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Kuznetsov IA, Kuznetsov AV. Simulating the effect of formation of amyloid plaques on aggregation of tau protein. Proc Math Phys Eng Sci. 2018;474(2220):20180511doi: 10.1098/rspa.2018.0511.
Kuznetsov, I. A., & Kuznetsov, A. V. (2018). Simulating the effect of formation of amyloid plaques on aggregation of tau protein. Proceedings. Mathematical, physical, and engineering sciences, 474(2220), 20180511. https://doi.org/10.1098/rspa.2018.0511
Kuznetsov, I A, and Kuznetsov, A V. "Simulating the effect of formation of amyloid plaques on aggregation of tau protein." Proceedings. Mathematical, physical, and engineering sciences vol. 474,2220 (2018): 20180511. doi: https://doi.org/10.1098/rspa.2018.0511
Kuznetsov IA, Kuznetsov AV. Simulating the effect of formation of amyloid plaques on aggregation of tau protein. Proc Math Phys Eng Sci. 2018 Dec;474(2220):20180511. doi: 10.1098/rspa.2018.0511. Epub 2018 Dec 12. PMID: 30602936; PMCID: PMC6304026.
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Proc Math Phys Eng Sci. 2018 Dec;474(2220):20180511. doi: 10.1098/rspa.2018.0511. Epub 2018 Dec 12.

Simulating the effect of formation of amyloid plaques on aggregation of tau protein.

Proceedings. Mathematical, physical, and engineering sciences

I A Kuznetsov, A V Kuznetsov

Affiliations

  1. Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA 19104, USA.
  2. Department of Bioengineering, University of Pennsylvania, Philadelphia, PA 19104, USA.
  3. Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, NC 27695-7910, USA.

PMID: 30602936 PMCID: PMC6304026 DOI: 10.1098/rspa.2018.0511

Abstract

In this paper, we develop a mathematical model that enables the investigation of the production and intracellular transport of amyloid precursor protein (APP) and tau protein in a neuron. We also investigate the aggregation of APP fragments into amyloid-β (Aβ) as well as tau aggregation into tau oligomers and neurofibrillary tangles. Using the developed model, we investigate how Aβ aggregation can influence tau transport and aggregation in both the soma and the axon. We couple the Aβ and tau agglomeration processes by assuming that the value of the kinetic constant that describes the autocatalytic growth (self-replication) reaction step of tau aggregation is proportional to the Aβ concentration. The model predicts that APP and tau are distributed differently in the axon. While APP has a uniform distribution along the axon, tau's concentration first decreases and then increases towards the synapse. Aβ is uniformly produced along the axon while misfolded tau protein is mostly produced in the proximal axon. The number of Aβ and tau polymers originating from the axon is much smaller than the number of Aβ and tau polymers originating from the soma. The rate of production of misfolded tau polymers depends on how strongly their production is facilitated by Aβ.

Keywords: Alzheimer's disease; amyloid precursor protein; axon; mathematical modelling; neuron; tau protein

Conflict of interest statement

We declare we have no competing interests.

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