An exact solution of transient equations describing slow axonal transport

Modeling anterograde and retrograde transport of short mobile microtubules from the site of axonal branch formation

This theoretical research is motivated by a recent model of microtubule (MT) transport put forward by Baas and Mozgova (Cytoskeleton 69:416-425, 2012). According to their model, in an axon all plus-end-distal mobile MTs move anterogradely while all minus-end-distal mobile MTs move retrogradely. Retrograde MT transport thus represents a mechanism by which minus-end-distal MTs are removed from the axon. We suggested equations that implement Baas and Mozgova's model. We employed these equations to simulate transport of short mobile MTs from a region (such as the site of axonal branch formation) where MT severing activity results in generation of a large number of short MTs of both orientations. We obtained the exact and approximate transient solutions of these equations utilizing the Laplace transform technique. We applied the obtained solutions to calculate the average rates of anterograde and retrograde transport of short MTs.

Analytical comparison between Nixon-Logvinenko's and Jung-Brown's theories of slow neurofilament transport in axons

This paper develops analytical solutions describing slow neurofilament (NF) transport in axons. The obtained solutions are based on two theories of NF transport: Nixon-Logvinenko's theory that postulates that most NFs are incorporated into a stationary cross-linked network and only a small pool is slowly transported and Jung-Brown's theory that postulates a single dynamic pool of NFs that are transported according to the stop-and-go hypothesis. The simplest two-kinetic state version of the model developed by Jung and Brown was compared with the theory developed by Nixon and Logvinenko. The model for Nixon-Logvinenko's theory included stationary, pausing, and running NF populations while the model used for Jung-Brown's theory only included pausing and running NF populations. Distributions of NF concentrations resulting from Nixon-Logvinenko's and Jung-Brown's theories were compared. In previous publications, Brown and colleagues successfully incorporated slowing of NF transport into their model by assuming that some kinetic constants depend on the distance from the axon hillock. In this paper we defined the average rate of NF transport as the rate of motion of the center of mass of radiolabeled NFs. We have shown that for this definition, if all kinetic rates are assumed constant, Jung-Brown's theory predicts a constant average rate of NF transport. We also demonstrated that Nixon-Logvinenko's theory predicts slowing of NF transport even if all kinetic rates are assumed constant, and the obtained slowing agrees well with published experimental data.