Diffusion of protein receptors on a cylindrical dendritic
membrane with partially absorbing traps
We present a model of protein receptor trafficking within the
membrane of a cylindrical dendrite containing small protrusions
called spines. Spines are the locus of most excitatory synapses in
the central nervous system and act as localized traps for receptors
diffusing within the dendritic membrane. We treat the transverse
intersection of a spine and dendrite as a spatially-extended,
partially-absorbing boundary and use singular perturbation theory to
analyze the steady-state distribution of receptors. We compare the
singular perturbation solutions with numerical solutions of the full
model and with solutions of a reduced one-dimensional model, and
find good agreement between them all. We also derive a system of
Fokker-Planck equations from our model and use it to exactly solve a
mean first passage time (MFPT) problem for a single receptor
traveling a fixed axial distance along the dendrite. This is then
used to calculate an effective diffusion coefficient for receptors
when spines are uniformly distributed along the length of the cable,
and to show how a non-uniform distribution of spines gives rise to
anomalous subdiffusion.
University of Utah
| Department of Mathematics
|
bressloff@math.utah.edu
Jan 2004.