Diffusion of protein receptors on a cylindrical dendritic membrane with partially absorbing traps

被引:53
作者
Bressloff, Paul C. [1 ]
Earnshaw, Berton A. [1 ]
Ward, Michael J. [2 ]
机构
[1] Univ Utah, Dept Math, Salt Lake City, UT 84112 USA
[2] Univ British Columbia, Dept Math, Vancouver, BC V6T 1Z2, Canada
基金
美国国家科学基金会;
关键词
protein receptor trafficking; diffusion-trapping; matched asymptotics; singular perturbation theory;
D O I
10.1137/070698373
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
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 nonuniform distribution of spines gives rise to anomalous subdiffusion.
引用
收藏
页码:1223 / 1246
页数:24
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