Biophysical models of alpha-amino-3-hydroxy-5-methyl-4-isoxazole-propionic acid receptor trafficking in dendrites

The trafficking of alpha-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) receptors in dendrites 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. The precise mechanisms underlying the activity-dependent regulation of AMPA receptor trafficking are currently unknown. However, they are likely to involve one or more of the following processes: changes in the interaction between receptors and other synaptic proteins, changes in the rates of exo/endocytosis, and modifications in membrane or receptor structure that alter the surface transport of receptors. Here we present biophysical models of AMPA receptor trafficking at single dendritic spines and between multiple dendritic spines distributed along the surface of a dendrite that take into account these modes of receptor trafficking. Solutions of these models reproduce a variety of experimental data including trafficking during plasticity, and allow us to make predictions concerning the important targets of second-messenger pathways activated during plasiticiy. For example, scaffolding protein numbers must be up- or down-regulated during plasticity in order for there to be a persistent change in the number of AMPA receptors at a synapse. We also derive an effective "cable equation" for receptor trafficking whose solutions determine the distribution of synaptic receptor numbers across multiple spines. These solutions allows us to examine how lateral diffusion regulates the strength of a synapse. In particular, our analysis suggests that (1) lateral membrane diffusion alone is an insufficient synaptic delivery mechanism, (2) local changes in the constitutive recycling of AMPA receptors induce nonlocal changes in synaptic strength, and (3) AMPA receptor trafficking is not likely to mediate heterosynaptic forms of plasticity.