Analytical modelling of retrograde transport of nerve growth factors in an axon: a transient problem

Abstract

The purpose of this paper was to develop an analytical solution describing retrograde transport of nerve growth factors (NGFs) from a target tissue to the neuron soma. The obtained solution is applied to describe two situations: (1) when all dynein motors are moving at a constant velocity and (2) when the dynein velocity distribution is described by a probability density function. The dynamics of NGF concentrations and fluxes is investigated. It is established that the magnitude of the diffusion flux forms a wave localised in space and propagating towards the neuron soma; the magnitude of this wave decreases as the wave propagates downstream. The dynein-driven flux of NGFs is demonstrated to be the main component in the NGF flux, which is shown to be strongly correlated with the NGF concentration.

Keywords:

• nerve growth factors
• neurotrophins
• dynein motors
• retrograde axonal transport