Synaptic Bistability Due to Nucleation and Evaporation of Receptor Clusters

We introduce a bistability mechanism for long-term synaptic plasticity based on switching between two metastable states that contain significantly different numbers of synaptic receptors. One state is characterized by a two-dimensional gas of mobile interacting receptors and is stabilized against clustering by a high nucleation barrier. The other state contains a receptor gas in equilibrium with a large cluster of immobile receptors, which is stabilized by the turnover rate of receptors into and out of the synapse. Transitions between the two states can be initiated by either an increase (potentiation) or a decrease (depotentiation) of the net receptor flux into the synapse. This changes the saturation level of the receptor gas and triggers nucleation or evaporation of receptor clusters.

Figure 1

Schematic representation of the PSD. The number of receptors (1) within the PSD is maintained by receptor recycling (2) and diffusion from extrasynaptic areas (3). Extra receptors can be delivered to the PSD from an intracellular pool (4) following an excitatory signal to form stable clusters (5), resulting in potentiation (strengthening) of the synapse. An inhibitory signal would cause an increase in the rate of receptor removal (endocytosis), resulting in receptor cluster evaporation and weakening of the synapse (depotentiation).

Figure 2

The energy change associated with cluster formation as a function of receptors number $n_{\mathrm{cl}}$. The energy was obtained by evaluating Eq. (2) for ${\epsilon }_{\mathrm{cl}}=5k_{\mathrm{B}}T$, $\gamma =1.646k_{\mathrm{B}}T$ and the triple ($P_{\mathrm{vap}}$, $S_0$, $y$) equal to: (1) (0.1, 500, 0.6); (2) (0.1, 500, 0.9); (3) (0.1, 500, 0.5); (4) (0.12, 500, 0.6); (5) (0.1, 300, 0.36). The last value of $y$ is chosen to keep $x_{\mathrm{vap}}(0)$ the same as in 1. Units of $y$ and $P_{\mathrm{vap}}$ are ${\min }^{-1}$ and $S_0$ is in $a^2$ units.

Figure 3

Evolution of the receptor numbers in the cluster $n_{\mathrm{cl}}$ (dark grey) obtained by kinetic Monte Carlo simulation using Eq. (3) with $P_{\mathrm{vap}}=0.1$, ${\epsilon }_{\mathrm{cl}}=5$, $\gamma =1.646$, $D={10}^{-2}{\mu }^2/\mathrm{s}$, $k_{\mathrm{int}}=1.3\times {10}^{-3}\mu /\mathrm{s}.(a)S_0=500$, $y_1=0.6$; (b) $S_0=300$, $y_1=0.36$. The values of $y$ and $P_{\mathrm{vap}}$ are given in ${\min }^{-1}$, and $S_0$ is given in $a^2$ units. Straight grey lines show $y=y_1+y_2$, where $y_1$ represents the background exocytosis rate due to receptor recycling and $y_2$ represents the spike in receptor influx from an intracellular pool (potentiation). Dashed line indicates the steady state cluster size. Black solid line indicates the spike in the endocytosis rate corresponding to a depotentiation signal.