Compatibility between itinerant synaptic receptors and stable postsynaptic structure

The density of synaptic receptors in front of presynaptic release sites is stabilized in the presence of scaffold proteins, but the receptors and scaffold molecules have local exchanges with characteristic times shorter than that of the receptor-scaffold assembly. We propose a mesoscopic model to account for the regulation of the local density of receptors as quasiequilibrium. It is based on two zones (synaptic and extrasynaptic) and multilayer (membrane, submembrane, and cytoplasmic) topological organization. The model includes the balance of chemical potentials associated with the receptor and scaffold protein concentrations in the various compartments. The model shows highly cooperative behavior including a “phase change” resulting in the formation of well-defined postsynaptic domains. This study provides theoretical tools to approach the complex issue of synaptic stability at the synapse, where receptors are transiently trapped yet rapidly diffuse laterally on the plasma membrane.

Figure 1

(Color online) (a) Generic description of molecular mechanisms involved in the accumulation of receptors in front of terminal buttons $\left(B\right)$. The arrow indicates (1) the membrane diffusion of receptors; (2) the cytoplasmic diffusion of scaffold proteins and their binding to receptors; and (3) the endocytosis and exocytosis of receptors. (b) Schematic representation of the diffusive motion of receptors at the cell surface [20].

Figure 2

(Color online) Kinetic and energetic components involved in receptor mobility and accumulation; (a), (b) Potential energy profile (thick wavy lines) for a receptor (green object). Note its alterations below the presynaptic button $\left(B\right)$, illustrating two extreme situations. Compared to an extrasynaptic membrane, the energy barrier can be higher (a) or the energy level lower (b). The consequences are that (a) the diffusion is slowed down beneath the synaptic button but the density of receptors can be identical at synaptic and extrasynaptic membranes in the steady state; (b) the diffusion coefficients can be identical within the two zones but receptor density is higher beneath the synaptic button. Experimental data (accumulation of receptors and lower diffusion coefficient) [20] indicate that a combination of the two is responsible for accumulation of receptors.

Figure 3

(Color online) Kinetic parameters and cellular biology of receptors. Exo- and endocytosis and synaptic to extrasynaptic transfer are characterized by specific rate constants $k_{\mathrm{endo}\left(\mathrm{exo}\right)}⪡k_{\text{on}\left(\text{off}\right)}$. The half-life of receptors in the plasma membrane (on the order of tens of minutes to half a day) and the dwell time of receptors at synapses are given in terms of these parameters.

Figure 4

(Color online) (a) Three-layer, two-zone model: The model assumes a three-layer partition of the postsynaptic cell, membrane layer, submembrane layer, and bulk layer. In the first two layers, we establish a spatial partition with two zones, a synaptic $\left(z\right)$ and an extrasynaptic $\left(x\right)$ zone, where the areal densities $\left(\sigma \right)$ are used as variables, and receptors $\left(R\right)$ and scaffold proteins $\left(s\right)$ are indicated as subscripts. In the bulk layer, the density of scaffold proteins corresponds to the chemical potential ${\mu }_{s,\text{bulk}}$. The receptors can diffuse within the membrane layer, and the scaffold proteins diffuse among the zones in both the submembrane and the bulk layer. (b) Correlations among molecules: The arrows indicate the molecular correlations taken into account in the present model. The numbers like (2), etc. correspond to those of equations in the text.

Figure 5

$U_s\left({\sigma }_s\right)$ vs ${\sigma }_s$ (top) and $v\left({\sigma }_s\right)$ vs ${\sigma }_s$ (bottom).

Figure 6

(Color online) (a) Transition (switching) induced by the chemical potential of the scaffold protein in the bulk cytoplasm, ${\mu }_{s,\text{bulk}}$ (horizontal axis). (The value of $h_0$ is fixed at $h_0=1$.) Top $\left({\sigma }_R\right)$: Densities of the membrane receptors in the membrane layer. Middle $\left({\sigma }_s\right)$: Densities of the scaffold proteins in the submembrane layer. The red (blue) curves represent, respectively, the densities in the synaptic (extrasynaptic) zones. Bottom $\left(G\right)$: Free energy of the system. The vertical dashed line passing through the figures marks the point of phase change, to switch the branch of solutions. Those parts represented by dashed curves are not realizable as quasiequilibrium. (b) Switching induced by the transmembrane signal $h_0$. (The value of ${\mu }_{s,\text{bulk}}$ is fixed at ${\mu }_{s,\text{bulk}}=-7.747$.)

Figure 7

(a) (Color online) Densities of receptors (in green) and scaffold proteins (in cyan) in the nonlocalized (top) and localized states (bottom) are shown schematically by concentration of the colors. (b) Phase diagram of localized vs nonlocalized phases on the plane of the controlling parameters. The almost straight diagonal curve is the numerical result.