Diffusion-trapping model of receptor trafficking in dendrites

We present a model for the diffusive trafficking of protein receptors along the surface of a neuron's dendrite. Distributed along the dendrite are spatially localized trapping regions that represent submicrometer mushroom-like protrusions known as dendritic spines. Within these trapping regions receptors can be internalized via endocytosis and either reinserted into the surface via exocytosis or degraded. We calculate the steady-state distribution of receptors along the dendrite assuming a constant flux of receptors inserted at one end, adjacent to the soma where receptors are synthesized, and use this to investigate the effectiveness of membrane diffusion as a transport mechanism. We also calculate the mean first passage time of a receptor to travel a certain distance along the cable and use this to derive an effective surface diffusivity.