Cable theory of protein receptor trafficking in a dendritic tree.

We develop an application of linear cable theory to protein receptor trafficking in the surface membrane of a neuron's dendritic tree. We assume that receptors diffuse freely in the dendritic membrane but exhibit periods of confined motion through interactions with small mushroomlike protrusions known as dendritic spines. We use cable theory to determine how receptor trafficking depends on the geometry of the dendritic tree and various important biophysical parameters such as membrane diffusivity, the density of spines, the strength of diffusive coupling between dendrites and spines, and the rates of constitutive recycling of receptors between the surface of spines and intracellular pools. We also use homogenization theory to determine corrections to cable theory arising from the discrete nature of spines.