Equations describing molecular-motor-assisted transport in dendrites with a non-uniform cross-sectional area

The purpose of this paper is to develop new transport equations describing transport of intracellular organelles by a combined effect of diffusion and molecular-motor-driven transport in dendrites of neuron cells that have a non-uniform cross-sectional area which depends on the distance from the neuron soma. The obtained equations are solved numerically for two types of microtubule (MT) orientations that are experimentally found in dendrites. In one type of dendrites, which is found in cultured rat hippocampal neurons, MTs have a mixed polarity orientation while in the second type, which is found in Drosophila neurons, MTs have the minus-end-out polarity orientation. Simulations show important differences in organelle transport in these two types of dendrites. The conclusion is that the MT orientation has a profound effect on the total rate of organelle transfer toward the growth cone of a dendrite and consequently determines its growth potential and its growth rate.