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Investigation of the role of diffusivity on spreading, rate, and merging of the bell‐shaped waves in slow axonal transport
Author(s) -
Kuznetsov A. V.,
Avramenko A. A.,
Blinov D. G.
Publication year - 2011
Publication title -
international journal for numerical methods in biomedical engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.741
H-Index - 63
eISSN - 2040-7947
pISSN - 2040-7939
DOI - 10.1002/cnm.1417
Subject(s) - thermal diffusivity , merge (version control) , physics , amplitude , mechanics , mechanical wave , wave propagation , longitudinal wave , optics , computer science , thermodynamics , information retrieval
This paper investigates the role of diffusivity on spreading, rate, and merging of two waves transporting the same type of cytoskeletal elements (CEs) in slow axonal transport. The two waves (each wave physically represents the total probability density function for the CEs) can be generated by simultaneous microinjections of radiolabeled CEs in two different locations. Alternatively, two waves, one behind another, can be produced by injecting CEs at the same location twice, with a time interval between the injections. Since the waves become wider as they propagate downstream, the two waves eventually merge; this results in the formation of a single wave that moves down the axon. The amplitudes of the waves (before as well as after they merge) decrease as the waves propagate downstream; in addition, the waves spread out during their propagation. The waves spread out faster when diffusivity of free CEs is increased; this agrees with experimental data for the transport of neurofilaments, which are characterized by smaller diffusivity, versus transport of tubulin oligomers, which are characterized by larger diffusivity. The average velocity of CE transport first increases (which is explained by the effect of the initial condition; this effect is somewhat artificial) and then attains an asymptotic value. The case of merging of three waves is also briefly investigated. Copyright © 2010 John Wiley & Sons, Ltd.