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Spatially-extended nucleation-aggregation-fragmentation models for the dynamics of prion-like neurodegenerative protein-spreading in the brain and its connectome

Sveva Fornari, Amelie Schäfer, View ORCID ProfileEllen Kuhl, View ORCID ProfileAlain Goriely
doi: https://doi.org/10.1101/692038
Sveva Fornari
Living Matter Laboratory, Stanford University, Stanford, USA
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Amelie Schäfer
Living Matter Laboratory, Stanford University, Stanford, USA
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Ellen Kuhl
Living Matter Laboratory, Stanford University, Stanford, USA
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Alain Goriely
Mathematical Institute, University of Oxford, Oxford UK
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  • ORCID record for Alain Goriely
  • For correspondence: goriely@maths.ox.ac.uk
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Abstract

The prion-like hypothesis of neurodegenerative diseases states that the accumulation of misfolded proteins in the form of aggregates is responsible for tissue death and its associated neurodegenerative pathology and cognitive decline. Some disease-specific misfolded proteins can interact with healthy proteins to form long chains that are transported through the brain along axonal pathways. Since aggregates of different sizes have different transport properties and toxicity, it is important to follow independently their evolution in space and time. Here, we model the spreading and propagation of aggregates of misfolded proteins in the brain using the general Smoluchowski theory of nucleation, aggregation, and fragmentation. The transport processes considered here are either anisotropic diffusion along axonal bundles or discrete Laplacian transport along a network. In particular, we model the spreading and aggregation of both amyloid-β and τ molecules in the brain connectome. We show that these two models lead to different size distributions and different propagation along the network. A detailed analysis of these two models reveals the existence of four different stages with different dynamics and invasive properties.

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The copyright holder for this preprint is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under a CC-BY-NC-ND 4.0 International license.
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Posted July 04, 2019.
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Spatially-extended nucleation-aggregation-fragmentation models for the dynamics of prion-like neurodegenerative protein-spreading in the brain and its connectome
Sveva Fornari, Amelie Schäfer, Ellen Kuhl, Alain Goriely
bioRxiv 692038; doi: https://doi.org/10.1101/692038
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Spatially-extended nucleation-aggregation-fragmentation models for the dynamics of prion-like neurodegenerative protein-spreading in the brain and its connectome
Sveva Fornari, Amelie Schäfer, Ellen Kuhl, Alain Goriely
bioRxiv 692038; doi: https://doi.org/10.1101/692038

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