Modeling of Tau Protein Transport in Axons

2013 ◽  
Author(s):  
Ivan A. Kuznetsov ◽  
Andrey V. Kuznetsov
Keyword(s):  
Analytical Solution ◽  
Axonal Transport ◽  
Tau Protein ◽  
Protein Transport ◽  
State Model ◽  
Tau Proteins ◽  
Transition Rates ◽  
Slow Axonal Transport ◽  
Transport Velocity ◽  
And Diffusion

This paper develops a simplified analytical solution for the slow axonal transport of tau proteins. A six kinetic state model developed in Jung and Brown [1] was used to simulate transport of tau. The model was extended by accounting for tau degradation and diffusion in the off-track kinetic states. The analytical solution was obtained by assuming that transitions between anterograde and retrograde states are infrequent. This assumption was validated through an analysis of the sensitivity of the solution to changes in the values of the two kinetic constants that describe the transition rates between the anterograde and retrograde states, and by a comparison with the experimentally measured tau distributions reported in Konzack et al. [2]. The predicted average transport velocity of tau was also in the experimentally reported range.

Effect of kinesin velocity distribution on slow axonal transport

Open Physics ◽  
2012 ◽  
Vol 10 (4) ◽  
Author(s):  
Andrey Kuznetsov
Keyword(s):  
Experimental Data ◽  
Velocity Distribution ◽  
Axonal Transport ◽  
State Model ◽  
Concentration Wave ◽  
Slow Axonal Transport ◽  
Kinesin Motor ◽  
Analytical Expression ◽  
Stop And Go ◽  
Probability Density Function Pdf

AbstractThe 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.

scholarly journals Braiding Braak and Braak: Staging patterns and model selection in network neurodegeneration

2021 ◽  
Author(s):  
Prama Putra ◽  
Travis Thompson ◽  
Alain Goriely
Keyword(s):  
Alzheimer’S Disease ◽  
Alzheimer's Disease ◽  
Tau Protein ◽  
Tau Proteins ◽  
Histopathological Analysis ◽  
Braak Staging ◽  
New Methods ◽  
Tau Aggregation ◽  
The Brain ◽  
And Diffusion

AbstractA hallmark of Alzheimer’s disease is the aggregation of insoluble amyloid-beta plaques and tau protein neurofibrillary tangles. A key histopathological observation is that tau protein aggregates follow a clear progression pattern through the brain; characterized by six distinct stages. This so-called ‘Braak staging pattern’ has become the gold standard for Alzheimer’s disease progression. It has also been suggested, via a histopathological analysis, that soluble seed-competent tau seeding precedes tau aggregation in the same manner. Mathematical models such as prion-like propagation on networks have the ability to capture key feature of the dynamics. Here, we study the staging of tau proteins using a model of proteopathy that include both local growth due to autocatalytic effects and diffusion along axonal pathways. We develop new methods to capture the staging patterns and use these as a qualitative criterion to identify the best model for diffusion process on networks and to identify possible parameter regimes. Our analysis provides a systematic way to study Braak staging in neurodegenerative processes.

Analytical solution of equations describing slow axonal transport based on the stop-and-go hypothesis

Open Physics ◽  
2011 ◽  
Vol 9 (3) ◽  
Author(s):  
Andrey Kuznetsov
Keyword(s):  
Analytical Solution ◽  
Axonal Transport ◽  
Molecular Motor ◽  
Governing Equations ◽  
Slow Axonal Transport ◽  
Stop And Go ◽  
Solution Of Equations ◽  
Physical Insight ◽  
The Difference ◽  
Insight Into

AbstractThis 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).

scholarly journals A possible mechanism for neurofilament slowing down in myelinated axon: Phosphorylation-induced variation of NF kinetics

PLoS ONE ◽  
2021 ◽  
Vol 16 (3) ◽  
pp. e0247656
Author(s):  
Zelin Jia ◽  
Yinyun Li
Keyword(s):  
Molecular Motors ◽  
Average Velocity ◽  
Node Of Ranvier ◽  
Myelinated Axon ◽  
State Model ◽  
Slow Axonal Transport ◽  
Model And Simulation ◽  
Stop And Go ◽  
Transport Velocity ◽  
Kinetics Of

Neurofilaments(NFs) are the most abundant intermediate filaments that make up the inner volume of axon, with possible phosphorylation on their side arms, and their slow axonal transport by molecular motors along microtubule tracks in a “stop-and-go” manner with rapid, intermittent and bidirectional motion. The kinetics of NFs and morphology of axon are dramatically different between myelinate internode and unmyelinated node of Ranvier. The NFs in the node transport as 7.6 times faster as in the internode, and the distribution of NFs population in the internode is 7.6 folds as much as in the node of Ranvier. We hypothesize that the phosphorylation of NFs could reduce the on-track rate and slow down their transport velocity in the internode. By modifying the ‘6-state’ model with (a) an extra phosphorylation kinetics to each six state and (b) construction a new ‘8-state’ model in which NFs at off-track can be phosphorylated and have smaller on-track rate, our model and simulation demonstrate that the phosphorylation-induced decrease of on-track rate could slow down the NFs average velocity and increase the axonal caliber. The degree of phosphorylation may indicate the extent of velocity reduction. The Continuity equation used in our paper predicts that the ratio of NFs population is inverse proportional to the ratios of average velocity of NFs between node of Ranvier and internode. We speculate that the myelination of axon could increase the level of phosphorylation of NF side arms, and decrease the possibility of NFs to get on-track of microtubules, therefore slow down their transport velocity. In summary, our work provides a potential mechanism for understanding the phosphorylation kinetics of NFs in regulating their transport and morphology of axon in myelinated axons, and the different kinetics of NFs between node and internode.

scholarly journals Kinesin Mutations Cause Motor Neuron Disease Phenotypes by Disrupting Fast Axonal Transport in Drosophila

Genetics ◽  
1996 ◽  
Vol 144 (3) ◽  
pp. 1075-1085 ◽  
Author(s):  
Daryl D Hurd ◽  
William M Saxton
Keyword(s):  
Motor Neuron ◽  
Axonal Transport ◽  
Action Potentials ◽  
Light And Electron Microscopy ◽  
Synaptic Membrane ◽  
Slow Axonal Transport ◽  
Fast Axonal Transport ◽  
Motor Neuron Diseases ◽  
Transmitter Secretion ◽  
Axon Terminals

Abstract Previous work has shown that mutation of the gene that encodes the microtubule motor subunit kinesin heavy chain (Khc) in Drosophila inhibits neuronal sodium channel activity, action potentials and neurotransmitter secretion. These physiological defects cause progressive distal paralysis in larvae. To identify the cellular defects that cause these phenotypes, larval nerves were studied by light and electron microscopy. The axons of Khc mutants develop dramatic focal swellings along their lengths. The swellings are packed with fast axonal transport cargoes including vesicles, synaptic membrane proteins, mitochondria and prelysosomal organelles, but not with slow axonal transport cargoes such as cytoskeletal elements. Khc mutations also impair the development of larval motor axon terminals, causing dystrophic morphology and marked reductions in synaptic bouton numbers. These observations suggest that as the concentration of maternally provided wild-type KHC decreases, axonal organelles transported by kinesin periodically stall. This causes organelle jams that disrupt retrograde as well as anterograde fast axonal transport, leading to defective action potentials, dystrophic terminals, reduced transmitter secretion and progressive distal paralysis. These phenotypes parallel the pathologies of some vertebrate motor neuron diseases, including some forms of amyotrophic lateral sclerosis (ALS), and suggest that impaired fast axonal transport is a key element in those diseases.

Sign in / Sign up

Export Citation Format

Share Document