Investigation of the role of diffusivity on spreading, rate, and merging of the bell-shaped waves in slow axonal transport

Abstract

SUMMARYThis 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.

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

“…Since NF diffusivity is quite small (0.43 lm 2 /s [39]), we found that the effect of diffusivity on NF transport is small. However, the effect is more pronounced for other slow axonal transport cargos, such as tubulin, which has a diffusivity approximately 20 times larger (8.6 lm 2 /s [39]) than that of NFs; see modeling results for tubulin in [38]. transition to the stationary phase) while the rates of wave spreading are approximately the same.…”

“…An extension of Jung-Brown's model, which accounts for diffusivity of slowly transported cargos, was developed in Kuznetsov et al [38]. It was shown that accounting for diffusivity of cargos results in a faster spread of the total concentration wave but does not affect the wave velocity.…”

Effect of cytoskeletal element degradation on merging of concentration waves in slow axonal transport

“…This model was numerically investigated in [20]. In the present paper we extend the model developed in [19] to account for the halflife of CEs (the model suggested in Jung and Brown [19] assumes that the half-life of CEs is infinitely long while a recent work by Millecamps et al [21] suggests that there is degradation of proteins along the length of the axon).…”

Effect of kinesin velocity distribution on slow axonal transport

“…The basic model (the one utilized in the present research) accounts only for two kinetic states of NFs, pausing and running. Numerical and perturbation solutions of equations developed in [23] were reported in [24][25][26][27][28][29][30].…”