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Effect of kinesin velocity distribution on slow axonal transport

100%
Kuznetsov A.
|
EN
The goal of this paper is to investigate the effect that a distribution of kinesin motor velocities could have on cytoskeletal element (CE) concentration waves in slow axonal transport. Previous models of slow axonal transport based on the stop-and-go hypothesis (P. Jung, A. Brown, Modeling the slowing of neurofilament transport along the mouse sciatic nerve, Physical Biology 6 (2009) 046002) assumed that in the anterograde running state all CEs move with one and the same velocity as they are propelled by kinesin motors. This paper extends the aforementioned theoretical approach by allowing for a distribution of kinesin motor velocities; the distribution is described by a probability density function (PDF). For a two kinetic state model (that accounts for the pausing and running populations of CEs) an analytical solution describing the propagation of the CE concentration wave is derived. Published experimental data are used to obtain an analytical expression for the PDF characterizing the kinesin velocity distribution; this analytical expression is then utilized as an input for computations. It is demonstrated that accounting for the kinesin velocity distribution increases the rate of spreading of the CE concentration waves, which is a significant improvement in the two kinetic state model.
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Analytical solution of equations describing slow axonal transport based on the stop-and-go hypothesis

86%
Kuznetsov A.
Open Physics
|
2011
|
vol. 9
|
issue 3
662-673
EN
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).
3
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Effect of cytoskeletal element degradation on merging of concentration waves in slow axonal transport

86%
Kuznetsov A., Avramenko A., Blinov D.
Open Physics
|
2011
|
vol. 9
|
issue 4
898-908
EN
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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