Nonlocal Multiscale Interactions in Brain Neurodegenerative Protein Dynamics and Coupled Proteopathic Processes

Abstract

We take a heterodimer multiscale reaction-diffusion model as a starting point and modify it to account for the nonlocality of the underlying processes. The resulting model is a coupled system of integro-differential equations. The effect of nonlocal interactions is quantified based on the comparisons of the newly developed model with its local counterpart. Our primary focus is given to the estimation of conversion times from healthy to toxic proteins. This is done based on the stability analysis of a simplified model, as well as on the fully coupled numerical implementation. Several clinically relevant patient proteopathies are highlighted. They include the primary tauopathy, as well as the secondary tauopathy where the sustained presence of toxic tau protein requires also to be accompanied by toxic amyloid-beta peptides. We demonstrate the dynamics of concentrations of toxic proteins under several clinically realistic scenarios. Finally, we carry out a detailed parametric study, providing further insight into the role of nonlinear effects controlled via the Holling type II functional response.

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