Speaker
Description
Pathological accumulations of hyperphosphorylated tau protein aggregates, known as neurofibrillary tangles, are detected in several neurodegenerative tauopathies, including Alzheimer's disease \cite{GS:2017}. Tau is a highly soluble, natively unfolded protein which is predominantly located in the axons of neurons of the central nervous system. Here, its physiological function is to support assembly and stabilization of axonal microtubules. Under pathological conditions, tau can assume abnormal conformations. In particular, hyperphosphorylation has a negative impact on the biological function of tau proteins, since it inhibits the binding to microtubules, compromising their stabilization and axonal transport, and promotes self-aggregation. Recent evidences have demonstrated that the progression of tau pathology reflects cell-to-cell propagation of the disease, achieved through the release of tau into the extracellular space and the uptake by surrounding healthy neurons \cite{YAM:2017}. In this work, we prove a two-scale homogenization result for a set of diffusion-coagulation Smoluchowski-type equations with transmission boundary conditions. This system is meant to describe the aggregation and diffusion of pathological tau proteins inside the axons and in the extracellular space. We prove the existence, uniqueness, positivity and boundedness of solutions to the model equations derived at the microscale (that is, the scale of single neurons). Then, we study the convergence of the homogenization process to the solution of a macro-model asymptotically consistent with the microscopic one \cite{FL:2024}.
Bibliography
@article{GS:2017,
title= {Propagation of tau aggregates},
author = {Goedert, Michel and Spillantini, Maria Grazia},
journal = {Mol. Brain},
volume = {10},
number= {1},
pages = {18--26},
year = {2017},
publisher={Springer}}
@article{YAM:2017,
title= {Extracellular tau and its potential role in the propagation of tau pathology},
author = {Yamada, Kaoru},
journal = {Front. Neurosci},
volume = {11},
number= {NOV},
pages = {667--671},
year = {2017},
publisher={Frontiers Media S.A.}}
@article{FL:2024,
title= {Homogenization of Smoluchowski-type equations with transmission boundary conditions},
author = {Franchi, Bruno and Lorenzani, Silvia},
journal = {Adv. Nonlinear Stud.},
volume = {24},
number= {4},
pages = {952--991},
year = {2024},
publisher={De Gruyter}}
