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Open Physics

formerly Central European Journal of Physics


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Analytical solution of equations describing slow axonal transport based on the stop-and-go hypothesis

1Dept. of Mechanical and Aerospace Engineering, North Carolina State University, Campus Box 7910, Raleigh, NC, 27695-7910, USA

© 2010 Versita Warsaw. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. (CC BY-NC-ND 3.0)

Citation Information: Open Physics. Volume 9, Issue 3, Pages 662–673, ISSN (Online) 2391-5471, DOI: 10.2478/s11534-010-0066-0, February 2011

Publication History

Published Online:
2011-02-26

Abstract

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).

Keywords: molecular motors; neurons; axons; slow axonal transport; stop-and-go hypothesis; analytical solution

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