  We present a coarse-grained model for stochastic transport of noninteracting
chemical signals inside neuronal dendrites and show how first-passage
properties depend on the key structural factors affected by neurodegenerative
disorders or aging: the extent of the tree, the topological bias induced by
segmental decrease of dendrite diameter, and the trapping probabilities in
biochemical cages and growth cones. We derive an exact expression for the
distribution of first-passage times, which follows a universal exponential
decay in the long-time limit. The asymptotic mean first-passage time exhibits a
crossover from power-law to exponential scaling upon reducing the topological
bias. We calibrate the coarse-grained model parameters and obtain the variation
range of the mean first-passage time when the geometrical characteristics of
the dendritic structure evolve during the course of aging or neurodegenerative
disease progression (A few disorders are chosen and studied for which clear
trends for the pathological changes of dendritic structure have been reported
in the literature). We prove the validity of our analytical approach under
realistic fluctuations of structural parameters, by comparing to the results of
Monte Carlo simulations. Moreover, by constructing local structural
irregularities, we analyze the resulting influence on transport of chemical
signals and formation of heterogeneous density patterns. Since neural functions
rely on chemical signal transmission to a large extent, our results open the
possibility to establish a direct link between the disease progression and
neural functions.
