A mathematical model for the proliferation, accumulation and spread of pathogenic proteins along neuronal pathways with locally anomalous trapping

Article


Angstmann, C. N., Donnelly, I. C., Henry, B. I. and Langlands, T. A. M.. 2016. "A mathematical model for the proliferation, accumulation and spread of pathogenic proteins along neuronal pathways with locally anomalous trapping." Mathematical Modelling of Natural Phenomena (MMNP). 11 (3), pp. 142-156. https://doi.org/10.1051/mmnp/20161139
Article Title

A mathematical model for the proliferation, accumulation and spread of pathogenic proteins along neuronal pathways with locally anomalous trapping

ERA Journal ID32402
Article CategoryArticle
AuthorsAngstmann, C. N. (Author), Donnelly, I. C. (Author), Henry, B. I. (Author) and Langlands, T. A. M. (Author)
Journal TitleMathematical Modelling of Natural Phenomena (MMNP)
Journal Citation11 (3), pp. 142-156
Number of Pages15
Year2016
Place of PublicationFrance
ISSN0973-5348
1760-6101
Digital Object Identifier (DOI)https://doi.org/10.1051/mmnp/20161139
Web Address (URL)https://www.mmnp-journal.org/articles/mmnp/abs/2016/03/mmnp2016113p142/mmnp2016113p142.html
Abstract

There is growing evidence that many neurodegenerative disease processes involve the proliferation, accumulation and spread of pathogenic proteins. The transport of proteins in the brain is typically hindered on small scales by micro-domain traps and binding sites but it may be enhanced on larger scales by neuronal pathways identified as white matter transport networks. We have introduced a mathematical network model to simulate a pathogenic protein neurodegenerative disease in the brain taking into account the anomalous transport. The proliferation and accumulation of pathogenic proteins is modelled using a set of reaction kinetics equations on the nodes of a network. Transport of the proteins on the network is modelled as a continuous time random walk with power law distributed waiting times on the nodes. This power law waiting time distribution is shown to be consistent with anomalously slowed diffusion on local scales but transport is enhanced on larger scales by the jumps between nodes. The model reveals that the disease spreads as a propagating front throughout the brain. The anomalous behaviour leads to a lessor variation in the concentration of pathogenic proteins. The enhanced transport on the network ensures that the approach to equilibrium is dominated by the short time behaviour of the waiting time density, hence the effects of subdiffusion are not as pronounced as in a spatial continuum.

Keywordsanomalous transport, fractional diffusion, prion disease
Contains Sensitive ContentDoes not contain sensitive content
ANZSRC Field of Research 2020490303. Numerical solution of differential and integral equations
490102. Biological mathematics
Public Notes

File reproduced in accordance with the copyright policy of the publisher/author.

Byline AffiliationsUniversity of New South Wales
Computational Engineering and Science Research Centre
Institution of OriginUniversity of Southern Queensland
Funding source
Australian Research Council (ARC)
Grant ID
DP140101193
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