and ESM, denoted by h̄II, whereas the dashed curves show corresponding receptor numbers when h̄II is increased by a factor of 10. Receptor number increases with increasing exocytosis, and dependence becomes weaker with increasing hopping rate between the PSD and ESM. The nonlinear dependence of the total number of receptors near σII = 0 represents the transition from unsaturated to saturated binding sites. In A–D, the point corresponding to basal conditions is indicated by a filled circle on the solid black curve. Note that the number of free receptors is approximately equal to one-half the total number of receptors. E, Variation of receptor number with the ratio of type II binding rate to unbinding rate. Total receptor number increases with increasing αII/βII and saturates near αII/βII = 1, indicating that all binding sites are full. This is attributable to the large number of free GluR2/3 receptors in the PSD, which fill available binding sites and replace bound GluR1/2 receptors. Dependence is weak near the basal value of αII/βII = 10 (data not shown), indicating a strong affinity of GluR2/3 receptors for binding sites. Receptor numbers are relatively insensitive to αI/βI (data not shown).
- Figure 3.
Time course of AMPA receptors after blocking exocytosis/endocytosis. A, Blocking exocytosis. With receptors at basal steady state at time t < 0, exocytosis is blocked by setting σj = 0 (j = 1,2) at t = 0. The number of AMPA receptors in the PSD almost halves in <10 min (because of the loss of free receptors) and decreases to ∼1 over ∼10 d (data not shown). B, Blocking endocytosis. Endocytosis is blocked by setting kj = 0 (j = 1,2) at t = 0. The number of AMPA receptors in the PSD nearly doubles within 1 h (because of the addition of free receptors) and reaches a new steady-state value of ∼84. These results are consistent with those of Luscher et al. (1999).
- Figure 4.
Time course of AMPA receptors during LTP. A, B, With receptors at basal steady state for t < 0, LTP is induced at time t = 0 by making the following changes to the basal GluR1/2 parameter values listed in Table 1 and numerically solving Equations 1–4: binding rate αI = 0.001 μm2 s−1, exocytic rate per receptor κI = 0.0556 s−1, and hopping rate hI = 0.01 μm s−1. Binding site trafficking is also activated according to Equation 11 with c = 0.65. A shows the variation in the total number of receptors (solid black curve) and the number of binding sites (solid green curve) within the PSD, whereas B shows the corresponding variation in the total number of receptors in the ESM (solid black curve) and the number of intracellular receptors (solid gray curve). The contributions from the various receptor types are also shown in A. The number of receptors in the ESM rises transiently because of the exocytosis of intracellular GluR1/2 receptors. Some of these newly exocytosed receptors enter the PSD and are immobilized by the newly available binding sites. These results are consistent with experimentally recorded EPSPs after LTP induction (Hanse and Gustafsson, 1992; O'Connor et al., 2005). C, D, Time course of synaptic receptors (C) and extrasynaptic receptors (D) without synaptic targeting. Labeling of various curves is as in A and B. With receptors at basal steady state at time t < 0, the rate of GluR1/2 exocytosis is increased by setting κI = 0.0556 s−1 at time t = 0. However, the hopping rate and binding affinity of GluR1/2 receptors and the number of binding sites remain at basal levels. The concentration in the ESM rises transiently as GluR1/2 receptors from the intracellular pool are exocytosed there, as in the case of LTP, but now there is only a small transient rise in the number of synaptic receptors. These results illustrate that both exocytosis and synaptic targeting are required for LTP. This is consistent with the suggestion that stargazin plays a role in transporting GluR1/2 receptors to the membrane surface, whereas its interaction with PSD-95 is required for synaptic targeting (Schnell et al., 2002). E, Exchange of GluR1/2 and GluR2/3 AMPA receptors. After 1 h of maintaining LTP parameters, all parameters are returned to their basal values except the binding site concentration L, at which time GluR2/3 receptors begin to replace GluR1/2 receptors at the binding sites. These results are consistent with those of McCormack et al. (2006).
- Figure 5.
Time course of AMPA receptors during and after LTD. The variation in the total number of receptors (solid black curves) and binding sites (solid green curves) in the PSD are shown together with contributions from the various receptor types. A, With receptors at basal steady state for t < 0, LTD is induced at time t = 0 by increasing from zero the transition rate μ from GluR2/3–GRIP to GluR2/3–PICK and maintaining this for 900 s. We numerically solve the LTD model in which GluR2/3 receptors within the PSD evolve according to 9 and 10 and the concentration of binding sites decreases according to Equation 12. LTD parameter values are μ = 0.01 s−1, ν = 0.01 s−1, βII* = 0.1 s−1, kII* = kII = 0.1667 s−1, and γ = 0.001 s−1. All other parameters are as listed in Table 1. GluR2/3–GRIP is rapidly converted to GluR2/3–PICK during the first few minutes of LTD; afterward, this conversion occurs at a slower rate. Bound GluR2/3–PICK quickly releases from binding sites, and free GluR2/3-PICK exits the PSD and is endocytosed. Notice how the number of binding sites follows the loss of bound receptors. LTD induction ends at 900 s such that μ and γ return to zero, and GluR2/3–PICK rapidly converts back to GluR2/3–GRIP at the rate ν. However, the new steady-state number of receptors in the PSD is much lower because of the loss of binding sites. The variation in the number of synaptic receptors is consistent with typical recordings of EPSPs during LTD [Dudek and Bear (1992), their Fig. 2A]. B, Time course of receptors in the PSD during LTD with moderate frequency stimulus. LTD is induced as in A, except that γ = 0 s−1 throughout. Although these time courses are similar to those in A, the number of binding sites remains unchanged, so that the number of AMPA receptors in the PSD returns to its initial steady-state value after LTD induction terminates. This result is consistent with Dudek and Bear (1992), their Fig. 2B. C, Saturation of LTD. LTD is induced as in A, except that it is followed by 45 min of basal activity, and this 1 h epoch is repeated three times, followed by the induction of LTP. (LTP is induced as in Fig. 4, except c = 0.325.) Notice that the loss of PSD receptors decreases in each consecutive epoch, proportional to the number of binding sites at the beginning of each epoch. Saturation occurs because only bound, and not free, receptors are lost during LTD. The variation in the number of synaptic receptors is consistent with Dudek and Bear (1993), their Fig. 7.
Tables
Parameter Symbol ValueI ValueII Units Reference Surface area of PSD APSD 0.1257a μm2 Sorra and Harris, 2000 Surface area of ESM AESM 1.257a μm2 Sorra and Harris, 2000 Concentration of binding sites L 159.15a μm−2 This paper Number of intracellular receptors S 500 100 This paper Exocytic rate per intracellular receptor κ 0.0005556 0.001667 s−1 Passafaro et al., 2001 Rate of exocytosis σ 0.2778 0.1667 s−1 Passafaro et al., 2001 Rate of endocytosis k 0.01667 0.01667 s−1 Ehlers, 2000 PSD–ESM hopping rate h 0.001257 0.001257 μm2 s−1 This paper ESM–dendrite hopping rate Ω 0.001257 0.001257 μm2 s−1 This paper Background receptor concentration R̄ 10 0 μm−2 Cottrell et al., 2000 Binding rate to scaffolding protein α 10−6 10−4 μm2 s−1 This paper Release rate from scaffolding protein β 10−5 10−5 s−1 This paper -
↵aThe nontrafficking parameters do not have particular type I and II values.
-
