Modeling the role of lateral membrane diffusion in AMPA receptor trafficking along a spiny dendrite.

AMPA receptor trafficking in dendritic spines is emerging as a major postsynaptic mechanism for the expression of plasticity at glutamatergic synapses. AMPA receptors within a spine are in a continuous state of flux, being exchanged with local intracellular pools via exo/endocytosis and with the surrounding dendrite via lateral membrane diffusion. This suggests that one cannot treat a single spine in isolation. Here we present a model of AMPA receptor trafficking between multiple dendritic spines distributed along the surface of a dendrite. Receptors undergo lateral diffusion within the dendritic membrane, with each spine acting as a spatially localized trap where receptors can bind to scaffolding proteins or be internalized through endocytosis. Exocytosis of receptors occurs either at the soma or at sites local to dendritic spines via constitutive recycling from intracellular pools. We derive a reaction-diffusion equation for receptor trafficking that takes into account these various processes. Solutions of this equation allow us to calculate the distribution of synaptic receptor numbers across the population of spines, and hence determine how lateral diffusion contributes to the strength of a synapse. A number of specific results follow from our modeling and analysis. (1) Lateral membrane diffusion alone is insufficient as a mechanism for delivering AMPA receptors from the soma to distal dendrites. (2) A source of surface receptors at the soma tends to generate an exponential-like distribution of receptors along the dendrite, which has implications for synaptic democracy. (3) Diffusion mediates a heterosynaptic interaction between spines so that local changes in the constitutive recycling of AMPA receptors induce nonlocal changes in synaptic strength. On the other hand, structural changes in a spine following long term potentiation or depression have a purely local effect on synaptic strength. (4) A global change in the rates of AMPA receptor exo/endocytosis is unlikely to be the sole mechanism for homeostatic synaptic scaling. (5) The dynamics of AMPA receptor trafficking occurs on multiple timescales and varies according to spatial location along the dendrite. Understanding such dynamics is important when interpreting data from inactivation experiments that are used to infer the rate of relaxation to steady-state.