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

An analytical solution describing the propagation of positive injury signals in an axon: effect of dynein velocity distribution

A model describing the propagation of positive injury signals from the lesion site in an axon towards the neuron soma is described. It is assumed that these signals are driven by dynein molecular motors. An analytical solution that accounts for the probability density function (pdf) of a dynein velocity distribution is obtained. Two examples of pdf of dynein velocity distributions that follow from the results published in Ross et al. (2006, Processive bidirectional motion of dynein-dynactin complexes in vitro. Nat Cell Biol. 8:562-570) and Deinhardt et al. (2006, Rab5 and Rab7 control endocytic sorting along the axonal retrograde transport pathway. Neuron 52:293-305) are considered. The effect of dynein velocity distribution on the rate of spreading of the signal wave is discussed. It is demonstrated that the obtained solution can be applied to the problem of how neurons measure the distance between the lesion site and the neuron soma.