Effect of protein degradation in the axon on the speed of the bell-shaped concentration wave in slow axonal transport

Кузнецов, А. В.; Авраменко, А. А.; Blinov, D.G.

doi:10.1016/j.icheatmasstransfer.2009.04.002

Cited by 13 publications

(21 citation statements)

References 17 publications

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“…The time the cargo transported by slow axonal transport spends pausing explains the low average velocity of this transport mode. Kuznetsov et al [9] extended the theory developed in Brown et al [6] and Craciun et al [7] for rapidly diffusible soluble proteins while Kuznetsov et al [10] extended this theory to account for the effect of protein degradation and investigated the possibility of traffic jam formation in slow axonal transport if MTs at a certain location in the axon are severed by the action of MT-severing proteins.…”

Section: Introductionmentioning

confidence: 99%

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

Кузнецов

Авраменко

Blinov

2010

Int. J. Numer. Meth. Biomed. Engng.

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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.

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Section: Introductionmentioning

confidence: 99%

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

Кузнецов

Авраменко

Blinov

2010

Int. J. Numer. Meth. Biomed. Engng.

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“…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). The effect of the half-life of CEs on slow axonal transport was first modeled in [22], based on the original model of slow axonal transport developed in Craciun et al [7]. The present paper also extends the model developed in [19] by accounting for the diffusivity of free (off-track) CEs (in [19] the diffusivity of NFs, which is indeed small, was neglected).…”

Section: Introductionmentioning

confidence: 83%

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

2011

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Abstract: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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“…Recently, Jung & Brown (2009) developed several models of various complexities based on this hypothesis. Some extensions of these models that included accounting for diffusivity of CEs, and numerical and perturbation solutions of Jung-Brown equations were reported in Kuznetsov et al (2009aKuznetsov et al ( ,b, 2010aKuznetsov et al ( ,b, 2011a and Kuznetsov (2011).…”

Section: Introductionmentioning

confidence: 99%

An exact solution describing slow axonal transport of cytoskeletal elements: the effect of a finite half-life

Кузнецов

2012

Proc. R. Soc. A.

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This paper presents an exact solution for a two kinetic state model of slow axonal transport that is based on the stop-and-go hypothesis. The model accounts for two populations of cytoskeletal elements (CEs): pausing and running. The model also accounts for a finite half-life of CEs involved in slow axonal transport. It is assumed that initially CEs are injected into the axon such that their concentration forms a rectangular pulse; initially all CEs are assumed to be in the pausing state. Kinetic processes quickly redistribute CEs between the pausing and running states. After less than a minute, equilibrium is established, forming two pulses, representing concentrations of pausing and running CEs, respectively. As these pulses propagate, their shape changes and they turn to bell-shaped waves. The amplitude of the waves decreases, and the waves spread out as they propagate down the axon. The rate of the amplitude decrease is larger for CEs with a shorter half-life, but even if CE half-life is infinitely long, some decrease of the waves' amplitudes is observed. The velocity of the waves' propagation is found to be independent of the CE half-life and is in good agreement with published experimental data for slow axonal transport of neurofilaments.

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Effect of protein degradation in the axon on the speed of the bell-shaped concentration wave in slow axonal transport

Cited by 13 publications

References 17 publications

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

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

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

An exact solution describing slow axonal transport of cytoskeletal elements: the effect of a finite half-life

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