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1
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Merging of viral concentration waves in retrograde viral transport in axons

100%
Kuznetsov A.
Open Physics
|
2011
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vol. 9
|
issue 6
1493-1502
EN
This paper develops an analytical solution describing propagation of two viral waves in an axon and applies the obtained analytical solution to investigating the dynamics of merging of these two waves as they move retrogradely toward the neuron body. The viral diffusivity and viral degradation are accounted for in the model. Computational results are presented for two situations: when all dynein motors move with the same velocity and when dynein motor velocity distribution is characterized by a probability density function (pdf). The effect of various model parameters on the time it takes for the waves to merge is discussed. It is proposed that observing the dynamics of wave merging can be used for determining parameters characterizing viral transport, such as the viral diffusivity. This may contribute toward better understanding of viral transport properties and potentially help in developing novel viral detection techniques.
2
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Analytical solution of equations describing slow axonal transport based on the stop-and-go hypothesis

100%
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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A four kinetic state model of fast axonal transport: Model formulation and perturbation solution

100%
Kuznetsov A.
Open Physics
|
2011
|
vol. 9
|
issue 1
146-156
EN
This paper formulates a four kinetic state model for fast axonal transport. The paper further develops the Smith-Simmons model that is based on equations governing intracellular molecular-motor-assisted transport; these equations are extended by considering four rather than three kinetic states for organelles. The model considers plus-end and minus-end-oriented organelles that can be either free (suspended in the cytosol) or attached to microtubules (MTs) (in the latter case organelles are transported by molecular motors). The paper then develops a method for uncoupling differential equations of the proposed model. A perturbation solution of this problem is obtained. The effect of transition between plus-end-oriented and minus-end oriented organelles is discussed. The accuracy of the obtained perturbation solution is evaluated by comparing the zero-order and the first-order results with a high-accuracy numerical solution.
4
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Analytical investigation of various regimes of retrograde trafficking of neurotropic viruses in axons

100%
Kuznetsov A.
Open Physics
|
2011
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vol. 9
|
issue 5
1372-1378
EN
A model of retrograde axonal transport of neurotropic viruses is developed. The model accounts for active viral transport by dynein motors as well as for passive transport by diffusion; the destruction of the virus as it propagates toward the neuron soma is modeled utilizing a first-order decay rate process. The effect of a limited time during which the axonal synapse is exposed to the virus is incorporated. An analytical solution is obtained. The obtained solution makes it possible to identify four different regimes of viral transport in the axon that correspond to the following situations: (1) Small viral diffusivity and small rate of viral destruction; (2) Large viral diffusivity and small rate of viral destruction; (3) Small viral diffusivity and large rate of viral destruction; (4) Large viral diffusivity and large rate of viral destruction. Characteristic features of these regimes are discussed.
5
Content available remote

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.
6
Content available remote

A model of axonal transport drug delivery

100%
Kuznetsov A.
Open Physics
|
2012
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vol. 10
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issue 2
320-328
EN
In this paper a model of targeted drug delivery by means of active (motor-driven) axonal transport is developed. The model is motivated by recent experimental research by Filler et al. (A.G. Filler, G.T. Whiteside, M. Bacon, M. Frederickson, F.A. Howe, M.D. Rabinowitz, A.J. Sokoloff, T.W. Deacon, C. Abell, R. Munglani, J.R. Griffiths, B.A. Bell, A.M.L. Lever, Tri-partite complex for axonal transport drug delivery achieves pharmacological effect, Bmc Neuroscience 11 (2010) 8) that reported synthesis and pharmacological efficiency tests of a tri-partite complex designed for axonal transport drug delivery. The developed model accounts for two populations of pharmaceutical agent complexes (PACs): PACs that are transported retrogradely by dynein motors and PACs that are accumulated in the axon at the Nodes of Ranvier. The transitions between these two populations of PACs are described by first-order reactions. An analytical solution of the coupled system of transient equations describing conservations of these two populations of PACs is obtained by using Laplace transform. Numerical results for various combinations of parameter values are presented and their physical significance is discussed.
7
Content available remote

Analytical investigation of transient molecular-motor-assisted transport in elongated cells

64%
Kuznetsov A., Avramenko A.
|
EN
This paper investigates analytically the molecular-motor-assisted transport between the cell nucleus and cell membrane in an elongated cell, which allows the formulation of governing equations in a cylindrical coordinate system. This problem is relevant to biomimetic transport systems as well as to many biological processes occurring in living cells, such as the viral infection of a cell. The obtained analytical solution is shown to agree well with a high-accuracy numerical solution of the same problem. The developed analytical technique extends the applicability of the generalized Fourier series method to a new type of problems involving intracellular transport of organelles.
8
Content available remote

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

51%
Kuznetsov A., Avramenko A., Blinov D.
Open Physics
|
2011
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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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