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Open Physics
tom 9
nr 3
This paper presents an analytical solution for slow axonal transport in an axon. The governing equations for slow axonal transport are based on the stop-and-go hypothesis which assumes that organelles alternate between short periods of rapid movement on microtubules (MTs), short on-track pauses, and prolonged off-track pauses, when they temporarily disengage from MTs. The model includes six kinetic states for organelles: two for off-track organelles (anterograde and retrograde), two for running organelles, and two for pausing organelles. An analytical solution is obtained for a steady-state situation. To obtain the analytical solution, the governing equations are uncoupled by using a perturbation method. The solution is validated by comparing it with a high-accuracy numerical solution. Results are presented for neurofilaments (NFs), which are characterized by small diffusivity, and for tubulin oligomers, which are characterized by large diffusivity. The difference in transport modes between these two types of organelles in a short axon is discussed. A comparison between zero-order and first-order approximations makes it possible to obtain a physical insight into the effects of organelle reversals (when organelles change the type of a molecular motor they are attached to, an anterograde versus retrograde motor).
The aim of this paper is to investigate, by means of a numerical simulation, the effect of the half-life of cytoskeletal elements (CEs) on superposition of several waves representing concentrations of running, pausing, and off-track anterograde and retrograde CE populations. The waves can be induced by simultaneous microinjections of radiolabeled CEs in different locations in the vicinity of a neuron body; alternatively, the waves can be induced by microinjecting CEs at the same location several times, with a time interval between the injections. Since the waves spread out as they propagate downstream, unless their amplitude decreases too fast, they eventually superimpose. As a result of superposition and merging of several waves, for the case with a large half-life of CEs, a single wave is formed. For the case with a small half-life the waves vanish before they have enough time to merge.
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